30.ACCELERATORPHYSICSOFCOLLIDERS -...

30. Accelerator physics of colliders 429

30. ACCELERATOR PHYSICS OF COLLIDERS

Revised August 2015 by M.J. Syphers (NIU/FNAL) and F. Zimmer-mann (CERN).

30.1. Luminosity

This article provides background for the High-Energy ColliderParameter Tables that follow. The number of events, Nexp, is theproduct of the cross section of interest, σexp, and the time integralover the instantaneous luminosity, L :

Nexp = σexp ×∫

L (t)dt. (30.1)

Today’s colliders all employ bunched beams. If two bunches containingn1 and n2 particles collide head-on with frequency fcoll, a basicexpression for the luminosity is

L = fcoll

n1n2

4πσxσy(30.2)

where σx and σy characterize the rms transverse beam sizes in thehorizontal (bend) and vertical directions. In this form it is assumedthat the bunches are identical in transverse profile, that the profilesare Gaussian and independent of position along the bunch, and theparticle distributions are not altered during bunch crossing. Nonzerobeam crossing angles and long bunches will reduce the luminosityfrom this value.

Whatever the distribution at the source, by the time the beam reacheshigh energy, the normal form is a useful approximation as suggestedby the σ-notation. In the case of an electron storage ring, synchrotronradiation leads to a Gaussian distribution in equilibrium, but even inthe absence of radiation the central limit theorem of probability andthe diminished importance of space charge effects produce a similarresult.

The luminosity may be obtained directly by measurement of thebeam properties in Eq. (30.2). For continuous measurements, anexpression similar to Eq. (30.1) with Nref from a known referencecross section, σref , may be used to determine σexp according toσexp = (Nexp/Nref )σref .

In the Tables, luminosity is stated in units of cm−2s−1. Integratedluminosity, on the other hand is usually quoted as the inverse of thestandard measures of cross section such as femtobarns and, recently,attobarns. Subsequent sections in this report briefly expand on thedynamics behind collider design, comment on the realization of colliderperformance in a selection of today’s facilities, and end with someremarks on future possibilities.

30.2. Beam Dynamics

The first concern of beam dynamics is stability. While a referenceparticle proceeds along the design, or reference, trajectory otherparticles in the bunch are to remain close by. Assume that thereference particle carries a right-handed Cartesian coordinate system,with the z-coordinate pointed in the direction of motion along thereference trajectory. The independent variable is the distance s ofthe reference particle along this trajectory rather than time, and forsimplicity this path is taken to be planar. The transverse coordinatesare x and y, where x, z defines the plane of the reference trajectory.

Several time scales are involved, and the approximations used inwriting the equations of motion reflect that circumstance. All oftoday’s high energy colliders are alternating-gradient synchrotronsor, respectively, storage rings [1,2], and the shortest time scale isthat associated with transverse motion, that is described in termsof betatron oscillations, so called because of their analysis for thebetatron accelerator species years ago. The linearized equations ofmotion of a particle displaced from the reference particle are

x′′ + Kxx = 0, Kx ≡ q

p

∂B

∂x+

1

ρ2

y′′ + Kyy = 0, Ky ≡ − q

p

∂B

∂x

z′ = −x/ρ

(30.3)

where the magnetic field B(s) along the design trajectory is onlyin the y direction, contains only dipole and quadrupole terms, andis treated as static here. The radius of curvature due to the fieldon the reference orbit is ρ; z represents the longitudinal distancefrom the reference particle; p and q are the particle’s momentumand charge, respectively. The prime denotes d/ds. The pair (x, x′)describes approximately-canonical variables. For more general cases(e.g. acceleration) one should use (x, px) instead, where px denotesthe transverse momentum in the x-direction.

The equations for x and y are those of harmonic oscillators but witha restoring force periodic in s; that is, they are instances of Hill’sequation. The solution may be written in the form

x(s) = Ax

√

βx cosψx

x′(s) = − Ax√βx

[αx cosψx + sin ψx](30.4)

where Ax is a constant of integration, αx ≡ −(1/2)dβx(s)/ds, and theenvelope of the motion is modulated by the amplitude function, βx. Asolution of the same form describes the motion in y. The subscriptswill be suppressed in the following discussion.

The amplitude function satisfies

2ββ′′ − β′2 + 4β2K = 4, (30.5)

and in a region free of magnetic field it should be noted that thesolution of Eq. (30.5) is a parabola. Expressing A in terms of x, x′

yieldsA2 = γx2 + 2αxx′ + βx′2

=1

β

[

x2 + (αx + βx′)2] (30.6)

with γ ≡ (1 + α2)/β. In a single pass system such as a linac, theCourant-Snyder parameters α, β, γ may be selected to match the x, x′

distribution of the input beam; in a recursive system, the parametersare usually defined by the structure rather than by the beam.

The relationships between the parameters and the structure may beseen by treatment of a simple lattice consisting of equally-spacedthin-lens quadrupoles whose magnetic-field gradients are equal inmagnitude but alternating in sign. For this discussion, the weakfocusing effects of the bending magnets may be neglected. Thepropagation of X ≡ x, x′ through a repetition period may bewritten X2 = MX1, with the matrix M = FODO composed of thematrices

F =

(

1 0−1/f 1

)

, D =

(

1 01/f 1

)

, O =

(

1 L0 1

)

,

where f is the magnitude of the focal length and L the lens spacing.Then

M =

1 +L

f2L +

L2

f

− L

f21 − L

f− L2

f2

. (30.7)

The matrix for y is identical in form differing only by a change in signof the terms linear in 1/f . An eigenvector-eigenvalue analysis of thematrix M shows that the motion is stable provided f > L/2. Whilethat criterion is easily met, in practice instability may be caused bymany other factors, including the beam-beam interaction itself.

Standard focus-drift-defocus-drift, or FODO, cells such as character-ized in simple form by Eq. (30.7) occupy most of the layout of alarge collider ring and may be used to set the scale of the amplitudefunction and related phase advance. Conversion of Eq. (30.4) to amatrix form equivalent to Eq. (30.7) (but more generally valid, i.e. forany stable periodic linear motion) gives

M =

(

C + αS βS−γS C − αS

)

(30.8)

where C ≡ cos∆ψ, S ≡ sin ∆ψ, and the relation between structureand amplitude function is specified by setting the values of the

430 30. Accelerator physics of colliders

latter to be the same at both ends of the cell. By comparison ofEq. (30.7) and Eq. (30.8) one finds C = 1 − L2/(2f2), so that thechoice f = L/

√2 would give a phase advance ∆ψ of 90 degrees for

the standard cell. The amplitude function would have a maximumat the focusing quadrupole of magnitude β = 2.7L, illustrating therelationship of alternating gradient focusing amplitudes to relativelylocal aspects of the design. Other functionalities such as injection,extraction, and HEP experiments are included by lattice sectionsmatched to the standard cell parameters (β, α) at the insertion points.

The phase advances according to dψ/ds = 1/β; that is, β also playsthe role of a local λ/2π, and the tune, ν, is the number of suchoscillations per turn about the closed path. In the neighborhood of aninteraction point (IP), the beam optics of the ring is configured so asto produce a narrow focus; the value of the amplitude function at thispoint is designated β∗.

The motion as it develops with s describes an ellipse in x, x′ ≡ dx/dsphase space, the area of which is πA2, where A is the constant inEq. (30.4). If the interior of that ellipse is populated by an ensembleof non-interacting particles, that area, given the name emittance anddenoted by ε, would change only with energy. More precisely, fora beam with a Gaussian distribution in x, x′, the area containingone standard deviation σx, divided by π, is used as the definition ofemittance in the Tables:

εx ≡ σ2x

βx, (30.9)

with a corresponding expression in the other transverse direction, y.This definition includes 39% of the beam. For most of the entries inthe Tables the standard deviation is used as the beam radius.

To complete the coordinates used to describe the motion, we take asthe variable conjugate to z the fractional momentum deviation δp/pfrom that of the reference particle. Radiofrequency electric fields inthe s direction provide a means for longitudinal oscillations, and thefrequency determines the bunch length. The frequency of this systemappears in the Tables as does the rms value of δp/p characterized as“energy spread” of the beam.

For HEP bunch length is a significant quantity for a variety of reasons,but in the present context if the bunch length becomes larger thanβ∗ the luminosity is adversely affected. This is because β growsparabolically as one proceeds away from the interaction point andso the beam size increases thus lowering the contribution to theluminosity from such locations. This is often called the “hourglass”effect.

The other major external electromagnetic field interaction in the singleparticle context is the production of synchrotron radiation due tocentripetal acceleration, given by the Larmor formula multiplied by arelativistic magnification factor of γ4 [3]. In the case of electron ringsthis process determines the equilibrium emittance through a balancebetween radiation damping and excitation of oscillations, and furtherserves as a barrier to future higher energy versions in this variety ofcollider. A related phenomenon is beamstrahlung, i.e. the synchrotronradiation emitted during the collision in the field of the opposingbeam, which is relevant for both linear colliders (where it degradesthe luminosity spectrum) and future highest-energy circular colliders(where it limits the beam lifetime). For both types of colliders thebeamstrahlung is mitigated by making the colliding beams as flat aspossible (σ∗

x ≫ σ∗y).

A more comprehensive discussion of betatron oscillations, longitudinalmotion, and synchrotron radiation is available in the 2008 version ofthe PDG review [4].

30.3. Road to High Luminosity

Eq. (30.2) can be recast in terms of emittances and amplitudefunctions as

L = fn1n2

4π√

ǫx β∗x ǫy β∗

y

. (30.10)

So to achieve high luminosity, all one has to do is make high populationbunches of low emittance collide at high frequency at locations where

the beam optics provides as low values of the amplitude functions aspossible.

Such expressions as Eq. (30.10) of the luminosity are special cases ofthe more general forms available elsewhere [5], wherein the reductiondue to crossing angle and other effects can be found. But whilethere are no fundamental limits to the process, there are certainlychallenges. Here we have space to mention only a few of these. Thebeam-beam tune shift appears in the Tables. A bunch in beam 1presents a (nonlinear) lens to a particle in beam 2 resulting in changesto the particle’s transverse tune with a range characterized by theparameter [5]

ξy,2 =µ0

8π2

q1q2n1β∗y,2

mA,2γ2σy,1(σx,1 + σy,1)(30.11)

where q1 (q2) denotes the particle charge of beam 1 (2) in units ofthe elementary charge, mA,2 the mass of beam-2 particles, and µ0 thevacuum permeability. The transverse oscillations are susceptible toresonant perturbations from a variety of sources such as imperfectionsin the magnetic guide field, so that certain values of the tune mustbe avoided. Accordingly, the tune spread arising from ξ is limited,but limited to a value difficult to predict. But a glance at the Tablesshows that electrons are more forgiving than protons thanks to thedamping effects of synchrotron radiation; the ξ-values for the formerare about an order of magnitude larger than those for protons.

A subject of present intense interest is the electron-cloud effect [6,7];actually a variety of related processes come under this heading.They typically involve a buildup of electron density in the vacuumchamber due to emission from the chamber walls stimulated byelectrons or photons originating from the beam itself. For instance,there is a process closely resembling the multipacting effects familiarfrom radiofrequency system commissioning. Low energy electronsare ejected from the walls by photons from positron or protonbeam-produced synchrotron radiation. These electrons are acceleratedtoward a beam bunch, but by the time they reach the center ofthe vacuum chamber the bunch has gone and so the now-energeticelectrons strike the opposite wall to produce more secondaries. Thesesecondaries are now accelerated by a subsequent bunch, and soon. Among the disturbances that this electron accumulation canproduce is an enhancement of the tune spread within the bunch; thenear-cancellation of bunch-induced electric and magnetic fields is nolonger in effect.

If the luminosity of Eq. (30.10) is rewritten in terms of the beam-beamparameter, Eq. (30.11)), the emittance itself disappears. However, theemittance must be sufficiently small to realize a desired magnitude ofbeam-beam parameter, but once ξy reaches this limit, further loweringthe emittance does not lead to higher luminosity.

For electron synchrotrons and storage rings, radiation dampingprovides an automatic route to achieve a small emittance. In fact,synchrotron radiation is of key importance in the design andoptimization of e+e− colliders. While vacuum stability and electronclouds can be of concern in the positron rings, synchrotron radiationalong with the restoration of longitudinal momentum by the RFsystem has the positive effect of generating very small transversebeam sizes and small momentum spread. Further reduction of beamsize at the interaction points using standard beam optics techniquesand successfully contending with high beam currents has led to recordluminosities in these rings, exceeding those of hadron colliders. Tomaximize integrated luminosity the beam can be “topped off” byinjecting new particles without removing existing ones – a featuredifficult to imitate in hadron colliders.

For hadrons, particularly antiprotons, two inventions have played aprominent role. Stochastic cooling [8] was employed first to preparebeams for the SppS and subsequently in the Tevatron and inRHIC [9,10]. Electron cooling [11] was also used in the Tevatroncomplex to great advantage. Further innovations are underway drivenby the needs of potential future projects; these are noted in the finalsection.


30.4. Recent High Energy Colliders

Collider accelerator physics of course goes far beyond the elements ofthe preceding sections. In this and the following section elaborationis made on various issues associated with some of the recentlyoperating colliders, particularly factors which impact integratedluminosity. The various colliders utilizing hadrons each have uniquecharacteristics and are, therefore, discussed separately. As spaceis limited, general references are provided where much furtherinformation can be obtained. A more complete list of recent collidersand their parameters can be found in the High-Energy ColliderParameters tables.

30.4.1. Tevatron : [12] The first synchrotron in history usingsuperconducting magnets, the Tevatron, was the highest energycollider for 25 years. Operation was terminated in September 2011,after delivering more than 10 fb−1 to the p-p collider experimentsCDF and D0. The route to high integrated luminosity in the Tevatronwas governed by the antiproton production rate, the turn-aroundtime to produce another store, and the resulting optimization of storetime. The proton and antiproton beams in the Tevatron circulatedin a single vacuum pipe and thus were placed on separated orbitswhich wrapped around each other in a helical pattern outside of theinteraction regions. Hence, long-range encounters played an importantrole here as well, with the 70 long-range encounters distributed aboutthe synchrotron, and mitigation was limited by the available aperture.The Tevatron ultimately achieved luminosities a factor of 400 over itsoriginal design specification.

30.4.2. HERA : [13] HERA, operated between 1992 and 2007,delivered nearly 1 fb−1 of integrated luminosity to the electron-proton collider experiments H1 and ZEUS. HERA was the firsthigh-energy lepton-hadron collider, and also the first facility to employboth applications of superconductivity: magnets and acceleratingstructures. The proton beams of HERA had a maximum energy of920 GeV. The lepton beams (positrons or electrons) were providedby the existing DESY complex, and were accelerated to 27.5GeV using conventional magnets. At collision a 4-times higherfrequency RF system, compared with the injection RF, was used togenerate shorter bunches, thus helping alleviate the hourglass effectat the collision points. The lepton beam naturally would becometransversely polarized (within about 40 minutes) and “spin rotators”were implemented on either side of an IP to produce longitudinalpolarization at the experiment.

30.4.3. LEP : [14] Installed in a tunnel of 27 km circumference, LEPwas the largest circular e+e− collider built so far. It was operatedfrom 1989 to 2000 with beam energies ranging from 45.6 to 104.5 GeVand a maximum luminosity of 1032 cm−2s−1, at 98 GeV, surpassingall relevant design parameters.

30.4.4. SLC : [15] Based on an existing 3-km long S-band linac, theSLC was the first and only linear collider. It was operated from 1987to 1998 with a constant beam energy of 45.6 GeV, up to about 80%electron-beam polarization, quasi-flat beams, and, in its last year, atypical peak luminosity of 2 × 1030 cm−2s−1, a third of the designvalue.

30.5. Present Collider Facilities

30.5.1. LHC : [16] The superconducting Large Hadron Collideris the world’s highest energy collider. In 2012 operation for HEPhas been at 4 TeV per proton [17]. The beam energy increasedto 6.5 TeV in 2015. The current status is best checked at the Website [18]. To meet its luminosity goals the LHC will have to contendwith a high beam current of 0.5 A, leading to stored energies of severalhundred MJ per beam. Component protection, beam collimation,and controlled energy deposition are given very high priorities.Additionally, at energies of 5-7 TeV per particle, synchrotron radiation

will move from being a curiosity to a challenge in a hadron acceleratorfor the first time. At design beam current the cryogenic system mustremove roughly 7 kW due to synchrotron radiation, intercepted at atemperature of 4.5-20 K. As the photons are emitted their interactionswith the vacuum chamber wall can generate free electrons, withconsequent “electron cloud” development. Much care was taken todesign a special beam screen for the chamber to mitigate this issue.

The two proton beams are contained in separate pipes throughoutmost of the circumference, and are brought together into a singlepipe at the interaction points. The large number of bunches, andsubsequent short bunch spacing, would lead to approximately 30head-on collisions through 120 m of common beam pipe at each IP.Thus, a small crossing angle is employed, which reduces the luminosityby about 15%. Still, the bunches moving in one direction will havelong-range encounters with the counter-rotating bunches and theresulting perturbations of the particle motion constitute a continuedcourse of study. The luminosity scale is absolutely calibrated by the“van der Meer method” as was invented for the ISR [19], and followedby multiple, redundant luminosity monitors (see for example [20] andreferences therein). The Tables also show the performance anticipatedfor Pb-Pb collisions. The ALICE [21] experiment is designed toconcentrate on these high energy-density phenomena, which arestudied as well by ATLAS and CMS. The LHC can also provide Pb-pcollisions as it did in early 2013.

In the coming years, an ambitious upgrade program, HL-LHC [22],has as its target an order-of-magnitude increase in luminosity throughthe utilization of Nb3Sn superconducting magnets, superconductingcompact “crab” cavities and luminosity leveling as key ingredients.

30.5.2. e+e− Rings : Asymmetric energies of the two beams haveallowed for the enhancement of B-physics research and for interestinginteraction region designs. As the bunch spacing can be quite short,the lepton beams sometimes pass through each other at an angleand hence have reduced luminosity. Recently, however, the use ofhigh frequency “crab crossing” schemes has produced full restorationof the luminous region. KEK-B attained over 1 fb−1 of integratedluminosity in a single day, and its upgrade, SuperKEKB, is aiming forluminosities of 8× 1035 cm−2s−1 [23]. A different collision approach,called “crab waist”, which relies on special sextupoles togetherwith a large crossing angle, has been successfully implemented atDAΦNE [24]. Other e+e− ring colliders in operation are BEPC-II,VEPP-2000 and VEPP-4M [23].

30.5.3. RHIC : [25] The Relativistic Heavy Ion Collider employssuperconducting magnets, and collides combinations of fully-strippedions such as H-H (p-p), U-U, Au-Au, Cu-Au, Cu-Cu, and d-Au. Thehigh charge per particle (+79 for gold, for instance) makes intra-beamscattering of particles within the bunch a special concern, even forseemingly moderate bunch intensities. In 2012, 3-D stochastic coolingwas successfully implemented in RHIC, reducing the transverseemittances of heavy ion beams by a factor of 5 [10]. Anotherspecial feature of accelerating heavy ions in RHIC is that the beamsexperience a “transition energy” during acceleration – a point wherethe derivative with respect to momentum of the revolution periodis zero. This is more typical of low-energy accelerators, where thenecessary phase jump required of the RF system is implementedrapidly and little time is spent near this condition. In the case ofRHIC with heavy ions, the superconducting magnets do not ramp veryquickly and the period of time spent crossing transition is long andmust be dealt with carefully. For p-p operation the beams are alwaysabove their transition energy and so this condition is completelyavoided.

RHIC is also distinctive in its ability to accelerate and collide polarizedproton beams. As proton beam polarization must be maintained fromits low-energy source, successful acceleration through the myriad ofdepolarizing resonance conditions in high energy circular acceleratorshas taken years to accomplish. An energy of 255 GeV per proton with> 50% final polarization per beam has been realized. As part of ascheme to compensate the head-on beam-beam effect, electron lensesoperated routinely during the polarized proton operation in 2015.


Table 30.1: Tentative parameters of selected future high-energy colliders. Parameters of HL-LHC, ILC and CLIC can befound in the High-Energy Collider Parameters tables.

LHeC FCC-ee CEPC FCC-hh SPPC µ collider

Species ep e+e− e+e− pp pp µ+µ−

Beam Energy (TeV) 0.06(e), 7 (p) 0.046 0.120 0.175 0.120 50 35 0.063

Circumference (km) 9(e), 27 (p) 100 54 100 54 0.3

Interaction regions 1 2 2 2 (4) 2 1

Estimated integrated luminosityper exp. (ab−1/year)

0.1 10 1.0 0.2 0.25 0.2–1.0 0.5 0.001

Peak luminosity (1034 cm−2 s−1) 1 100 9 2 2 5–29 12 0.008

Time between collisions (µs) 0.025 0.005 0.6 6.0 3.6 0.025 0.025 1

Energy spread (rms, 10−3) 0.03 (e), 0.1(p) 1.3 1.7 2.5 1.6 0.1 0.2 0.04

Bunch length (rms, mm) 0.06 (e), 75.5(p) 3.3 2.6 2.8 2.7 80 75.5 63

IP beam size (µm) 4.1 (round) 8(H),

0.03(V)

22(H),

0.03(V)

31(H),

0.05(V)

70(H),

0.15(V)

6.8 (inj.) 9.0 (inj.) 75

Injection energy (GeV) 1(e), 450(p) on energy on energy ∼3000 2100 on energy

(topping off) (topping off) (topping off)

Transverse emittance (rms, nm) 0.43(e),

0.34(p)

0.13(H),

0.001(V)

1.0(H),

0.001(V)

2.0(H),

0.002(V)

6.1(H),

0.02(V)

0.04 (inj.) 0.11 335

β∗, amplitude function at interac-tion point (cm)

4.7(e),

5.0(p)

50(H),

0.1(V)

50(H),

0.1(V)

50(H),

0.1(V)

80(H),

0.12(V)

110–30 75 1.7

Beam-beam tune shift per cross-ing (10−3)

−(e), 0.4(p) 140 100 90 118 5–15 6 20

RF frequency (MHz) 800(e), 400(p) 400 650 400 400/200 805

Particles per bunch (1010) 0.25(e), 22(p) 50 10 20 38 10 20 400

Bunches per beam −(e), 2808 60000 625 60 50 10600 5798 1

Average beam current (mA) 16(e), 883(p) 1450 30 6.6 16.6 500 1000 640

Length of standard cell (m) 52.4(e arc), 107(p) 50 50 50 47 213 148 N/A

Phase advance per cell (deg) 310(eH), 90(eV),

90(p)

90(H), 60(V) 60 90 90 N/A

Peak magnetic field (T) 0.264(e), 8.33(p) 0.01 0.03 0.05 0.07 16 20 10

Polarization (%) 90(e), 0(p) ≥10 0 0 0 0 0 0

SR power loss/beam (MW) 30(e), 0.01(p) 50 52 2.4 2.1 3 × 10−5

Novel technology high-energy ERL — — 16 T Nb3Snmagnets

20 T HTSmagnets

ioniz. cool.high-p. target

30.6. Future High Energy Colliders and Prospects

Recent accomplishments of particle physics have been obtainedthrough high-energy and high-intensity experiments using hadron-hadron, lepton-lepton, and lepton-proton colliders. Following thediscovery of the Higgs particle at the LHC and in view of ongoingsearches for “new physics” and rare phenomena, various options areunder discussions and development to pursue future particle-physicsresearch at higher energy and with appropriate luminosity. This is thebasis for various new projects, ideas, and R&D activities, which canonly briefly be summarized here. Specifically, the following projectsare noted: two approaches to an electron-positron linear collider, alarger 100-km circular tunnel supporting e+e− collisions up to 350 or500 GeV in the centre of mass along with a 100-TeV proton-protoncollider, a muon ring collider, and potential use of plasma accelerationand other advanced schemes. Complementary studies are ongoing ofa high-energy lepton-hadron collider bringing into collision a 60-GeVelectron beam from an energy-recovery linac with the 7-TeV protonscirculating in the LHC (LHeC) [26,27], and of γγ collider Higgsfactories based on recirculating electron linacs (e.g. SAPPHiRE atCERN [28], HFiTT at FNAL [29]) . Tentative parameters of some ofthe colliders discussed, or mentioned, in this section are summarizedin Table 30.1.30.6.1. Electron-Positron Linear Colliders : For three decadesefforts have been devoted to develop high-gradient technology e+e−

colliders in order to overcome the synchrotron radiation limitations ofcircular e+e− machines in the TeV energy range.

The primary challenge confronting a high energy, high luminositysingle pass collider design is the power requirement, so that measures

must be taken to keep the demand within bounds as illustrated in atransformed Eq. (30.2) [30]:

L ≈ 137

8πre

Pwall

Ecm

η

σ∗y

Nγ HD . (30.12)

Here, Pwall is the total wall-plug power of the collider, η ≡ Pb/Pwall

the efficiency of converting wall-plug power into beam powerPb = fcollnEcm, Ecm the cms energy, n (= n1 = n2) the bunchpopulation, and σ∗

y the vertical rms beam size at the collision point.

In formulating Eq. (30.12) the number of beamstrahlung photonsemitted per e±, was approximated as Nγ ≈ 2αren/σ∗

x, where αdenotes the fine-structure constant. The management of Pwall leadsto an upward push on the bunch population n with an attendant risein the energy radiated due to the electromagnetic field of one bunchacting on the particles of the other. Keeping a significant fraction ofthe luminosity close to the nominal energy represents a design goal,which is met if Nγ does not exceed a value of about 1. A consequenceis the use of flat beams, where Nγ is managed by the beam width, andluminosity adjusted by the beam height, thus the explicit appearanceof the vertical beam size σ∗

y . The final factor in Eq. (30.12), HD,represents the enhancement of luminosity due to the pinch effectduring bunch crossing (the effect of which has been neglected in theexpression for Nγ).

The approach designated by the International Linear Collider (ILC)is presented in the Tables, and the contrast with the collision-pointparameters of the circular colliders is striking, though reminiscent indirection of those of the SLAC Linear Collider. The ILC Technical

Design Report [31] has a baseline cms energy of 500 GeV with upgrade


provision for 1 TeV, and luminosity comparable to the LHC. The ILCis based on superconducting accelerating structures of the 1.3 GHzTESLA variety.

At CERN, a design effort is underway on the Compact Linear Collider(CLIC), each linac of which is itself a two-beam accelerator, in thata high energy, low current beam is fed by a low energy, high currentdriver [32]. The CLIC design employs normal conducting 12 GHzaccelerating structures at a gradient of 100 MeV/m, some three timesthe current capability of the superconducting ILC cavities. The designcms energy is 3 TeV.

30.6.2. Future Circular Colliders : The discovery, in 2012, ofthe Higgs boson at the LHC has stimulated interest in constructinga large circular tunnel which could host a variety of energy-frontiermachines, including high-energy electron-positron, proton-proton, andlepton-hadron colliders. Such projects are under study by a globalcollaboration hosted at CERN (FCC) [33] and another one centeredin China (CEPC/SPPC) [34], following earlier proposals for a VeryLarge Hadron Collider (VLHC) [35] and a Very Large Lepton Collider(VLLC) in the US, which would have been housed in the same 230-kmlong tunnel.

The maximum beam energy of a hadron collider is directly proportionalto the magnetic field and to the ring circumference. The LHC magnets,based on Nb-Ti superconductor, achieve a maximum operational fieldof 8.33 T. The HL-LHC project develops the technology of higherfield Nb3Sn magnets as well as cables made from high-temperaturesuperconductor (HTS). Nb3Sn dipoles could ultimately reach anoperational field around 15 T, and HTS inserts, requiring newengineering materials and substantial dedicated R&D, could boost thisfurther. A cost-effective hybrid magnet design incorporating Nb-Ti,two types of Nb3Sn, and an inner layer of HTS could provide a fieldof 20 T [36]. If installed in the LHC tunnel, such dipoles wouldincrease the beam energy by a factor 2.5 compared with the LHC. Thevacuum system for such a machine has not yet been designed. Warmphoton absorbers installed in the magnet interconnections are oneof the proposed approaches, requiring experimental tests for designvalidation.

Further substantial increases in collision energy are possible only witha larger tunnel. The FCC hadron collider (FCC-hh) [37], formerlycalled VHE-LHC [38], is based on a new tunnel of about 100 kmcircumference, which would allow exploring energies up to 100 TeV inthe centre of mass with proton-proton collisions, using 16 T magnets.This new tunnel could also accommodate a high-luminosity circulare+e− Higgs factory (FCC-ee) as well as a lepton-hadron collider(FCC-he).

In order to serve as a Higgs factory a new circular e+e− colliderneeds to achieve a cms energy of at least 240 GeV. FCC-ee (formerlyTLEP [39]) , installed in the ∼100 km tunnel of the FCC-hh, couldreach even higher energies, e.g. 350 GeV cms for tt production, or up to500 GeV for ZHH and Htt physics. At these energies, the luminosity,limited by the synchrotron radiation power, would still be close to1034 cm−2s−1 at each of four collision points. At lower energies (Zpole and WW threshold) FCC-ee could deliver up to three ordersof magnitude higher luminosities, and also profit from radiative selfpolarization for precise energy calibration. The short beam lifetimeat the high target luminosity, due to radiative Bhabha scattering,requires FCC-ee to be constructed as a double ring, where the colliderring operating at constant energy is complemented by a secondinjector ring installed in the same tunnel to “top off” the collidercurrent. Beamstrahlung, i.e. synchrotron radiation emitted during thecollision in the field of the opposing beam, introduces an additionalbeam lifetime limitation depending on momentum acceptance (so thatachieving sufficient off-momentum dynamic aperture becomes one ofthe design challenges), as well as some bunch lengthening.

30.6.3. Muon Collider : The muon to electron mass ratio of 210implies less concern about synchrotron radiation by a factor of about2 × 109 and its 2.2 µs lifetime means that it will last for some 150Bturns in a ring about half of which is occupied by bend magnets withaverage field B (Tesla). Design effort became serious in the mid 1990sand a collider outline emerged quickly.

Removal of the synchrotron radiation barrier reduces the scale of amuon collider facility to a level compatible with on-site placement atexisting accelerator laboratories. The Higgs production cross sectionin the s-channel is enhanced by a factor of (mµ/me)

2 compared tothat in e+e− collisions. And a neutrino factory could potentially berealized in the course of construction [40].

The challenges to luminosity achievement are clear and amenable toimmediate study: targeting, collection, and emittance reduction areparamount, as well as the bunch manipulation required to produce> 1012 muons per bunch without emittance degradation. The protonsource needs to deliver a beam power of several MW, collection wouldbe aided by magnetic fields common on neutron stars (though scaledback for application on earth), and the emittance requirements haveinspired fascinating investigations into phase space manipulations thatare finding applications in other facilities. The status was summarizedin a White Paper submitted to “Snowmass 2013” [41].

30.6.4. Plasma Acceleration and Other Advanced Concepts

: At the 1956 CERN Symposium, a paper by Veksler, in which hesuggested acceleration of protons to the TeV scale using a bunchof electrons, anticipated current interest in plasma acceleration [42].A half-century later this is more than a suggestion, with thedemonstration, as a striking example, of electron energy doubling from42 to 84 GeV over 85 cm at SLAC [43].

Whether plasma acceleration will find application in an HEP facilityis not yet clear, given the necessity of staging and phase-lockingacceleration in multiple plasma chambers. Maintaining beam qualityand beam position as well as the acceleration of high-repetition bunchtrains are also primary feasibility issues, addressed by active R&D.For recent discussions of parameters for a laser-plasma based electronpositron collider, see, for example, relevant papers in an AdvancedAccelerator Concepts Workshop [44] and the ICFA-ICUIL WhitePaper from 2011 [45].

Additional approaches aiming at accelerating gradients higher, ormuch higher, than those achievable with conventional metal cavitiesinclude the use of dielectric materials and, for the long-term future,crystals. Combining several innovative ideas, even a linear crystalmuon collider driven by X-ray lasers has been proposed [46].

Not only the achievable accelerating gradient, but also the overallpower efficiency, e.g. the attainable luminosity as a function ofelectrical input power, will determine the suitability of any noveltechnology for use in future high-energy accelerators.

References:

1. E. D. Courant and H. S. Snyder, Ann. Phys. 3, 1 (1958). This isthe classic article on the alternating gradient synchrotron.

2. A.W. Chao et al., eds., Handbook of Accelerator Physics and

Engineering, World Science Publishing Co. (Singapore, 2ndedition, 2013.), Sec. 2.1, 2.2.

3. H. Wiedemann, Handbook of Accelerator Physics and Engineering,ibid, Sec. 3.1.

4. C. Amsler et al. (Particle Data Group), Phys. Lett. B667, 1(2008)[http://pdg.lbl.gov/2008/reviews/contents sports.html].

5. M.A. Furman and M.S. Zisman, Handbook of Accelerator Physics

and Engineering, ibid, Sec. 4.1.6. M.A. Furman, Handbook of Accelerator Physics and Engineering,

ibid, Sec. 2.4.14.7. http://ab-abp-rlc.web.cern.ch/ab-abp-rlc-ecloud/. This

site contains many references as well as videos of electron cloudsimulations.

8. D. Mohl et al., Phys. Reports 58, 73 (1980).9. M. Blaskiewicz, J.M. Brennan, and K. Mernick, Phys. Rev. Lett.

105, 094801 (2010).10. J. M. Brennan, M. Blaskiewicz, K. Mernick, “Stochastic Cooling

in RHIC,” Proc. IPAC’12, New Orleans.11. G.I. Budker, Proc. Int. Symp. Electron & Positron Storage

Rings, (1966).12. H.T. Edwards, “The Tevatron Energy Doubler: A Supercon-

ducting Accelerator,” Ann. Rev. Nucl. and Part. Sci. 35, 605(1985).


13. Brief history athttp://en.wikipedia.org/wiki/Hadron Elektron Ring Anlage.

14. R. Assmann et al., Nucl. Phys. (Proc. Supp.) B9, 17 (2002).15. N. Phinney, arXiv:physics/0010008 (2000).16. L. Evans, “The Large Hadron Collider,” Ann. Rev. Nucl. and

Part. Sci. 61, 435 (2011).17. M. Draper, ed., Proc. Chamonix 2014: LHC Performance Work-

shop, CERN-2015-002, http://cds.cern.ch/record/2020930(2015).

18. Detailed information from the multi-volume design report topresent status may be found at http://lhc.web.cern.ch/lhc/.

19. S. van der Meer, “Calibration of the Effective Beam Height atthe ISR,” CERN-ISR-PO/68-31 (1968).

20. ATLAS Collaboration, “Improved Luminosity Determination inpp Collisions at

√s = 7 TeV using the ATLAS Detector at the

LHC,” Eur. Phys. J. C73, 2518 (2013).21. http://aliceinfo.cern.ch/Public/Welcome.html.22. http://hilumilhc.web.cern.ch.23. An overview of electron-positron colliders past and present

may be found in ICFA Beam Dynamics Newsletter No. 46,April 2009, http://www-bd.fnal.gov/icfabd/. A day-by-dayaccount of the luminosity progress at KEK-B may be found athttp://belle.kek.jp/bdocs/lumi belle.png.

24. M. Zobov et al., “Test of ‘Crab-Waist‘ Collisions at the DAΦNEΦ Factory,” Phys. Rev. Lett. 104, 174801 (2010).

25. M. Harrison, T. Ludlam, and S. Ozaki, eds., “Special Issue:The Relativisitic Heavy Ion Collider Project: RHIC and itsDetectors,” Nucl. Instrum. Methods A499, 1 (2003).

26. J.L. Abelleira et al., J. Phys. G39, 075001 (2012).27. J.L. Abelleira et al., arXiv:1211.5102 (2012).28. S.A. Bogacz et al., arXiv:1208.2827 (2012).29. W. Chou et al., arXiv:1305.5202 (2013).

30. F. Zimmermann, “Tutorial on Linear Colliders,” AIPConf. Proc. 592, 494 (2001).

31. www.linearcollider.org/ILC/Publications/Technical-

Design-Report.32. http://lcd.web.cern.ch/lcd/CDR/CDR.html.33. http://www.cern.ch/fcc.34. http://cepc.ihep.ac.cn.35. http://vlhc.org.36. L. Rossi, E. Todesco, arXiv:1108:1619, in Proc. HE-LHC10,

Malta, 14–16 October 2010, CERN Yellow Report CERN-2011-

003.37. F. Zimmermann et al., “Challenges for Highest Energy Circular

Colliders,” Proc. IPAC’14 Dresden.38. C.O. Dominguez, F. Zimmermann, “Beam Parameters and Lumi-

nosity Time Evolution for an 80-km VHE-LHC,” Proc. IPAC’13

Shanghai.39. http://www.cern.ch/tlep.40. http://en.wikipedia.org/wiki/Neutrino Factory.41. J.P. Delahaye et al., arXiv:1308.0494 (2013).42. V.I. Veksler, CERN Symposium on High Energy Accelerators and

Pion Physics, 11–23 June 1956, p. 80. This paper may be down-loaded from http://cdsweb.cern.ch/record/1241563?ln=en.

43. I. Blumenfeld et al., Nature 445, 741 (2007).44. Advanced Accelerator Concepts, edited by R. Zgadzaj, E. Gaul

and M. Downer, AIP Conference Proceedings 1507, Austin TX10 – 15 June 2012.

45. White Paper of ICFA-ICUIL Joint Task Force — High PowerLaser Technology for Accelerators, published in ICFA BeamDynamics Newslettern No. 56, December 2011, http://www-

bd.fnal.gov/icfabd/.46. V. Shiltsev, Sov. Phys. Usp. 55, 965 (2012).

31. High-energy collider parameters 435

HIGH-ENERGY COLLIDER PARAMETERS: e+

e− Colliders (I)

Updated in January 2016 with numbers received from representatives of the colliders (contact S. Pagan Griso, LBNL). The table shows theparameter values achieved. Quantities are, where appropriate, r.m.s.; unless noted otherwise, energies refer to beam energy; H and V indicatehorizontal and vertical directions; s.c. stands for superconducting. Parameters for the defunct SPEAR, DORIS, PETRA, PEP, TRISTAN, andVEPP-2M colliders may be found in our 1996 edition (Phys. Rev. D54, 1 July 1996, Part I).

VEPP-2000(Novosibirsk)

VEPP-4M(Novosibirsk)

BEPC(China)

BEPC-II(China)

DAΦNE(Frascati)

Physics start date 2010 1994 1989 2008 1999

Physics end date — — 2005 — —

Maximum beam energy (GeV) 1.0 6 2.5 1.89 (2.3 max) 0.510

Delivered integrated lumi-nosity per exp. (fb−1)

0.030 0.027 0.11 10.3 ≈ 4.7 in 2001-2007≈ 2.7 w/crab-waist≈ 1.8 since Nov 2014

Luminosity (1030 cm−2s−1) 100 20 12.6 at 1.843 GeV5 at 1.55 GeV

853 453

Time between collisions (µs) 0.04 0.6 0.8 0.008 0.0027

Full crossing angle (µ rad) 0 0 0 2.2 × 104 5 × 104

Energy spread (units 10−3) 0.64 1 0.58 at 2.2 GeV 0.52 0.40

Bunch length (cm) 4 5 ≈ 5 ≈ 1.5 low current: 1at 15mA: 2

Beam radius (10−6 m) 125 (round) H : 1000V : 30

H : 890V : 37

H : 358V : 4.8

H : 260V : 4.8

Free space at interactionpoint (m)

±1 ±2 ±2.15 ±0.63 ±0.295

Luminosity lifetime (hr) continuous 2 7–12 1.5 0.2

Turn-around time (min) continuous 18 32 15 2 (topping up)

Injection energy (GeV) 0.2–1.0 1.8 1.55 1.89 on energy

Transverse emittance(10−9 m)

H : 250V : 250

H : 200V : 20

H : 660V : 28

H : 128V : 1.73

H : 260V : 2.6

β∗, amplitude function atinteraction point (m)

H : 0.06 − 0.11V : 0.06 − 0.10

H : 0.75V : 0.05

H : 1.2V : 0.05

H : 1.0V : 0.0135

H : 0.26V : 0.009

Beam-beam tune shiftper crossing (units 10−4)

H : 750V : 750

500 350 390 440(crab-waist test)

RF frequency (MHz) 172 180 199.53 499.8 356

Particles per bunch(units 1010)

16 15 20 at 2 GeV11 at 1.55 GeV

3.8 e−: 3.2e+: 2.1

Bunches per ringper species

1 2 1 92 100 to 105(120 buckets)

Average beam currentper species (mA)

150 80 40 at 2 GeV22 at 1.55 GeV

701 e−: 1250e+: 800

Circumference or length (km) 0.024 0.366 0.2404 0.23753 0.098

Interaction regions 2 1 2 1 1

Magnetic length of dipole (m) 1.2 2 1.6 outer ring: 1.6inner ring: 1.41

outer ring: 1.2inner ring: 1

Length of standard cell (m) 12 7.2 6.6 outer ring: 6.6inner ring: 6.2

n/a

Phase advance per cell (deg) H : 738V : 378

65 ≈ 60 60–90non-standard cells

—

Dipoles in ring 8 78 40 + 4 weak 84 + 8 weak 8

Quadrupoles in ring 20 150 68 134+2 s.c. 48

Peak magnetic field (T) 2.4 0.6 0.903at 2.8 GeV

outer ring: 0.677inner ring: 0.766

1.2

436 31. High-energy collider parameters


e− Colliders (II)

Updated in January 2016 with numbers received from representatives of the colliders (contact S. Pagan Griso, LBNL). The table shows theparameter values achieved. For future colliders, design values are quoted. Quantities are, where appropriate, r.m.s.; unless noted otherwise,energies refer to beam energy; H and V indicate horizontal and vertical directions; s.c. stands for superconducting.

CESR(Cornell)

CESR-C(Cornell)

LEP(CERN)

SLC(SLAC)

ILC(TBD)

CLIC(TBD)

Physics start date 1979 2002 1989 1989 TBD TBD

Physics end date 2002 2008 2000 1998 — —

Maximum beam energy (GeV)6 6 100 - 104.6 50 250

(upgradeable to 500)1500

(first phase: 190)

Delivered integrated luminosityper experiment (fb−1)

41.5 2.0 0.221 at Z peak0.501 at 65 − 100 GeV

0.022 — —

0.275 at >100 GeV

Luminosity (1030 cm−2s−1) 1280 at5.3 GeV

76 at2.08 GeV

24 at Z peak100 at > 90 GeV

2.5 1.5 × 104‡ 6 × 104

Time between collisions (µs) 0.014 to 0.22 0.014 to 0.22 22 8300 0.55† 0.0005†

Full crossing angle (µ rad) ±2000 ±3300 0 0 14000 20000

Energy spread (units 10−3) 0.6 at5.3 GeV

0.82 at2.08 GeV

0.7→1.5 1.2 1 3.4

Bunch length (cm) 1.8 1.2 1.0 0.1 0.03 0.0044

Beam radius (µm) H : 460V : 4

H : 340V : 6.5

H : 200 → 300V : 2.5 → 8

H : 1.5V : 0.5

H : 0.474V : 0.0059

H : 0.045V : 0.0009

∗


±2.2 (±0.6

to REC quads)

±2.2 (±0.3

to PM quads)±3.5 ±2.8 ±3.5 ±3.5

Luminosity lifetime (hr) 2–3 2–3 20 at Z peak10 at > 90 GeV

— n/a n/a

Turn-around time (min) 5 (topping up) 1.5 (topping up) 50 120 Hz (pulsed) n/a n/a

Injection energy (GeV) 1.8–6 1.5–6 22 45.64 n/a n/a


H : 210V : 1

H : 120V : 3.5

H : 20–45V : 0.25 → 1

H : 0.5V : 0.05

H : 0.02V : 7 × 10−5

H : 2.2 × 10−4

V : 6.8 × 10−6


H : 1.0V : 0.018

H : 0.94V : 0.012

H : 1.5V : 0.05

H : 0.0025V : 0.0015

H : 0.01V : 5 × 10−4

H : 0.0069V : 6.8 × 10−5

Beam-beam tune shift percrossing (10−4) or disruption

H : 250V : 620

e−: 420 (H), 280 (V )

e+: 410 (H), 270 (V )830 0.75 (H)

2.0 (V )n/a 7.7

RF frequency (MHz) 500 500 352.2 2856 1300 11994


1.15 4.7 45 in collision60 in single beam

4.0 2 0.37


9 trainsof 5 bunches

8 trainsof 3 bunches

4 trains of 1 or 2 1 1312 312 (in train)


340 72 4 at Z peak4→6 at > 90 GeV

0.0008 6(in pulse)

1205 (in train)

Beam polarization (%) — — 55 at 45 GeV5 at 61 GeV

e−: 80 e−: > 80%e+: < 60%

e−: 70% at IP

Circumference or length (km) 0.768 0.768 26.66 1.45 +1.47 31 50

Interaction regions 1 1 4 1 1 1

Magnetic length of dipole (m) 1.6–6.6 1.6–6.6 11.66/pair 2.5 n/a n/a

Length of standard cell (m) 16 16 79 5.2 n/a n/a

Phase advance per cell (deg) 45–90 (no

standard cell)

45–90 (no

standard cell)102/90 108 n/a n/a

Dipoles in ring 86 84 3280 + 24 inj. + 64 weak460+440

n/a n/a

Quadrupoles in ring 101 + 4 s.c. 101 + 4 s.c. 520 + 288 + 8 s.c. — n/a n/a

Peak magnetic field (T) 0.3 / 0.8at 8 GeV

0.3 / 0.8 at 8 GeV,2.1 wigglers at 1.9 GeV

0.135 0.597 n/a n/a

†Time between bunch trains: 200ms (ILC) and 20ms (CLIC).‡Geometrical luminosity. The actual value may vary by ≈ 20% depending on assumptions.∗Effective beam size including non-linear and chromatic effects.



e− Colliders (III)

Updated in January 2016 with numbers received from representatives of the colliders (contact S. Pagan Griso, LBNL). The table shows theparameter values achieved. For future colliders, design values are quoted. Quantities are, where appropriate, r.m.s.; unless noted otherwise,energies refer to beam energy; H and V indicate horizontal and vertical directions; s.c. stands for superconducting.

KEKB(KEK)

PEP-II(SLAC)

SuperKEKB(KEK)

Physics start date 1999 1999 2017

Physics end date 2010 2008 —

Maximum beam energy (GeV) e−: 8.33 (8.0 nominal)

e+: 3.64 (3.5 nominal)

e−: 7–12 (9.0 nominal)

e+: 2.5–4 (3.1 nominal)

e−: 7e+: 4

Delivered integrated lumi-nosity per exp. (fb−1)

1040 557 —

Luminosity (1030 cm−2s−1) 21083 12069(design: 3000)

8 × 105

Time between collisions (µs) 0.00590 or 0.00786 0.0042 0.004

Full crossing angle (µ rad) ±11000† 0 ±41500

Energy spread (units 10−3) 0.7 e−/e+: 0.61/0.77 e−/e+: 0.64/0.81

Bunch length (cm) 0.65 e−/e+: 1.1/1.0 e−/e+: 0.5/0.6

Beam radius (µm) H: 124 (e−), 117 (e+)V: 1.9

H : 157V : 4.7

e−: 11 (H), 0.062 (V )

e+: 10 (H), 0.048 (V )


+0.75/−0.58

(+300/−500) mrad cone±0.2,

±300 mrad conee− : +1.20/− 1.28, e+ : +0.78/− 0.73

(+300/−500) mrad cone

Luminosity lifetime (hr) continuous continuous continuous

Turn-around time (min) continuous continuous continuous

Injection energy (GeV) e−/e+ : 8.0/3.5 (nominal) e−/e+ : 9.0/3.1 (nominal) e−/e+ : 7/4


e−: 24 (57∗) (H), 0.61 (V )

e+: 18 (55∗) (H), 0.56 (V )

e−: 48 (H), 1.8 (V )

e+: 24 (H), 1.8 (V )

e−: 4.6 (H), 0.013 (V )

e+: 3.2 (H), 0.0086 (V )


e−: 1.2 (0.27∗) (H), 0.0059 (V )

e+: 1.2 (0.23∗) (H), 0.0059 (V )

e−: 0.50 (H), 0.012 (V )

e+: 0.50 (H), 0.012 (V )

e−: 0.025 (H), 3 × 10−4 (V )

e+: 0.032 (H), 2.7 × 10−4 (V )


e−: 1020 (H), 900 (V )

e+: 1270 (H), 1290 (V )

e−: 703 (H), 498 (V )

e+: 510 (H), 727 (V )

e−: 12 (H), 807 (V )

e+: 28 (H), 881 (V )

RF frequency (MHz) 508.887 476 508.887


e−/e+: 4.7/6.4 e−/e+: 5.2/8.0 e−/e+: 6.53/9.04


1585 1732 2500


e−/e+: 1188/1637 e−/e+: 1960/3026 e−/e+: 2600/3600

Beam polarization (%) — — —

Circumference or length (km) 3.016 2.2 3.016

Interaction regions 1 1 1

Magnetic length of dipole (m) e−/e+ : 5.86/0.915 e−/e+: 5.4/0.45 e−/e+ : 5.9/4.0

Length of standard cell (m) e−/e+ : 75.7/76.1 15.2 e−/e+ : 75.7/76.1

Phase advance per cell (deg) 450 e−/e+: 60/90 450

Dipoles in ring e−/e+ : 116/112 e−/e+: 192/192 e−/e+ : 116/112

Quadrupoles in ring e−/e+ : 452/452 e−/e+: 290/326 e−/e+ : 466/460

Peak magnetic field (T) e−/e+ : 0.25/0.72 e−/e+: 0.18/0.75 e−/e+ : 0.22/0.19

†KEKB was operated with crab crossing from 2007 to 2010.∗With dynamic beam-beam effect.

438 31. High-energy collider parameters

HIGH-ENERGY COLLIDER PARAMETERS: ep, pp, pp Colliders

Updated in January 2016 with numbers received from representatives of the colliders (contact S. Pagan Griso, LBNL). The table shows theparameter values achieved. For LHC, the parameters expected at the ATLAS and CMS experiments for a high-luminosity upgrade (HL-LHC)are also given. Parameters for the defunct SppS collider may be found in our 2002 edition (Phys. Rev. D66, 010001 (2002)). Quantities are,where appropriate, r.m.s.; unless noted otherwise, energies refer to beam energy; H and V indicate horizontal and vertical directions; s.c. standsfor superconducting.

HERA(DESY)

TEVATRON∗

(Fermilab)RHIC

(Brookhaven)LHC

(CERN)

Physics start date 1992 1987 2001 2009 2015 2024 (HL-LHC)

Physics end date 2007 2011 — —

Particles collided ep pp pp (polarized) pp

Maximum beamenergy (TeV)

e: 0.030p: 0.92

0.980 0.25553% polarization

4.0 6.5 7.0

Maximum delivered integratedluminosity per exp. (fb−1)

0.8 12 0.38 at 100 GeV0.75 at 250/255 GeV

23.3 at 4.0 TeV6.1 at 3.5 TeV

4.2 250/y

Luminosity(1030 cm−2s−1)

75 431 245 (pk)

160 (avg)7.7 × 103 5 × 103 5.0 × 104

(leveled)

Time betweencollisions (ns)

96 396 107 49.90 24.95 24.95

Full crossing angle (µ rad) 0 0 0 290 290 590

Energy spread (units 10−3) e: 0.91p: 0.2

0.14 0.15 0.1445 0.105 0.123

Bunch length (cm) e: 0.83p: 8.5

p: 50p: 45

60 9.4 9 9

Beam radius(10−6 m)

e: 110(H), 30(V )

p: 111(H), 30(V )p: 28p: 16

85 18.8 21 7

Free space atinteraction point (m)

±2 ±6.5 16 38 38 38

Initial luminosity decaytime, −L/(dL/dt) (hr)

10 6 (avg) 7.5 ≈ 6 ≈ 30 ≈ 6 (leveled)

Turn-around time (min) e: 75, p: 135 90 25 180 134 180

Injection energy (TeV) e: 0.012p: 0.040

0.15 0.023 0.450 0.450 0.450


e: 20(H), 3.5(V )

p: 5(H), 5(V )p: 3p: 1

13 0.59 0.5 0.34

β∗, ampl. function atinteraction point (m)

e: 0.6(H), 0.26(V )

p: 2.45(H), 0.18(V )0.28 0.65 0.6 0.8 0.15


e: 190(H), 450(V )

p: 12(H), 9(V )p: 120p: 120

73 72 37 110

RF frequency (MHz) e: 499.7p: 208.2/52.05

53 accel: 9store: 28

400.8 400.8 400.8


e: 3p: 7

p: 26p: 9

18.5 16 12 22


e: 189p: 180

36 111 1380 22442232 (i.r. 1/5†)

27482736 (i.r. 1/5†)


e: 40p: 90

p: 70p: 24

257 400 467 1200

Circumference (km) 6.336 6.28 3.834 26.659

Interaction regions 2 colliding beams 2 high L 6 total, 2 high L 4 total, 2 high L1 fixed target (e beam)

Magnetic lengthof dipole (m)

e: 9.185p: 8.82

6.12 9.45 14.3

Length of standard cell (m) e: 23.5p: 47

59.5 29.7 106.90

Phase advance per cell (deg) e: 60p: 90

67.8 84 90

Dipoles in ring e: 396p: 416

774 192 per ring+ 12 common

1232main dipoles

Quadrupoles in ring e: 580p: 280

216 246 per ring 482 2-in-124 1-in-1

Magnet types e: C-shapedp: s.c., collared, warm iron

s.c., cos θwarm iron

s.c., cos θcold iron

s.c., 2 in 1cold iron

Peak magnetic field (T) e: 0.274, p: 5 4.4 3.5 8.3‡

∗Additional TEVATRON parameters: p source accum. rate: 25×1010 hr−1; max. no. of p stored: 3.4×1012 (Accumulator),6.1×1012 (Recycler).†Number of bunches colliding at the interaction regions (i.r.) 1 (ATLAS) and 5 (CMS).‡Value for design beam energy of 7 TeV.


HIGH-ENERGY COLLIDER PARAMETERS: Heavy Ion Colliders

Updated in January 2016 with numbers received from representatives of the colliders (contact S. Pagan Griso, LBNL). The table shows theparameter values achieved. For LHC, the parameters expected at the ATLAS experiment for running in 2016 and the design values for ahigh-luminosity upgrade are also given. Quantities are, where appropriate, r.m.s.; unless noted otherwise, energies refer to beam energy; s.c.stands for superconducting. pk and avg denote peak and average values.

RHIC(Brookhaven)

LHC(CERN)

Physics start date 2000 2012 / 2012 / 2004 / 2014

2002 / 2015 / 20152010 2012 2016

(expected)

≥ 2021

(high lum.)‡

Physics end date — —

Particles collided Au Au U U / Cu Au / Cu Cu / h Au

d Au / p Au / p AlPb Pb p Pb p Pb Pb Pb

Maximum beamenergy (TeV/n)

0.1 0.1 2.51 p: 4Pb: 1.58

p: 6.5Pb: 2.56

2.76

√sNN (TeV) 0.2 0.2 5.02 5.0 8.16 5.5

Max. delivered int. nucleon-pair lumin. per exp. (pb−1)

1484(at 100 GeV/n)

21 / 167 / 65 / 43

103 / 125 / 64 (all at 100 GeV/n)30.3 6.6 ≈ 10/y ≈ 75 − 90/y

Luminosity(1027 cm−2s−1)

pk: 8.4avg: 8.0

pk: 0.9 / 12 / 20 / 170

270 / 880 / 7150avg: 0.6 / 10 / 0.8 / 100

140 / 450 / 4000

3.6 100 (leveled)

116 (ATLAS/CMS)≈ 500 6 (leveled)

Time betweencollisions (ns)

107 107 / 107 / 321 / 107

107 / 107 / 10799.8 / 149.7 199.6 / 224.6 99.8 / 149.7 49.9

Full crossing angle (µ rad) 0 0 290 120 290 > 200

Energy spread (units 10−3) 0.75 0.75 0.11 0.11 0.11 0.11

Bunch length (cm) 30 30 8.0 p / Pb: 9 / 11.5 p / Pb: 9 / 11.5 7.9

Beam radius(10−6 m)

55 50 / 160 / 145 / 135

145 / 145 / 14555 p: 19

Pb: 2717 16

Free space atinteraction point (m)

16 16 38 38 38 38

Initial luminosity decaytime, −L/(dL/dt) (hr)

1 -0.35†/ ∞†/ 1.8 / 0.6

1.5 / 0.5 / 0.252.6 ≈ 6 ≈ 2 ≈ 2

Turn-around time (min) 30 60 / 160 / 90 / 45

90 / 60 / 50≈ 180 ≈ 240 ≈ 180 ≈ 180

Injection energy (TeV/n) 0.011 0.011 0.177 p / Pb: 0.45 / 0.177 p / Pb: 0.45 / 0.177 0.177


6 4 / 11 / 23 / 18

25 / 25 / 231.5 p: 0.5

Pb: 0.90.29 0.5

β∗, ampl. function atinteraction point (m)

0.5 0.7 / 0.7 / 0.9 / 1.0

0.85 / 0.8 / 0.80.8 0.8 0.5 0.5


257 / 14 (Cu), 14 (Au) / 30

42 (h), 22 (Au) / 21 (d), 17 (Au)53 (p), 41 (Au) / 73 (p) 57 (Au)

9 p: 9Pb: 10

1010

RF frequency (MHz) accel: 28store: 197

accel: 28store: 197

400.8 400.8 400.8 400.8


0.160.03 / 0.4 (Cu), 0.13 (Au) / 0.45

4.5 (h), 0.13 (Au) / 10 (d), 0.1 (Au)22.5 (p), 0.16 (Au) / 24 (p), 1.1 (Al)

0.019(r.m.s.)

p: 1.6Pb: 0.014

p: 1.8Pb: 0.019

0.017


111 111 / 111 / 37 / 111

95 / 111 / 111518 338 518

≈ 1100


17638 / 159 (Cu), 138 (Au) / 60

125 (h), 143 (Au) / 119 (d), 94 (Au)312 (p), 176 (Au) / 333 (p), 199 (Al)

14.9 p: 9.7Pb: 7

p: 17Pb: 15

28

Circumference (km) 3.834 26.659

Interaction regions 6 total, 2 high L 3 high L + 1

Magnetic length of dipole (m) 9.45 14.3

Length of standard cell (m) 29.7 106.90

Phase advanceper cell (deg)

9384 / 84 / 84 / 93

84 (d), 93 (Au) / 84 (p), 93 (Au)84 (p), 93 (Al)

90

Dipoles in ring 192 per ring, + 12 common 1232, main dipoles

Quadrupoles in ring 246 per ring 482 2-in-1, 24 1-in-1

Magnet Type s.c. cos θ, cold iron s.c., 2 in 1, cold iron

Peak magnetic field (T) 3.5 8.3

†Negative or infinite decay time is effect of cooling.‡High luminosity upgrade expected >= 2021; will extend throughout HL-LHC running. Very preliminary, conservative estimates.

440 32. Neutrino beam lines at high-energy proton synchrotrons

32. NEUTRINO BEAM LINES AT HIGH-ENERGY PROTON SYNCHROTRONS

Revised January 2016 with numbers verified by representatives of the synchrotrons (contact C.-J. Lin, LBNL). For existing (future) neutrinobeam lines the latest achieved (design) values are given.

The main source of neutrinos at proton synchrotrons is from the decay of pions and kaons produced by protons striking a nuclear target.There are different schemes to focus the secondary particles to enhance neutrino flux and/or tune the neutrino energy profile. In wide-bandbeams (WBB), the neutrino parent mesons are focused over a wide momentum range to obtain maximum neutrino intensity. In narrow-bandbeams (NBB), the secondary particles are first momentum-selected to produce a monochromatic parent beam. Another approach to generatea narrow-band neutrino spectrum is to select neutrinos that are emitted off-axis relative to the momentum of the parent mesons. For acomprehensive review of the topic, including other historical neutrino beam lines, see the article by S. E. Kopp, “Accelerator-based neutrinobeams,” Phys. Rept. 439, 101 (2007).

PS(CERN)

SPS(CERN)

PS(KEK)

Main Ring(JPARC)

Date 1963 1969 1972 1983 1977 1977 1995 2006 1999 2009

Proton KineticEnergy (GeV)

20.6 20.6 26 19 350 350 450 400 12 30(50)

Protons perCycle (1012)

0.7 0.6 5 5 10 10 36 48 6 200(330)

Cycle Time(s)

3 2.3 - - - - 14.4 6 2.2 2.48(3.5)

Beam Power(kW)

0.8 0.9 - - - - 180 510 5 390(750)

Target - - - - - - Be Graphite Al Graphite

Target Length(cm)

- - - - - - 290 1000 66 91

SecondaryFocussing

1-hornWBB

3-hornWBB

2-hornWBB

baretarget

dichromaticNBB

2-hornWBB

2-hornWBB

2-hornWBB

2-hornWBB

3-hornoff-axis

Decay PipeLength (m)

- - - - - - 110 130 200 96

〈Eν〉 (GeV) 1.5 1.5 1.5 1 50,150† 20 24.3 17 1.3 0.6

Experiments HLBC,Spark Ch.

HLBC,Spark Ch.

GGM,Aachen-

CDHS,CHARM

CDHS,CHARM,

GGM,CDHS,CHARM,

NOMAD,CHORUS

OPERA,ICARUS K2K T2K

Padova BEBC BEBC

Main Ring(Fermilab)

Booster(Fermilab)

Main Injector(Fermilab)

Date 1975 1975 1974 1979 1976 1991 1998 2002 2005 2016

Proton KineticEnergy (GeV)

300,400 300,400 300 400 350 800 800 8 120 120

Protons perCycle (1012)

10 10 10 10 13 10 12 4.5 37 43(49)

Cycle Time(s)

- - - - - 60 60 0.2 2 1.333

Beam Power(kW)

- - - - - 20 25 29 350 580(700)

Target - - - - - - BeO Be Graphite Graphite

Target Length(cm)

- - - - - - 31 71 95 120

SecondaryFocussing

baretarget

quad trip.,SSBT

dichromaticNBB

2-hornWBB

1-hornWBB

quadtrip.

SSQTWBB

1-hornWBB

2-hornWBB

2-hornoff-axis

Decay PipeLength (m)

350 350 400 400 400 400 400 50 675 675

〈Eν〉 (GeV) 40 50,180† 50,180† 25 100 90,260 70,180 1 3-20‡ 2

Experiments

HPWFCITF,HPWF

CITF,HPWF, 15’ BC

HPWF15’ BC

15’ BC,CCFRR NuTeV

MiniBooNE,SciBooNE,

MINOS,MINERνA

NOνA,MINERνA,

15’ BC MicroBooNE MINOS+

†Pion and kaon peaks in the momentum-selected channel. ‡Tunable WBB energy spectrum.

33. Passage of particles through matter 441

33. PASSAGE OF PARTICLES THROUGH MATTER

33. PASSAGE OF PARTICLES THROUGHMATTER . . . . . . . . . . . . . . . . . . . . . . 441

33.1. Notation . . . . . . . . . . . . . . . . . . . . 441

33.2. Electronic energy loss by heavy particles . . . . . . 441

33.2.1. Moments and cross sections . . . . . . . . . . 441

33.2.2. Maximum energy transfer in a singlecollision . . . . . . . . . . . . . . . . . . . . . 442

33.2.3. Stopping power at intermediate ener-gies . . . . . . . . . . . . . . . . . . . . . . 442

33.2.4. Mean excitation energy . . . . . . . . . . . . 443

33.2.5. Density effect . . . . . . . . . . . . . . . . 443

33.2.6. Energy loss at low energies . . . . . . . . . . 444

33.2.7. Energetic knock-on electrons (δ rays) . . . . . 444

33.2.8. Restricted energy loss rates for rela-tivistic ionizing

particles . . . . . . . . . . . . . . . . . . . . 444

33.2.9. Fluctuations in energy loss . . . . . . . . . . 445

33.2.10. Energy loss in mixtures and com-pounds . . . . . . . . . . . . . . . . . . . . . 446

33.2.11. Ionization yields . . . . . . . . . . . . . . 446

33.3. Multiple scattering through small angles . . . . . . 446

33.4. Photon and electron interactions in mat-ter . . . . . . . . . . . . . . . . . . . . . . . . 447

33.4.1. Collision energy losses by e± . . . . . . . . . 447

33.4.2. Radiation length . . . . . . . . . . . . . . 447

33.4.3. Bremsstrahlung energy loss by e± . . . . . . . 447

33.4.4. Critical energy . . . . . . . . . . . . . . . 448

33.4.5. Energy loss by photons . . . . . . . . . . . . 448

33.4.6. Bremsstrahlung and pair productionat very high energies . . . . . . . . . . . . . . . 448

33.4.7. Photonuclear and electronuclear in-teractions at still higher energies . . . . . . . . . . 450

33.5. Electromagnetic cascades . . . . . . . . . . . . . 450

33.6. Muon energy loss at high energy . . . . . . . . . 451

33.7. Cherenkov and transition radiation . . . . . . . . 452

33.7.1. Optical Cherenkov radiation . . . . . . . . . 452

33.7.2. Coherent radio Cherenkov radiation . . . . . . 453

33.7.3. Transition radiation . . . . . . . . . . . . . 453

Revised August 2015 by H. Bichsel (University of Washington), D.E.Groom (LBNL), and S.R. Klein (LBNL).

This review covers the interactions of photons and electricallycharged particles in matter, concentrating on energies of interestfor high-energy physics and astrophysics and processes of interestfor particle detectors (ionization, Cherenkov radiation, transitionradiation). Much of the focus is on particles heavier than electrons(π±, p, etc.). Although the charge number z of the projectile isincluded in the equations, only z = 1 is discussed in detail. Muonradiative losses are discussed, as are photon/electron interactions athigh to ultrahigh energies. Neutrons are not discussed.

33.1. Notation

The notation and important numerical values are shown inTable 33.1.

Table 33.1: Summary of variables used in this section.The kinematic variables β and γ have their usual relativisticmeanings.

Symbol Definition Value or (usual) units

mec2 electron mass × c2 0.510 998 928(11) MeV

re classical electron radius

e2/4πǫ0mec2 2.817 940 3267(27) fm

α fine structure constant

e2/4πǫ0~c 1/137.035 999 074(44)

NA Avogadro’s number 6.022 141 29(27)× 1023 mol−1

ρ density g cm−3

x mass per unit area g cm−2

M incident particle mass MeV/c2

E incident part. energy γMc2 MeV

T kinetic energy, (γ − 1)Mc2 MeV

W energy transfer to an electron MeV

in a single collision

k bremsstrahlung photon energy MeV

z charge number of incident particle

Z atomic number of absorber

A atomic mass of absorber g mol−1

K 4πNAr2emec

2 0.307 075 MeV mol−1 cm2

I mean excitation energy eV (Nota bene!)

δ(βγ) density effect correction to ionization energy loss

~ωp plasma energy√

ρ 〈Z/A〉 × 28.816 eV√

4πNer3e mec

2/α |−→ ρ in g cm−3

Ne electron density (units of re)−3

wj weight fraction of the jth element in a compound or mixture

nj ∝ number of jth kind of atoms in a compound or mixture

X0 radiation length g cm−2

Ec critical energy for electrons MeV

Eµc critical energy for muons GeV

Es scale energy√

4π/α mec2 21.2052 MeV

RM Moliere radius g cm−2

33.2. Electronic energy loss by heavy particles [1–33]

33.2.1. Moments and cross sections :

The electronic interactions of fast charged particles with speedv = βc occur in single collisions with energy losses W [1], leading toionization, atomic, or collective excitation. Most frequently the energylosses are small (for 90% of all collisions the energy losses are less than100 eV). In thin absorbers few collisions will take place and the totalenergy loss will show a large variance [1]; also see Sec. 33.2.9 below.For particles with charge ze more massive than electrons (“heavy”particles), scattering from free electrons is adequately described bythe Rutherford differential cross section [2],

dσR(W ; β)

dW=

2πr2emec

2z2

β2

(1 − β2W/Wmax)

W 2, (33.1)

442 33. Passage of particles through matter

where Wmax is the maximum energy transfer possible in a singlecollision. But in matter electrons are not free. W must be finite anddepends on atomic and bulk structure. For electrons bound in atomsBethe [3] used “Born Theorie” to obtain the differential cross section

dσB(W ; β)

dW=

dσR(W, β)

dWB(W ) . (33.2)

Electronic binding is accounted for by the correction factor B(W ).Examples of B(W ) and dσB/dW can be seen in Figs. 5 and 6 ofRef. 1.

Bethe’s theory extends only to some energy above which atomiceffects are not important. The free-electron cross section (Eq. (33.1))can be used to extend the cross section to Wmax. At high energies σB

is further modified by polarization of the medium, and this “densityeffect,” discussed in Sec. 33.2.5, must also be included. Less importantcorrections are discussed below.

The mean number of collisions with energy loss between W andW + dW occurring in a distance δx is Neδx (dσ/dW )dW , wheredσ(W ; β)/dW contains all contributions. It is convenient to define themoments

Mj(β) = Ne δx

∫

W j dσ(W ; β)

dWdW , (33.3)

so that M0 is the mean number of collisions in δx, M1 is the meanenergy loss in δx, (M2 − M1)

2 is the variance, etc. The number ofcollisions is Poisson-distributed with mean M0. Ne is either measuredin electrons/g (Ne = NAZ/A) or electrons/cm3 (Ne = NA ρZ/A).The former is used throughout this chapter, since quantities of interest(dE/dx, X0, etc.) vary smoothly with composition when there is nodensity dependence.

Muon momentum

1

10

100

Mas

s st

oppi

ng p

ower

[M

eV c

m2 /

g]

Lin

dhar

d-S

char

ff

Bethe Radiative

Radiativeeffects

reach 1%

Without δ

Radiativelosses

βγ0.001 0.01 0.1 1 10 100

1001010.1

1000 104 105

[MeV/c]100101

[GeV/c]100101

[TeV/c]

Minimumionization

Eµc

Nuclearlosses

µ−µ+ on Cu

Anderson-Ziegler

Figure 33.1: Mass stopping power (= 〈−dE/dx〉) for positive muons in copper as afunction of βγ = p/Mc over nine orders of magnitude in momentum (12 orders ofmagnitude in kinetic energy). Solid curves indicate the total stopping power. Data belowthe break at βγ ≈ 0.1 are taken from ICRU 49 [4], and data at higher energies are fromRef. 5. Vertical bands indicate boundaries between different approximations discussed inthe text. The short dotted lines labeled “µ− ” illustrate the “Barkas effect,” the dependenceof stopping power on projectile charge at very low energies [6]. dE/dx in the radiativeregion is not simply a function of β.

33.2.2. Maximum energy transfer in a single collision :

For a particle with mass M ,

Wmax =2mec

2 β2γ2

1 + 2γme/M + (me/M)2. (33.4)

In older references [2,8] the “low-energy” approximation Wmax =2mec

2 β2γ2, valid for 2γme ≪ M , is often implicit. For a pion incopper, the error thus introduced into dE/dx is greater than 6% at100 GeV. For 2γme ≫ M , Wmax = Mc2 β2γ.

At energies of order 100 GeV, the maximum 4-momentum transferto the electron can exceed 1 GeV/c, where hadronic structure

effects significantly modify the cross sections. This problem has beeninvestigated by J.D. Jackson [9], who concluded that for hadrons (butnot for large nuclei) corrections to dE/dx are negligible below energieswhere radiative effects dominate. While the cross section for rare hardcollisions is modified, the average stopping power, dominated by manysofter collisions, is almost unchanged.

33.2.3. Stopping power at intermediate energies :

The mean rate of energy loss by moderately relativistic chargedheavy particles, M1/δx, is well-described by the “Bethe equation,”

⟨

−dE

dx

⟩

= Kz2Z

A

1

β2

[

1

2ln

2mec2β2γ2Wmax

I2− β2 − δ(βγ)

2

]

.

(33.5)It describes the mean rate of energy loss in the region 0.1 <∼ βγ <∼ 1000for intermediate-Z materials with an accuracy of a few percent.

This is the mass stopping power ; with the symbol definitions andvalues given in Table 33.1, the units are MeV g−1cm2. As can be seenfrom Fig. 33.2, 〈−dE/dx〉 defined in this way is about the same formost materials, decreasing slowly with Z. The linear stopping power,in MeV/cm, is 〈−dE/dx〉 ρ, where ρ is the density in g/cm3.

Wmax is defined in Sec. 33.2.2. At the lower limit the projec-tile velocity becomes comparable to atomic electron “velocities”(Sec. 33.2.6), and at the upper limit radiative effects begin tobe important (Sec. 33.6). Both limits are Z dependent. A minordependence on M at the highest energies is introduced through Wmax,but for all practical purposes 〈dE/dx〉 in a given material is a functionof β alone.

Few concepts in high-energy physics are as misused as 〈dE/dx〉.The main problem is that the mean is weighted by very rare eventswith large single-collision energy deposits. Even with samples ofhundreds of events a dependable value for the mean energy losscannot be obtained. Far better and more easily measured is the mostprobable energy loss, discussed in Sec. 33.2.9. The most probableenergy loss in a detector is considerably below the mean given by theBethe equation.

In a TPC (Sec. 34.6.5), the mean of 50%–70% of the samples withthe smallest signals is often used as an estimator.

Although it must be used with cautions and caveats, 〈dE/dx〉


1

2

3

4

5

6

8

10

1.0 10 100 1000 10 0000.1

Pion momentum (GeV/c)

Proton momentum (GeV/c)

1.0 10 100 10000.1

1.0 10 100 10000.1

βγ = p/Mc

Muon momentum (GeV/c)

H2 liquid

He gas

CAl

FeSn

Pb⟨–dE

/dx⟩

(M

eV g

—1 c

m2 )

1.0 10 100 1000 10 0000.1

Figure 33.2: Mean energy loss rate in liquid (bubble chamber)hydrogen, gaseous helium, carbon, aluminum, iron, tin, and lead.Radiative effects, relevant for muons and pions, are not included.These become significant for muons in iron for βγ >∼ 1000, and atlower momenta for muons in higher-Z absorbers. See Fig. 33.23.

as described in Eq. (33.5) still forms the basis of much of ourunderstanding of energy loss by charged particles. Extensive tablesare available[4,5, pdg.lbl.gov/AtomicNuclearProperties/].

For heavy projectiles, like ions, additional terms are required toaccount for higher-order photon coupling to the target, and to accountfor the finite size of the target radius. These can change dE/dx bya factor of two or more for the heaviest nuclei in certain kinematicregimes [7].

0.5

1.0

1.5

2.0

2.5

1 2 5 10 20 50 100Z

H He Li Be B C NO Ne SnFe

SolidsGases

H2 gas: 4.10H2 liquid: 3.97

2.35 — 0.28 ln(Z)

⟨–dE

/dx⟩

(M

eV g

—1 c

m2 )

Figure 33.3: Mass stopping power at minimum ionization forthe chemical elements. The straight line is fitted for Z > 6. Asimple functional dependence on Z is not to be expected, since〈−dE/dx〉 also depends on other variables.

The function as computed for muons on copper is shown as the“Bethe” region of Fig. 33.1. Mean energy loss behavior below thisregion is discussed in Sec. 33.2.6, and the radiative effects at highenergy are discussed in Sec. 33.6. Only in the Bethe region is ita function of β alone; the mass dependence is more complicatedelsewhere. The stopping power in several other materials is shown inFig. 33.2. Except in hydrogen, particles with the same velocity havesimilar rates of energy loss in different materials, although there isa slow decrease in the rate of energy loss with increasing Z. Thequalitative behavior difference at high energies between a gas (He inthe figure) and the other materials shown in the figure is due to thedensity-effect correction, δ(βγ), discussed in Sec. 33.2.5. The stoppingpower functions are characterized by broad minima whose position

drops from βγ = 3.5 to 3.0 as Z goes from 7 to 100. The values ofminimum ionization as a function of atomic number are shown inFig. 33.3.

In practical cases, most relativistic particles (e.g., cosmic-raymuons) have mean energy loss rates close to the minimum; they are“minimum-ionizing particles,” or mip’s.

0.05 0.10.02 0.50.2 1.0 5.02.0 10.0

Pion momentum (GeV/c)

0.1 0.50.2 1.0 5.02.0 10.0 50.020.0

Proton momentum (GeV/c)

0.050.02 0.1 0.50.2 1.0 5.02.0 10.0

Muon momentum (GeV/c)

βγ = p/Mc

1

2

5

10

20

50

100

200

500

1000

2000

5000

10000

20000

50000

R/M

(g c

m−2

G

eV

−1)

0.1 2 5 1.0 2 5 10.0 2 5 100.0

H2 liquid

He gas

Pb

FeC

Figure 33.4: Range of heavy charged particles in liquid (bubblechamber) hydrogen, helium gas, carbon, iron, and lead. Forexample: For a K+ whose momentum is 700 MeV/c, βγ = 1.42.For lead we read R/M ≈ 396, and so the range is 195 g cm−2

(17 cm).

Eq. (33.5) may be integrated to find the total (or partial)“continuous slowing-down approximation” (CSDA) range R for aparticle which loses energy only through ionization and atomicexcitation. Since dE/dx depends only on β, R/M is a functionof E/M or pc/M . In practice, range is a useful concept only forlow-energy hadrons (R <∼ λI , where λI is the nuclear interactionlength), and for muons below a few hundred GeV (above whichradiative effects dominate). R/M as a function of βγ = p/Mc isshown for a variety of materials in Fig. 33.4.

The mass scaling of dE/dx and range is valid for the electroniclosses described by the Bethe equation, but not for radiative losses,relevant only for muons and pions.

33.2.4. Mean excitation energy :

“The determination of the mean excitation energy is the principalnon-trivial task in the evaluation of the Bethe stopping-powerformula” [10]. Recommended values have varied substantially withtime. Estimates based on experimental stopping-power measurementsfor protons, deuterons, and alpha particles and on oscillator-strength distributions and dielectric-response functions were givenin ICRU 49 [4]. See also ICRU 37 [11]. These values, shown inFig. 33.5, have since been widely used. Machine-readable versions canalso be found [12].

33.2.5. Density effect :

As the particle energy increases, its electric field flattens andextends, so that the distant-collision contribution to Eq. (33.5)increases as ln βγ. However, real media become polarized, limiting thefield extension and effectively truncating this part of the logarithmicrise [2–8,15–16]. At very high energies,

δ/2 → ln(~ωp/I) + lnβγ − 1/2 , (33.6)


0 10 20 30 40 50 60 70 80 90 100 8

10

12

14

16

18

20

22I a

dj/

Z (

eV

)

Z

Barkas & Berger 1964

Bichsel 1992

ICRU 37 (1984) (interpolated values are not marked with points)

Figure 33.5: Mean excitation energies (divided by Z) asadopted by the ICRU [11]. Those based on experimentalmeasurements are shown by symbols with error flags; theinterpolated values are simply joined. The grey point is forliquid H2; the black point at 19.2 eV is for H2 gas. The opencircles show more recent determinations by Bichsel [13]. Thedash-dotted curve is from the approximate formula of Barkas [14]used in early editions of this Review.

where δ(βγ)/2 is the density effect correction introduced in Eq. (33.5)and ~ωp is the plasma energy defined in Table 33.1. A comparisonwith Eq. (33.5) shows that |dE/dx| then grows as ln βγ rather thanlnβ2γ2, and that the mean excitation energy I is replaced by theplasma energy ~ωp. The ionization stopping power as calculated withand without the density effect correction is shown in Fig. 33.1. Sincethe plasma frequency scales as the square root of the electron density,the correction is much larger for a liquid or solid than for a gas, as isillustrated by the examples in Fig. 33.2.

The density effect correction is usually computed using Stern-heimer’s parameterization [15]:

δ(βγ) =

2(ln 10)x − C if x ≥ x1;2(ln 10)x − C + a(x1 − x)k if x0 ≤ x < x1;0 if x < x0 (nonconductors);

δ0102(x−x0) if x < x0 (conductors)(33.7)

Here x = log10 η = log10(p/Mc). C (the negative of the C used inRef. 15) is obtained by equating the high-energy case of Eq. (33.7) withthe limit given in Eq. (33.6). The other parameters are adjusted togive a best fit to the results of detailed calculations for momenta belowMc exp(x1). Parameters for elements and nearly 200 compounds andmixtures of interest are published in a variety of places, notably inRef. 16. A recipe for finding the coefficients for nontabulated materialsis given by Sternheimer and Peierls [17], and is summarized in Ref. 5.

The remaining relativistic rise comes from the β2γ growth of Wmax,which in turn is due to (rare) large energy transfers to a few electrons.When these events are excluded, the energy deposit in an absorbinglayer approaches a constant value, the Fermi plateau (see Sec. 33.2.8below). At even higher energies (e.g., > 332 GeV for muons in iron,and at a considerably higher energy for protons in iron), radiativeeffects are more important than ionization losses. These are especiallyrelevant for high-energy muons, as discussed in Sec. 33.6.

33.2.6. Energy loss at low energies :

Shell corrections C/Z must be included in the square brackets ofof Eq. (33.5) [4,11,13,14] to correct for atomic binding having beenneglected in calculating some of the contributions to Eq. (33.5). TheBarkas form [14] was used in generating Fig. 33.1. For copper itcontributes about 1% at βγ = 0.3 (kinetic energy 6 MeV for a pion),and the correction decreases very rapidly with increasing energy.

Equation 33.2, and therefore Eq. (33.5), are based on a first-orderBorn approximation. Higher-order corrections, again important onlyat lower energies, are normally included by adding the “Blochcorrection” z2L2(β) inside the square brackets (Eq.(2.5) in [4]) .

An additional “Barkas correction” zL1(β) reduces the stoppingpower for a negative particle below that for a positive particle withthe same mass and velocity. In a 1956 paper, Barkas et al. noted that

negative pions had a longer range than positive pions [6]. The effecthas been measured for a number of negative/positive particle pairs,including a detailed study with antiprotons [18].

A detailed discussion of low-energy corrections to the Bethe formulais given in ICRU 49 [4]. When the corrections are properly included,the Bethe treatment is accurate to about 1% down to β ≈ 0.05, orabout 1 MeV for protons.

For 0.01 < β < 0.05, there is no satisfactory theory. For protons,one usually relies on the phenomenological fitting formulae developedby Andersen and Ziegler [4,19]. As tabulated in ICRU 49 [4],the nuclear plus electronic proton stopping power in copper is113 MeV cm2 g−1 at T = 10 keV (βγ = 0.005), rises to a maximumof 210 MeV cm2 g−1 at T ≈ 120 keV (βγ = 0.016), then falls to118 MeV cm2 g−1 at T = 1 MeV (βγ = 0.046). Above 0.5–1.0 MeVthe corrected Bethe theory is adequate.

For particles moving more slowly than ≈ 0.01c (more or lessthe velocity of the outer atomic electrons), Lindhard has beenquite successful in describing electronic stopping power, which isproportional to β [20]. Finally, we note that at even lower energies,e.g., for protons of less than several hundred eV, non-ionizing nuclearrecoil energy loss dominates the total energy loss [4,20,21].

33.2.7. Energetic knock-on electrons (δ rays) :

The distribution of secondary electrons with kinetic energies T ≫ Iis [2]

d2N

dTdx=

1

2Kz2Z

A

1

β2

F (T )

T 2 (33.8)

for I ≪ T ≤ Wmax, where Wmax is given by Eq. (33.4). Hereβ is the velocity of the primary particle. The factor F is spin-dependent, but is about unity for T ≪ Wmax. For spin-0 particlesF (T ) = (1 − β2T/Wmax); forms for spins 1/2 and 1 are also given byRossi [2]( Sec. 2.3, Eqns. 7 and 8). Additional formulae are given inRef. 22. Equation (33.8) is inaccurate for T close to I [23].

δ rays of even modest energy are rare. For a β ≈ 1 particle, forexample, on average only one collision with Te > 10 keV will occuralong a path length of 90 cm of Ar gas [1].

A δ ray with kinetic energy Te and corresponding momentum pe isproduced at an angle θ given by

cos θ = (Te/pe)(pmax/Wmax) , (33.9)

where pmax is the momentum of an electron with the maximumpossible energy transfer Wmax.

33.2.8. Restricted energy loss rates for relativistic ionizing

particles :Further insight can be obtained by examining the mean energy

deposit by an ionizing particle when energy transfers are restricted toT ≤ Wcut ≤ Wmax. The restricted energy loss rate is

−dE

dx

∣

∣

∣

∣

T<Wcut

= Kz2Z

A

1

β2

[

1

2ln

2mec2β2γ2Wcut

I2

−β2

2

(

1 +Wcut

Wmax

)

− δ

2

]

. (33.10)

This form approaches the normal Bethe function (Eq. (33.5)) asWcut → Wmax. It can be verified that the difference betweenEq. (33.5) and Eq. (33.10) is equal to

∫ Wmax

WcutT (d2N/dTdx)dT , where

d2N/dTdx is given by Eq. (33.8).Since Wcut replaces Wmax in the argument of the logarithmic

term of Eq. (33.5), the βγ term producing the relativistic rise inthe close-collision part of dE/dx is replaced by a constant, and|dE/dx|T<Wcut

approaches the constant “Fermi plateau.” (Thedensity effect correction δ eliminates the explicit βγ dependenceproduced by the distant-collision contribution.) This behavior isillustrated in Fig. 33.6, where restricted loss rates for two examplesof Wcut are shown in comparison with the full Bethe dE/dx andthe Landau-Vavilov most probable energy loss (to be discussed inSec. 33.2.9 below).

“Restricted energy loss” is cut at the total mean energy, not thesingle-collision energy above Wcut It is of limited use. The mostprobable energy loss, discussed in the next Section, is far more usefulin situations where single-particle energy loss is observed.


Landau/Vavilov/Bichsel ∆p/x for :

Bethe

Tcut = 10 dE/dx|minTcut = 2 dE/dx|min

Restricted energy loss for :

0.1 1.0 10.0 100.0 1000.0

1.0

1.5

0.5

2.0

2.5

3.0

MeV

g−1

cm

2 (E

lect

roni

c lo

sses

onl

y)

Muon kinetic energy (GeV)

Silicon

x/ρ = 1600 µm320 µm

80 µm

Figure 33.6: Bethe dE/dx, two examples of restricted energyloss, and the Landau most probable energy per unit thicknessin silicon. The change of ∆p/x with thickness x illustratesits a lnx + b dependence. Minimum ionization (dE/dx|min) is1.664 MeV g−1 cm2. Radiative losses are excluded. The incidentparticles are muons.

33.2.9. Fluctuations in energy loss :

For detectors of moderate thickness x (e.g. scintillators orLAr cells),* the energy loss probability distribution f(∆; βγ, x) isadequately described by the highly-skewed Landau (or Landau-Vavilov) distribution [24,25]. The most probable energy loss is [26]†

∆p = ξ

[

ln2mc2β2γ2

I+ ln

ξ

I+ j − β2 − δ(βγ)

]

, (33.11)

where ξ = (K/2) 〈Z/A〉 z2(x/β2) MeV for a detector with a thicknessx in g cm−2, and j = 0.200 [26]. ‡ While dE/dx is independent ofthickness, ∆p/x scales as a lnx + b. The density correction δ(βγ) wasnot included in Landau’s or Vavilov’s work, but it was later includedby Bichsel [26]. The high-energy behavior of δ(βγ) (Eq. (33.6)) issuch that

∆p −→βγ>∼100

ξ

[

ln2mc2ξ

(~ωp)2+ j

]

. (33.12)

Thus the Landau-Vavilov most probable energy loss, like the restrictedenergy loss, reaches a Fermi plateau. The Bethe dE/dx and Landau-Vavilov-Bichsel ∆p/x in silicon are shown as a function of muonenergy in Fig. 33.6. The energy deposit in the 1600 µm case is roughlythe same as in a 3 mm thick plastic scintillator.

The distribution function for the energy deposit by a 10 GeVmuon going through a detector of about this thickness is shown inFig. 33.7. In this case the most probable energy loss is 62% of themean (M1(〈∆〉)/M1(∞)). Folding in experimental resolution displacesthe peak of the distribution, usually toward a higher value. 90% ofthe collisions (M1(〈∆〉)/M1(∞)) contribute to energy deposits belowthe mean. It is the very rare high-energy-transfer collisions, extendingto Wmax at several GeV, that drives the mean into the tail of thedistribution. The large weight of these rare events makes the meanof an experimental distribution consisting of a few hundred eventssubject to large fluctuations and sensitive to cuts. The mean of theenergy loss given by the Bethe equation, Eq. (33.5), is thus ill-definedexperimentally and is not useful for describing energy loss by singleparticles. It rises as ln γ because Wmax increases as γ at high energies.

* G <∼ 0.05–0.1, where G is given by Rossi [Ref. 2, Eq. 2.7(10)]. It isVavilov’s κ [25]. It is proportional to the absorber’s thickness, and assuch parameterizes the constants describing the Landau distribution.These are fairly insensitive to thickness for G <∼ 0.1, the case for mostdetectors.

† Practical calculations can be expedited by using the tables of δ andβ from the text versions of the muon energy loss tables to be found atpdg.lbl.gov/AtomicNuclearProperties.

‡ Rossi [2], Talman [27], and others give somewhat different valuesfor j. The most probable loss is not sensitive to its value.

It does find application in dosimetry, where only bulk deposit isrelevant.

f(Δ

) [

MeV

−1]

Electronic energy loss Δ [MeV]

Energy loss [MeV cm2/g]

150

100

50

00.4 0.5 0.6 0.7 0.8 1.00.9

0.8

1.0

0.6

0.4

0.2

0.0

Mj(Δ

) /Mj(∞

)

Landau-Vavilov

Bichsel (Bethe-Fano theory)

Δp Δ

fwhm

M0(Δ)/M0(∞)

Μ1(Δ)/Μ1(∞)

10 GeV muon1.7 mm Si

1.2 1.4 1.6 1.8 2.0 2.2 2.4

< >

Figure 33.7: Electronic energy deposit distribution for a10 GeV muon traversing 1.7 mm of silicon, the stopping powerequivalent of about 0.3 cm of PVC scintillator [1,13,28]. TheLandau-Vavilov function (dot-dashed) uses a Rutherford crosssection without atomic binding corrections but with a kineticenergy transfer limit of Wmax. The solid curve was calculatedusing Bethe-Fano theory. M0(∆) and M1(∆) are the cumulative0th moment (mean number of collisions) and 1st moment (meanenergy loss) in crossing the silicon. (See Sec. 33.2.1. The fwhmof the Landau-Vavilov function is about 4ξ for detectors ofmoderate thickness. ∆p is the most probable energy loss, and〈∆〉 divided by the thickness is the Bethe 〈dE/dx〉.

100 200 300 400 500 6000.0

0.2

0.4

0.6

0.8

1.0

0.50 1.00 1.50 2.00 2.50

640 µm (149 mg/cm2)

320 µm (74.7 mg/cm2)

160 µm (37.4 mg/cm2)

80 µm (18.7 mg/cm2)

500 MeV pion in silicon

Mean energyloss rate

wf(∆

/x)

∆/x (eV/µm)

∆p/x

∆/x (MeV g−1 cm2)

Figure 33.8: Straggling functions in silicon for 500 MeV pions,normalized to unity at the most probable value δp/x. The widthw is the full width at half maximum.

The most probable energy loss should be used.A practical example: For muons traversing 0.25 inches of PVT

plastic scintillator, the ratio of the most probable E loss rate to themean loss rate via the Bethe equation is [0.69, 0.57, 0.49, 0.42, 0.38] forTµ = [0.01, 0.1, 1, 10, 100] GeV. Radiative losses add less than 0.5% tothe total mean energy deposit at 10 GeV, but add 7% at 100 GeV.The most probable E loss rate rises slightly beyond the minimumionization energy, then is essentially constant.

The Landau distribution fails to describe energy loss in thinabsorbers such as gas TPC cells [1] and Si detectors [26], asshown clearly in Fig. 1 of Ref. 1 for an argon-filled TPC cell. Alsosee Talman [27]. While ∆p/x may be calculated adequately withEq. (33.11), the distributions are significantly wider than the Landauwidth w = 4ξ [Ref. 26, Fig. 15]. Examples for 500 MeV pions incidenton thin silicon detectors are shown in Fig. 33.8. For very thickabsorbers the distribution is less skewed but never approaches aGaussian.

The most probable energy loss, scaled to the mean loss at minimumionization, is shown in Fig. 33.9 for several silicon detector thicknesses.


1 30.3 30 30010 100 1000

βγ (= p/m)

0.50

0.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90

0.95

1.00

(∆p/

x) /

dE

/dx

min

80 µm (18.7 mg/cm2)

160 µm (37.4 mg/cm2)

x = 640 µm (149 mg/cm2)

320 µm (74.7 mg/cm2)

Figure 33.9: Most probable energy loss in silicon, scaled to themean loss of a minimum ionizing particle, 388 eV/µm (1.66 MeVg−1cm2).

33.2.10. Energy loss in mixtures and compounds :

A mixture or compound can be thought of as made up of thinlayers of pure elements in the right proportion (Bragg additivity). Inthis case,

⟨

dE

dx

⟩

=∑

wj

⟨

dE

dx

⟩

j

, (33.13)

where dE/dx|j is the mean rate of energy loss (in MeV g cm−2)in the jth element. Eq. (33.5) can be inserted into Eq. (33.13) tofind expressions for 〈Z/A〉, 〈I 〉, and 〈δ〉; for example, 〈Z/A〉 =∑

wjZj/Aj =∑

njZj/∑

njAj . However, 〈I 〉 as defined this way isan underestimate, because in a compound electrons are more tightlybound than in the free elements, and 〈δ〉 as calculated this way has littlerelevance, because it is the electron density that matters. If possible,one uses the tables given in Refs. 16 and 29, that include effective exci-tation energies and interpolation coefficients for calculating the densityeffect correction for the chemical elements and nearly 200 mixtures andcompounds. Otherwise, use the recipe for δ given in Ref. 5 and 17, andcalculate 〈I〉 following the discussion in Ref. 10. (Note the “13%” rule!)

33.2.11. Ionization yields : Physicists frequently

relate total energy loss to the number of ion pairs produced nearthe particle’s track. This relation becomes complicated for relativisticparticles due to the wandering of energetic knock-on electrons whoseranges exceed the dimensions of the fiducial volume. For a qualitativeappraisal of the nonlocality of energy deposition in various mediaby such modestly energetic knock-on electrons, see Ref. 30. Themean local energy dissipation per local ion pair produced, W , whileessentially constant for relativistic particles, increases at slow particlespeeds [31]. For gases, W can be surprisingly sensitive to traceamounts of various contaminants [31]. Furthermore, ionization yieldsin practical cases may be greatly influenced by such factors assubsequent recombination [32].

33.3. Multiple scattering through small angles

A charged particle traversing a medium is deflected by many small-angle scatters. Most of this deflection is due to Coulomb scatteringfrom nuclei as described by the Rutherford cross section. (However,for hadronic projectiles, the strong interactions also contribute tomultiple scattering.) For many small-angle scatters the net scatteringand displacement distributions are Gaussian via the central limittheorem. Less frequent “hard” scatters produce non-Gaussian tails.These Coulomb scattering distributions are well-represented by thetheory of Moliere [34]. Accessible discussions are given by Rossi [2]and Jackson [33], and exhaustive reviews have been publishedby Scott [35] and Motz et al. [36]. Experimental measurementshave been published by Bichsel [37]( low energy protons) and byShen et al. [38]( relativistic pions, kaons, and protons).*

* Shen et al.’s measurements show that Bethe’s simpler methods ofincluding atomic electron effects agrees better with experiment thandoes Scott’s treatment.

If we define

θ0 = θ rmsplane =

1√2

θrmsspace , (33.14)

then it is sufficient for many applications to use a Gaussian approxi-mation for the central 98% of the projected angular distribution, withan rms width given by [39,40]

θ0 =13.6 MeV

βcpz

√

x/X0

[

1 + 0.038 ln(x/X0)]

. (33.15)

Here p, βc, and z are the momentum, velocity, and charge numberof the incident particle, and x/X0 is the thickness of the scatteringmedium in radiation lengths (defined below). This value of θ0 is froma fit to Moliere distribution for singly charged particles with β = 1 forall Z, and is accurate to 11% or better for 10−3 < x/X0 < 100.

Eq. (33.15) describes scattering from a single material, while theusual problem involves the multiple scattering of a particle traversingmany different layers and mixtures. Since it is from a fit to a Molieredistribution, it is incorrect to add the individual θ0 contributions inquadrature; the result is systematically too small. It is much moreaccurate to apply Eq. (33.15) once, after finding x and X0 for thecombined scatterer.

x

splaneyplane

Ψplane

θplane

x /2

Figure 33.10: Quantities used to describe multiple Coulombscattering. The particle is incident in the plane of the figure.

The nonprojected (space) and projected (plane) angular distribu-tions are given approximately by [34]

1

2π θ20

exp

−θ2space

2θ20

dΩ , (33.16)

1√2π θ0

exp

−θ2plane

2θ20

dθplane , (33.17)

where θ is the deflection angle. In this approximation, θ2space ≈

(θ2plane,x + θ2

plane,y), where the x and y axes are orthogonal to the

direction of motion, and dΩ ≈ dθplane,x dθplane,y. Deflections intoθplane,x and θplane,y are independent and identically distributed.

Fig. 33.10 shows these and other quantities sometimes used todescribe multiple Coulomb scattering. They are

ψ rmsplane =

1√3

θ rmsplane =

1√3

θ0 , (33.18)

y rmsplane =

1√3

x θ rmsplane =

1√3

x θ0 , (33.19)

s rmsplane =

1

4√

3x θ rms

plane =1

4√

3x θ0 . (33.20)

All the quantitative estimates in this section apply only in the limitof small θ rms

plane and in the absence of large-angle scatters. The random

variables s, ψ, y, and θ in a given plane are correlated. Obviously,y ≈ xψ. In addition, y and θ have the correlation coefficient ρyθ =√

3/2 ≈ 0.87. For Monte Carlo generation of a joint (y plane, θplane)distribution, or for other calculations, it may be most convenient towork with independent Gaussian random variables (z1, z2) with meanzero and variance one, and then set

yplane =z1 x θ0(1 − ρ2yθ)

1/2/√

3 + z2 ρyθx θ0/√

3 (33.21)

=z1 x θ0/√

12 + z2 x θ0/2 ; (33.22)

θplane =z2 θ0 . (33.23)

Note that the second term for y plane equals x θplane/2 and representsthe displacement that would have occurred had the deflection θplaneall occurred at the single point x/2.


For heavy ions the multiple Coulomb scattering has been measuredand compared with various theoretical distributions [41].

33.4. Photon and electron interactions in matter

At low energies electrons and positrons primarily lose energyby ionization, although other processes (Møller scattering, Bhabhascattering, e+ annihilation) contribute, as shown in Fig. 33.11. Whileionization loss rates rise logarithmically with energy, bremsstrahlunglosses rise nearly linearly (fractional loss is nearly independent ofenergy), and dominates above the critical energy (Sec. 33.4.4 below),a few tens of MeV in most materials

33.4.1. Collision energy losses by e± :

Stopping power differs somewhat for electrons and positrons, andboth differ from stopping power for heavy particles because of thekinematics, spin, charge, and the identity of the incident electron withthe electrons that it ionizes. Complete discussions and tables can befound in Refs. 10, 11, and 29.

For electrons, large energy transfers to atomic electrons (taken asfree) are described by the Møller cross section. From Eq. (33.4), themaximum energy transfer in a single collision should be the entirekinetic energy, Wmax = mec

2(γ − 1), but because the particles areidentical, the maximum is half this, Wmax/2. (The results are thesame if the transferred energy is ǫ or if the transferred energy isWmax − ǫ. The stopping power is by convention calculated for thefaster of the two emerging electrons.) The first moment of the Møllercross section [22]( divided by dx) is the stopping power:

⟨

−dE

dx

⟩

=1

2K

Z

A

1

β2

[

lnmec

2β2γ2mec2(γ − 1)/2

I2

+(1 − β2) − 2γ − 1

γ2ln 2 +

1

8

(

γ − 1

γ

)2

− δ

]

(33.24)

The logarithmic term can be compared with the logarithmic term inthe Bethe equation (Eq. (33.2)) by substituting Wmax = mec

2(γ−1)/2.The two forms differ by ln 2.

Electron-positron scattering is described by the fairly complicatedBhabha cross section [22]. There is no identical particle problem, soWmax = mec

2(γ−1). The first moment of the Bhabha equation yields⟨

−dE

dx

⟩

=1

2K

Z

A

1

β2

[

lnmec

2β2γ2mec2(γ − 1)

2I2 (33.25)

+2 ln 2 − β2

12

(

23 +14

γ + 1+

10

(γ + 1)2+

4

(γ + 1)3

)

− δ

]

.

Following ICRU 37 [11], the density effect correction δ has beenadded to Uehling’s equations [22] in both cases.

For heavy particles, shell corrections were developed assumingthat the projectile is equivalent to a perturbing potential whosecenter moves with constant velocity. This assumption has no soundtheoretical basis for electrons. The authors of ICRU 37 [11] estimatedthe possible error in omitting it by assuming the correction was twiceas great as for a proton of the same velocity. At T = 10 keV, the errorwas estimated to be ≈2% for water, ≈9% for Cu, and ≈21% for Au.

As shown in Fig. 33.11, stopping powers for e−, e+, and heavyparticles are not dramatically different. In silicon, the minimumvalue for electrons is 1.50 MeVcm2/g (at γ = 3.3); for positrons,1.46 MeV cm2/g (at γ = 3.7), and for muons, 1.66 MeVcm2/g (atγ = 3.58).

33.4.2. Radiation length :

High-energy electrons predominantly lose energy in matter bybremsstrahlung, and high-energy photons by e+e− pair production.The characteristic amount of matter traversed for these relatedinteractions is called the radiation length X0, usually measured ing cm−2. It is both (a) the mean distance over which a high-energyelectron loses all but 1/e of its energy by bremsstrahlung, and (b) 7

9 ofthe mean free path for pair production by a high-energy photon [42].It is also the appropriate scale length for describing high-energyelectromagnetic cascades. X0 has been calculated and tabulated byY.S. Tsai [43]:

1

X0= 4αr2

eNA

A

Z2[Lrad − f(Z)]

+ Z L′

rad

. (33.26)

For A = 1 g mol−1, 4αr2eNA/A = (716.408 g cm−2)−1. Lrad and

L′

rad are given in Table 33.2. The function f(Z) is an infinite sum, butfor elements up to uranium can be represented to 4-place accuracy by

f(Z) =a2[

(1 + a2)−1 + 0.20206

− 0.0369 a2 + 0.0083 a4 − 0.002 a6]

,

(33.27)

where a = αZ [44].

Table 33.2: Tsai’s Lrad and L′

rad, for use in calculating theradiation length in an element using Eq. (33.26).

Element Z Lrad L′

rad

H 1 5.31 6.144He 2 4.79 5.621Li 3 4.74 5.805Be 4 4.71 5.924

Others > 4 ln(184.15 Z−1/3) ln(1194 Z−2/3)

The radiation length in a mixture or compound may be approxi-mated by

1/X0 =∑

wj/Xj , (33.28)

where wj and Xj are the fraction by weight and the radiation lengthfor the jth element.

Figure 33.11: Fractional energy loss per radiation length inlead as a function of electron or positron energy. Electron(positron) scattering is considered as ionization when the energyloss per collision is below 0.255 MeV, and as Møller (Bhabha)scattering when it is above. Adapted from Fig. 3.2 from Messeland Crawford, Electron-Photon Shower Distribution FunctionTables for Lead, Copper, and Air Absorbers, Pergamon Press,1970. Messel and Crawford use X0(Pb) = 5.82 g/cm2, butwe have modified the figures to reflect the value given in theTable of Atomic and Nuclear Properties of Materials (X0(Pb) =6.37 g/cm2).

33.4.3. Bremsstrahlung energy loss by e± :

At very high energies and except at the high-energy tip of thebremsstrahlung spectrum, the cross section can be approximated inthe “complete screening case” as [43]

dσ/dk = (1/k)4αr2e

(43 − 4

3y + y2)[Z2(Lrad − f(Z)) + Z L′

rad]

+ 19 (1 − y)(Z2 + Z)

,(33.29)

where y = k/E is the fraction of the electron’s energy transferred tothe radiated photon. At small y (the “infrared limit”) the term on thesecond line ranges from 1.7% (low Z) to 2.5% (high Z) of the total.If it is ignored and the first line simplified with the definition of X0

given in Eq. (33.26), we have

dσ

dk=

A

X0NAk

(

43 − 4

3y + y2)

. (33.30)


This cross section (times k) is shown by the top curve in Fig. 33.12.

0

0.4

0.8

1.2

0 0.25 0.5 0.75 1

y = k/E

Bremsstrahlung

(X0

NA

/A

) y

dσ L

PM

/d

y

10 GeV

1 TeV

10 TeV

100 TeV

1 PeV

10 PeV

100 GeV

Figure 33.12: The normalized bremsstrahlung cross sectionk dσLPM/dk in lead versus the fractional photon energy y = k/E.The vertical axis has units of photons per radiation length.

This formula is accurate except in near y = 1, where screening maybecome incomplete, and near y = 0, where the infrared divergenceis removed by the interference of bremsstrahlung amplitudes fromnearby scattering centers (the LPM effect) [45,46] and dielectricsuppression [47,48]. These and other suppression effects in bulkmedia are discussed in Sec. 33.4.6.

With decreasing energy (E <∼ 10 GeV) the high-y cross sectiondrops and the curves become rounded as y → 1. Curves of this familarshape can be seen in Rossi [2] (Figs. 2.11.2,3); see also the review byKoch & Motz [49].

2 5 10 20 50 100 200

Copper X0 = 12.86 g cm−2

Ec = 19.63 MeV

dE

/dx ×

X0 (

MeV

)

Electron energy (MeV)

10

20

30

50

70

100

200

40

Brems = ionization

Ionization

Rossi: Ionization per X0 = electron energy

Total

Bre

ms

≈ EE

xact

brem

sstr

ahlu

ng

Figure 33.13: Two definitions of the critical energy Ec.

Except at these extremes, and still in the complete-screeningapproximation, the number of photons with energies between kminand kmax emitted by an electron travelling a distance d ≪ X0 is

Nγ =d

X0

[

4

3ln

(

kmax

kmin

)

− 4(kmax − kmin)

3E+

k2max − k2

min

2E2

]

.

(33.31)

33.4.4. Critical energy :

An electron loses energy by bremsstrahlung at a rate nearlyproportional to its energy, while the ionization loss rate varies onlylogarithmically with the electron energy. The critical energy Ec issometimes defined as the energy at which the two loss rates areequal [50]. Among alternate definitions is that of Rossi [2], whodefines the critical energy as the energy at which the ionization lossper radiation length is equal to the electron energy. Equivalently,it is the same as the first definition with the approximation|dE/dx|brems ≈ E/X0. This form has been found to describetransverse electromagnetic shower development more accurately (seebelow). These definitions are illustrated in the case of copper inFig. 33.13.

The accuracy of approximate forms for Ec has been limited by thefailure to distinguish between gases and solid or liquids, where thereis a substantial difference in ionization at the relevant energy becauseof the density effect. We distinguish these two cases in Fig. 33.14.

Ec

(MeV

)

Z1 2 5 10 20 50 100

5

10

20

50

100

200

400

610 MeV________ Z + 1.24

710 MeV________Z + 0.92

SolidsGases

H He Li Be B C NO Ne SnFe

Figure 33.14: Electron critical energy for the chemical elements,using Rossi’s definition [2]. The fits shown are for solids andliquids (solid line) and gases (dashed line). The rms deviationis 2.2% for the solids and 4.0% for the gases. (Computed withcode supplied by A. Fasso.)

Fits were also made with functions of the form a/(Z + b)α, but αwas found to be essentially unity. Since Ec also depends on A, I, andother factors, such forms are at best approximate.

Values of Ec for both electrons and positrons in more than 300materials can be found at pdg.lbl.gov/AtomicNuclearProperties.

33.4.5. Energy loss by photons :

Contributions to the photon cross section in a light element(carbon) and a heavy element (lead) are shown in Fig. 33.15. At lowenergies it is seen that the photoelectric effect dominates, althoughCompton scattering, Rayleigh scattering, and photonuclear absorptionalso contribute. The photoelectric cross section is characterized bydiscontinuities (absorption edges) as thresholds for photoionizationof various atomic levels are reached. Photon attenuation lengthsfor a variety of elements are shown in Fig. 33.18, and data for30 eV< k <100 GeV for all elements are available from the web pagesgiven in the caption. Here k is the photon energy.

The increasing domination of pair production as the energyincreases is shown in Fig. 33.16. Using approximations similar tothose used to obtain Eq. (33.30), Tsai’s formula for the differentialcross section [43] reduces to

dσ

dx=

A

X0NA

[

1 − 43x(1 − x)

]

(33.32)

in the complete-screening limit valid at high energies. Here x = E/kis the fractional energy transfer to the pair-produced electron (orpositron), and k is the incident photon energy. The cross section isvery closely related to that for bremsstrahlung, since the Feynmandiagrams are variants of one another. The cross section is of necessitysymmetric between x and 1 − x, as can be seen by the solid curve inFig. 33.17. See the review by Motz, Olsen, & Koch for a more detailedtreatment [53].

Eq. (33.32) may be integrated to find the high-energy limit for thetotal e+e− pair-production cross section:

σ = 79 (A/X0NA) . (33.33)

Equation (33.33) is accurate to within a few percent down to energiesas low as 1 GeV, particularly for high-Z materials.

33.4.6. Bremsstrahlung and pair production at very high en-ergies :

At ultrahigh energies, Eqns. 33.29–33.33 will fail because ofquantum mechanical interference between amplitudes from differentscattering centers. Since the longitudinal momentum transfer to agiven center is small (∝ k/E(E − k), in the case of bremsstrahlung),the interaction is spread over a comparatively long distance calledthe formation length (∝ E(E − k)/k) via the uncertainty principle.In alternate language, the formation length is the distance overwhich the highly relativistic electron and the photon “split apart.”The interference is usually destructive. Calculations of the “Landau-Pomeranchuk-Migdal” (LPM) effect may be made semi-classicallybased on the average multiple scattering, or more rigorously using aquantum transport approach [45,46].


Photon Energy

1 Mb

1 kb

1 b

10 mb10 eV 1 keV 1 MeV 1 GeV 100 GeV

(b) Lead (Z = 82)- experimental σtot

σp.e.

κe

Cro

ss s

ectio

n (

barn

s/at

om)

Cro

ss s

ectio

n (

barn

s/at

om)

10 mb

1 b

1 kb

1 Mb

(a) Carbon (Z = 6)

σRayleigh

σg.d.r.

σCompton

σCompton

σRayleigh

κnuc

κnuc

κe

σp.e.

- experimental σtot

Figure 33.15: Photon total cross sections as a function ofenergy in carbon and lead, showing the contributions of differentprocesses [51]:

σp.e. = Atomic photoelectric effect (electron ejection,photon absorption)

σRayleigh = Rayleigh (coherent) scattering–atom neitherionized nor excited

σCompton = Incoherent scattering (Compton scattering off anelectron)

κnuc = Pair production, nuclear fieldκe = Pair production, electron field

σg.d.r. = Photonuclear interactions, most notably the GiantDipole Resonance [52]. In these interactions, thetarget nucleus is broken up.

Original figures through the courtesy of John H. Hubbell(NIST).

In amorphous media, bremsstrahlung is suppressed if the photonenergy k is less than E2/(E + ELPM ) [46], where*

ELPM =(mec

2)2αX0

4π~cρ= (7.7 TeV/cm) × X0

ρ. (33.34)

Since physical distances are involved, X0/ρ, in cm, appears. Theenergy-weighted bremsstrahlung spectrum for lead, k dσLPM/dk,

* This definition differs from that of Ref. 54 by a factor of two.ELPM scales as the 4th power of the mass of the incident particle, sothat ELPM = (1.4 × 1010 TeV/cm) × X0/ρ for a muon.

is shown in Fig. 33.12. With appropriate scaling by X0/ρ, othermaterials behave similarly.

Figure 33.16: Probability P that a photon interaction willresult in conversion to an e+e− pair. Except for a few-percentcontribution from photonuclear absorption around 10 or 20MeV, essentially all other interactions in this energy range resultin Compton scattering off an atomic electron. For a photonattenuation length λ (Fig. 33.18), the probability that a givenphoton will produce an electron pair (without first Comptonscattering) in thickness t of absorber is P [1 − exp(−t/λ)].

0 0.25 0.5 0.75 10

0.25

0.50

0.75

1.00

x = E/k

Pair production

(X0

NA

/A

) d

σ LP

M/

dx

1 TeV

10 TeV

100 TeV

1 PeV

10 PeV

1 EeV

100 PeV

Figure 33.17: The normalized pair production cross sectiondσLPM/dy, versus fractional electron energy x = E/k.

For photons, pair production is reduced for E(k − E) > k ELPM .The pair-production cross sections for different photon energies areshown in Fig. 33.17.

k [eV]10

log10 12 14 16 18 20 22 24 26

(In

tera

ctio

n L

eng

th)

[m]

10

log

−1

0

1

2

3

4

5

BHσ

Migσ

Aγσ

Aγσ +

Migσ

Figure 33.19: Interaction length for a photon in ice as afunction of photon energy for the Bethe-Heitler (BH), LPM(Mig) and photonuclear (γA) cross sections [56]. The Bethe-Heitler interaction length is 9X0/7, and X0 is 0.393 m inice.


Photon energy

100

10

10–4

10–5

10–6

1

0.1

0.01

0.001

10 eV 100 eV 1 keV 10 keV 100 keV 1 MeV 10 MeV 100 MeV 1 GeV 10 GeV 100 GeV

Abso

rpti

on

len

gth

λ (g

/cm

2)

Si

C

Fe Pb

H

Sn

Figure 33.18: The photon mass attenuation length (or mean free path) λ = 1/(µ/ρ) for various elemental absorbers as a functionof photon energy. The mass attenuation coefficient is µ/ρ, where ρ is the density. The intensity I remaining after traversal ofthickness t (in mass/unit area) is given by I = I0 exp(−t/λ). The accuracy is a few percent. For a chemical compound or mixture,1/λeff ≈

∑

elements wZ/λZ , where wZ is the proportion by weight of the element with atomic number Z. The processes responsible forattenuation are given in Fig. 33.11. Since coherent processes are included, not all these processes result in energy deposition. The data for30 eV < E < 1 keV are obtained from http://www-cxro.lbl.gov/optical constants (courtesy of Eric M. Gullikson, LBNL). The datafor 1 keV < E < 100 GeV are from http://physics.nist.gov/PhysRefData, through the courtesy of John H. Hubbell (NIST).

If k ≪ E, several additional mechanisms can also producesuppression. When the formation length is long, even weak factorscan perturb the interaction. For example, the emitted photon cancoherently forward scatter off of the electrons in the media. Becauseof this, for k < ωpE/me ∼ 10−4, bremsstrahlung is suppressedby a factor (kme/ωpE)2 [48]. Magnetic fields can also suppressbremsstrahlung.

0.000

0.025

0.050

0.075

0.100

0.125

0

20

40

60

80

100

(1/

E0)d

E/

dt

t = depth in radiation lengths

Nu

mber

cross

ing p

lan

e

30 GeV electron incident on iron

Energy

Photons × 1/6.8

Electrons

0 5 10 15 20

Figure 33.20: An EGS4 simulation of a 30 GeV electron-induced cascade in iron. The histogram shows fractional energydeposition per radiation length, and the curve is a gamma-function fit to the distribution. Circles indicate the number ofelectrons with total energy greater than 1.5 MeV crossing planesat X0/2 intervals (scale on right) and the squares the number ofphotons with E ≥ 1.5 MeV crossing the planes (scaled down tohave same area as the electron distribution).

In crystalline media, the situation is more complicated, withcoherent enhancement or suppression possible. The cross sectiondepends on the electron and photon energies and the angles betweenthe particle direction and the crystalline axes [55].

33.4.7. Photonuclear and electronuclear interactions at stillhigher energies :

At still higher photon and electron energies, where the bremsstrah-lung and pair production cross-sections are heavily suppressed by theLPM effect, photonuclear and electronuclear interactions predominateover electromagnetic interactions.

At photon energies above about 1020 eV, for example, photonsusually interact hadronically. The exact cross-over energy dependson the model used for the photonuclear interactions. These processesare illustrated in Fig. 33.19. At still higher energies (>∼ 1023 eV),photonuclear interactions can become coherent, with the photoninteraction spread over multiple nuclei. Essentially, the photoncoherently converts to a ρ0, in a process that is somewhat similar tokaon regeneration [56].

Similar processes occur for electrons. As electron energies increaseand the LPM effect suppresses bremsstrahlung, electronuclearinteractions become more important. At energies above 1021eV, theseelectronuclear interactions dominate electron energy loss [56].

33.5. Electromagnetic cascades

When a high-energy electron or photon is incident on a thickabsorber, it initiates an electromagnetic cascade as pair productionand bremsstrahlung generate more electrons and photons with lowerenergy. The longitudinal development is governed by the high-energypart of the cascade, and therefore scales as the radiation length in thematerial. Electron energies eventually fall below the critical energy,and then dissipate their energy by ionization and excitation ratherthan by the generation of more shower particles. In describing showerbehavior, it is therefore convenient to introduce the scale variables

t = x/X0 , y = E/Ec , (33.35)

so that distance is measured in units of radiation length and energyin units of critical energy. Longitudinal profiles from an EGS4 [57]simulation of a 30 GeV electron-induced cascade in iron are shownin Fig. 33.20. The number of particles crossing a plane (very close toRossi’s Π function [2]) is sensitive to the cutoff energy, here chosen asa total energy of 1.5 MeV for both electrons and photons. The electron


number falls off more quickly than energy deposition. This is because,with increasing depth, a larger fraction of the cascade energy is carriedby photons. Exactly what a calorimeter measures depends on thedevice, but it is not likely to be exactly any of the profiles shown.In gas counters it may be very close to the electron number, but inglass Cherenkov detectors and other devices with “thick” sensitiveregions it is closer to the energy deposition (total track length). Insuch detectors the signal is proportional to the “detectable” tracklength Td, which is in general less than the total track length T .Practical devices are sensitive to electrons with energy above somedetection threshold Ed, and Td = T F (Ed/Ec). An analytic form forF (Ed/Ec) obtained by Rossi [2] is given by Fabjan in Ref. 58; seealso Amaldi [59].

The mean longitudinal profile of the energy deposition in anelectromagnetic cascade is reasonably well described by a gammadistribution [60]:

dE

dt= E0 b

(bt)a−1e−bt

Γ(a)(33.36)

The maximum tmax occurs at (a − 1)/b. We have made fits to showerprofiles in elements ranging from carbon to uranium, at energies from1 GeV to 100 GeV. The energy deposition profiles are well describedby Eq. (33.36) with

tmax = (a − 1)/b = 1.0 × (ln y + Cj) , j = e, γ , (33.37)

where Ce = −0.5 for electron-induced cascades and Cγ = +0.5 forphoton-induced cascades. To use Eq. (33.36), one finds (a − 1)/b fromEq. (33.37) and Eq. (33.35), then finds a either by assuming b ≈ 0.5or by finding a more accurate value from Fig. 33.21. The resultsare very similar for the electron number profiles, but there is somedependence on the atomic number of the medium. A similar form forthe electron number maximum was obtained by Rossi in the contextof his “Approximation B,” [2] (see Fabjan’s review in Ref. 58), butwith Ce = −1.0 and Cγ = −0.5; we regard this as superseded by theEGS4 result.

Carbon

Aluminum

Iron

Uranium

0.3

0.4

0.5

0.6

0.7

0.8

10 100 1000 10 000

b

y = E/Ec

Figure 33.21: Fitted values of the scale factor b for energydeposition profiles obtained with EGS4 for a variety of elementsfor incident electrons with 1 ≤ E0 ≤ 100 GeV. Values obtainedfor incident photons are essentially the same.

The “shower length” Xs = X0/b is less conveniently parameterized,since b depends upon both Z and incident energy, as shown inFig. 33.21. As a corollary of this Z dependence, the number of elec-trons crossing a plane near shower maximum is underestimated usingRossi’s approximation for carbon and seriously overestimated for ura-nium. Essentially the same b values are obtained for incident electronsand photons. For many purposes it is sufficient to take b ≈ 0.5.

The length of showers initiated by ultra-high energy photons andelectrons is somewhat greater than at lower energies since the firstor first few interaction lengths are increased via the mechanismsdiscussed above.

The gamma function distribution is very flat near the origin, whilethe EGS4 cascade (or a real cascade) increases more rapidly. As aresult Eq. (33.36) fails badly for about the first two radiation lengths;it was necessary to exclude this region in making fits.

Because fluctuations are important, Eq. (33.36) should be used onlyin applications where average behavior is adequate. Grindhammeret al. have developed fast simulation algorithms in which the varianceand correlation of a and b are obtained by fitting Eq. (33.36) toindividually simulated cascades, then generating profiles for cascadesusing a and b chosen from the correlated distributions [61].

The transverse development of electromagnetic showers in differentmaterials scales fairly accurately with the Moliere radius RM , givenby [62,63]

RM = X0 Es/Ec , (33.38)

where Es ≈ 21 MeV (Table 33.1), and the Rossi definition of Ec isused.

In a material containing a weight fraction wj of the element withcritical energy Ecj and radiation length Xj , the Moliere radius isgiven by

1

RM=

1

Es

∑ wj Ecj

Xj. (33.39)

Measurements of the lateral distribution in electromagneticcascades are shown in Refs. 62 and 63. On the average, only 10%of the energy lies outside the cylinder with radius RM . About99% is contained inside of 3.5RM , but at this radius and beyondcomposition effects become important and the scaling with RM fails.The distributions are characterized by a narrow core, and broaden asthe shower develops. They are often represented as the sum of twoGaussians, and Grindhammer [61] describes them with the function

f(r) =2r R2

(r2 + R2)2, (33.40)

where R is a phenomenological function of x/X0 and lnE.At high enough energies, the LPM effect (Sec. 33.4.6) reduces the

cross sections for bremsstrahlung and pair production, and hence cancause significant elongation of electromagnetic cascades [46].

33.6. Muon energy loss at high energy

At sufficiently high energies, radiative processes become moreimportant than ionization for all charged particles. For muons andpions in materials such as iron, this “critical energy” occurs at severalhundred GeV. (There is no simple scaling with particle mass, butfor protons the “critical energy” is much, much higher.) Radiativeeffects dominate the energy loss of energetic muons found in cosmicrays or produced at the newest accelerators. These processes arecharacterized by small cross sections, hard spectra, large energyfluctuations, and the associated generation of electromagnetic and (inthe case of photonuclear interactions) hadronic showers [64–72]. Asa consequence, at these energies the treatment of energy loss as auniform and continuous process is for many purposes inadequate.

It is convenient to write the average rate of muon energy lossas [73]

−dE/dx = a(E) + b(E)E . (33.41)

Here a(E) is the ionization energy loss given by Eq. (33.5), andb(E) is the sum of e+e− pair production, bremsstrahlung, andphotonuclear contributions. To the approximation that these slowly-varying functions are constant, the mean range x0 of a muon withinitial energy E0 is given by

x0 ≈ (1/b) ln(1 + E0/Eµc) , (33.42)

where Eµc = a/b. Fig. 33.22 shows contributions to b(E) for iron.Since a(E) ≈ 0.002 GeV g−1 cm2, b(E)E dominates the energy lossabove several hundred GeV, where b(E) is nearly constant. The ratesof energy loss for muons in hydrogen, uranium, and iron are shown inFig. 33.23 [5].

The “muon critical energy” Eµc can be defined more exactly as theenergy at which radiative and ionization losses are equal, and can befound by solving Eµc = a(Eµc)/b(Eµc). This definition correspondsto the solid-line intersection in Fig. 33.13, and is different from theRossi definition we used for electrons. It serves the same function:below Eµc ionization losses dominate, and above Eµc radiative effectsdominate. The dependence of Eµc on atomic number Z is shown inFig. 33.24.


Muon energy (GeV)

0

1

2

3

4

5

6

7

8

91

06 b

(E)

(g

−1cm

2)

Iron

btotal

bpair

bbremsstrahlung

bnuclear

102101 103 104 105

Figure 33.22: Contributions to the fractional energy loss bymuons in iron due to e+e− pair production, bremsstrahlung,and photonuclear interactions, as obtained from Groom et al. [5]except for post-Born corrections to the cross section for directpair production from atomic electrons.

Figure 33.23: The average energy loss of a muon in hydrogen,iron, and uranium as a function of muon energy. Contributionsto dE/dx in iron from ionization and the processes shown inFig. 33.22 are also shown.

___________

(Z + 2.03)0.879

___________

(Z + 1.47)0.838

100

200

400

700

1000

2000

4000

Eµc

(G

eV

)

1 2 5 10 20 50 100

Z

7980 GeV

5700 GeV

H He Li Be B CNO Ne SnFe

SolidsGases

Figure 33.24: Muon critical energy for the chemical elements,defined as the energy at which radiative and ionization energyloss rates are equal [5]. The equality comes at a higher energyfor gases than for solids or liquids with the same atomic numberbecause of a smaller density effect reduction of the ionizationlosses. The fits shown in the figure exclude hydrogen. Alkalimetals fall 3–4% above the fitted function, while most othersolids are within 2% of the function. Among the gases the worstfit is for radon (2.7% high).

The radiative cross sections are expressed as functions of thefractional energy loss ν. The bremsstrahlung cross section goesroughly as 1/ν over most of the range, while for the pair productioncase the distribution goes as ν−3 to ν−2 [74]. “Hard” losses are

therefore more probable in bremsstrahlung, and in fact energy lossesdue to pair production may very nearly be treated as continuous.The simulated [72] momentum distribution of an incident 1 TeV/cmuon beam after it crosses 3 m of iron is shown in Fig. 33.25. Themost probable loss is 8 GeV, or 3.4 MeV g−1cm2. The full widthat half maximum is 9 GeV/c, or 0.9%. The radiative tail is almostentirely due to bremsstrahlung, although most of the events in whichmore than 10% of the incident energy lost experienced relativelyhard photonuclear interactions. The latter can exceed detectorresolution [75], necessitating the reconstruction of lost energy. Tablesin Ref. 5 list the stopping power as 9.82 MeV g−1cm2 for a 1 TeVmuon, so that the mean loss should be 23 GeV (≈ 23 GeV/c), for afinal momentum of 977 GeV/c, far below the peak. This agrees withthe indicated mean calculated from the simulation. Electromagneticand hadronic cascades in detector materials can obscure muon tracksin detector planes and reduce tracking efficiency [76].

950 960 970 980 990 1000Final momentum p [GeV/c]

0.00

0.02

0.04

0.06

0.08

0.10

1 TeV muons on 3 m Fe

Mean 977 GeV/c

Median 987 GeV/c

dN

/d

p

[1

/(G

eV

/c)]

FWHM 9 GeV/c

Figure 33.25: The momentum distribution of 1 TeV/c muonsafter traversing 3 m of iron as calculated with the MARS15Monte Carlo code [72] by S.I. Striganov [5].

33.7. Cherenkov and transition radiation [33,77,78]

A charged particle radiates if its velocity is greater than thelocal phase velocity of light (Cherenkov radiation) or if it crossessuddenly from one medium to another with different optical properties(transition radiation). Neither process is important for energy loss,but both are used in high-energy and cosmic-ray physics detectors.

θc

γc

η

Cherenkov wavefront

Particle velocity v = βc

v = v g

Figure 33.26: Cherenkov light emission and wavefront angles.In a dispersive medium, θc + η 6= 900.

33.7.1. Optical Cherenkov radiation :

The angle θc of Cherenkov radiation, relative to the particle’sdirection, for a particle with velocity βc in a medium with index ofrefraction n is

cos θc = (1/nβ)

or tan θc =√

β2n2 − 1

≈√

2(1 − 1/nβ) for small θc, e.g. in gases.(33.43)

The threshold velocity βt is 1/n, and γt = 1/(1 − β2t )1/2. Therefore,

βtγt = 1/(2δ + δ2)1/2, where δ = n − 1. Values of δ for variouscommonly used gases are given as a function of pressure andwavelength in Ref. 79. For values at atmospheric pressure, seeTable 6.1. Data for other commonly used materials are given inRef. 80.


Practical Cherenkov radiator materials are dispersive. Let ω be thephoton’s frequency, and let k = 2π/λ be its wavenumber. The photonspropage at the group velocity vg = dω/dk = c/[n(ω) + ω(dn/dω)]. Ina non-dispersive medium, this simplies to vg = c/n.

In his classical paper, Tamm [81] showed that for dispersive mediathe radiation is concentrated in a thin conical shell whose vertex is atthe moving charge, and whose opening half-angle η is given by

cot η =

[

d

dω(ω tan θc)

]

ω0

=

[

tan θc + β2ω n(ω)dn

dωcot θc

]

ω0

, (33.44)

where ω0 is the central value of the small frequency range underconsideration. (See Fig. 33.26.) This cone has a opening half-angle η,and, unless the medium is non-dispersive (dn/dω = 0), θc + η 6= 900.The Cherenkov wavefront ‘sideslips’ along with the particle [82]. Thiseffect has timing implications for ring imaging Cherenkov counters [83],but it is probably unimportant for most applications.

The number of photons produced per unit path length of a particlewith charge ze and per unit energy interval of the photons is

d2N

dEdx=

αz2

~csin2 θc =

α2z2

re mec2

(

1 − 1

β2n2(E)

)

≈ 370 sin2 θc(E) eV−1cm−1 (z = 1) , (33.45)

or, equivalently,

d2N

dxdλ=

2παz2

λ2

(

1 − 1

β2n2(λ)

)

. (33.46)

The index of refraction n is a function of photon energy E = ~ω,as is the sensitivity of the transducer used to detect the light. Forpractical use, Eq. (33.45) must be multiplied by the the transducerresponse function and integrated over the region for which β n(ω) > 1.Further details are given in the discussion of Cherenkov detectors inthe Particle Detectors section (Sec. 34 of this Review).

When two particles are close together (lateral separation <∼ 1wavelength), the electromagnetic fields from the particles mayadd coherently, affecting the Cherenkov radiation. Because of theiropposite charges, the radiation from an e+e− pair at close separationis suppressed compared to two independent leptons [84].

33.7.2. Coherent radio Cherenkov radiation :

Coherent Cherenkov radiation is produced by many chargedparticles with a non-zero net charge moving through matter on anapproximately common “wavefront”—for example, the electrons andpositrons in a high-energy electromagnetic cascade. The signals canbe visible above backgrounds for shower energies as low as 1017 eV; seeSec. 35.3.3 for more details. The phenomenon is called the Askaryaneffect [85]. Near the end of a shower, when typical particle energiesare below Ec (but still relativistic), a charge imbalance develops.Photons can Compton-scatter atomic electrons, and positrons canannihilate with atomic electrons to contribute even more photonswhich can in turn Compton scatter. These processes result in aroughly 20% excess of electrons over positrons in a shower. The netnegative charge leads to coherent radio Cherenkov emission. Theradiation includes a component from the decelerating charges (asin bremsstrahlung). Because the emission is coherent, the electricfield strength is proportional to the shower energy, and the signalpower increases as its square. The electric field strength also increaseslinearly with frequency, up to a maximum frequency determined bythe lateral spread of the shower. This cutoff occurs at about 1 GHz inice, and scales inversely with the Moliere radius. At low frequencies,the radiation is roughly isotropic, but, as the frequency rises towardthe cutoff frequency, the radiation becomes increasingly peakedaround the Cherenkov angle. The radiation is linearly polarized inthe plane containing the shower axis and the photon direction. Ameasurement of the signal polarization can be used to help determinethe shower direction. The characteristics of this radiation have been

10−3

10−2

10−4

10−5101 100 1000

25 µm Mylar/1.5 mm airγ = 2 ×104

Without absorption

With absorption

200 foils

Single interface

x-ray energy ω (keV)

dS/d

( ω

), d

iffe

rent

ial y

ield

per

inte

rfac

e (k

eV/k

eV)

Figure 33.27: X-ray photon energy spectra for a radiatorconsisting of 200 25µm thick foils of Mylar with 1.5 mm spacingin air (solid lines) and for a single surface (dashed line). Curvesare shown with and without absorption. Adapted from Ref. 88.

nicely demonstrated in a series of experiments at SLAC [86]. Adetailed discussion of the radiation can be found in Ref. 87.

33.7.3. Transition radiation :

The energy radiated when a particle with charge ze crosses theboundary between vacuum and a medium with plasma frequency ωp is

I = αz2γ~ωp/3 , (33.47)

where

~ωp =√

4πNer3e mec

2/α =

√

ρ (in g/cm3) 〈Z/A〉 × 28.81 eV .

(33.48)For styrene and similar materials, ~ωp ≈ 20 eV; for air it is 0.7 eV.The number spectrum dNγ/d(~ω diverges logarithmically at low

energies and decreases rapidly for ~ω/γ~ωp > 1. About half the energyis emitted in the range 0.1 ≤ ~ω/γ~ωp ≤ 1. Inevitable absorption in apractical detector removes the divergence. For a particle with γ = 103,the radiated photons are in the soft x-ray range 2 to 40 keV. The γdependence of the emitted energy thus comes from the hardening ofthe spectrum rather than from an increased quantum yield.

The number of photons with energy ~ω > ~ω0 is given by theanswer to problem 13.15 in Ref. 33,

Nγ(~ω > ~ω0) =αz2

π

[

(

lnγ~ωp

~ω0− 1

)2

+π2

12

]

, (33.49)

within corrections of order (~ω0/γ~ωp)2. The number of photons

above a fixed energy ~ω0 ≪ γ~ωp thus grows as (ln γ)2, but the numberabove a fixed fraction of γ~ωp (as in the example above) is constant.For example, for ~ω > γ~ωp/10, Nγ = 2.519 αz2/π = 0.59%× z2.

The particle stays “in phase” with the x ray over a distance calledthe formation length, d(ω) = (2c/ω)(1/γ2 + θ2 + ω2

p/ω2)−1. Most ofthe radiation is produced in this distance. Here θ is the x-ray emissionangle, characteristically 1/γ. For θ = 1/γ the formation length has amaximum at d(γωp/

√2) = γc/

√2 ωp. In practical situations it is tens

of µm.Since the useful x-ray yield from a single interface is low, in practical

detectors it is enhanced by using a stack of N foil radiators—foils Lthick, where L is typically several formation lengths—separated bygas-filled gaps. The amplitudes at successive interfaces interfere tocause oscillations about the single-interface spectrum. At increasingfrequencies above the position of the last interference maximum(L/d(w) = π/2), the formation zones, which have opposite phase,overlap more and more and the spectrum saturates, dI/dω approachingzero as L/d(ω) → 0. This is illustrated in Fig. 33.27 for a realisticdetector configuration.


For regular spacing of the layers fairly complicated analyticsolutions for the intensity have been obtained [88,89]. Although onemight expect the intensity of coherent radiation from the stack of foilsto be proportional to N2, the angular dependence of the formationlength conspires to make the intensity ∝ N .

References:

1. H. Bichsel, Nucl. Instrum. Methods A562, 154 (2006).

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456 34. Detectors at accelerators

34. PARTICLE DETECTORS AT ACCELERATORS

34. PARTICLE DETECTORS AT ACCELERATORS . . . . 456

34.1. Introduction . . . . . . . . . . . . . . . . . . 456

34.2. Photon detectors . . . . . . . . . . . . . . . . 457

34.2.1. Vacuum photodetectors . . . . . . . . . . . 457

34.2.1.1. Photomultiplier tubes . . . . . . . . . . 457

34.2.1.2. Microchannel plates . . . . . . . . . . . 458

34.2.1.3. Hybrid photon detectors . . . . . . . . . 458

34.2.2. Gaseous photon detectors . . . . . . . . . . . 458

34.2.3. Solid-state photon detectors . . . . . . . . . 459

34.3. Organic scintillators . . . . . . . . . . . . . . . 459

34.3.1. Scintillation mechanism . . . . . . . . . . . 460

34.3.2. Caveats and cautions . . . . . . . . . . . . 460

34.3.3. Scintillating and wavelength-shifting fibers . . . 460

34.4. Inorganic scintillators . . . . . . . . . . . . . . 461

34.5. Cherenkov detectors . . . . . . . . . . . . . . . 463

34.6. Gaseous detectors . . . . . . . . . . . . . . . . 465

34.6.1. Energy loss and charge transport in gases . . . . 465

34.6.2. Multi-Wire Proportional and Drift Chambers . . 467

34.6.3. High Rate Effects . . . . . . . . . . . . . . 468

34.6.4. Micro-Pattern Gas Detectors . . . . . . . . . 468

34.6.5. Time-projection chambers . . . . . . . . . . 470

34.6.6. Transition radiation detectors (TRD’s) . . . . . 472

34.6.7. Resistive-plate chambers . . . . . . . . . . . 473

34.6.7.1. RPC types and applications . . . . . . . . 474

34.6.7.2. Time and space resolution . . . . . . . . 474

34.6.7.3. Rate capability and ageing . . . . . . . . 474

34.7. Semiconductor detectors . . . . . . . . . . . . . 474

34.7.1. Materials Requirements . . . . . . . . . . . 474

34.7.2. Detector Configurations . . . . . . . . . . . 475

34.7.3. Signal Formation . . . . . . . . . . . . . . 475

34.7.4. Radiation Damage . . . . . . . . . . . . . . 475

34.8. Low-noise electronics . . . . . . . . . . . . . . . 476

34.9. Calorimeters . . . . . . . . . . . . . . . . . . 478

34.9.1. Electromagnetic calorimeters . . . . . . . . . 479

34.9.2. Hadronic calorimeters . . . . . . . . . . . . 479

34.9.3. Free electron drift velocities in liquid ionizationchambers . . . . . . . . . . . . . . . . . . . . 482

34.10. Accelerator Neutrino Detectors . . . . . . . . . . 482

34.10.1. Introduction . . . . . . . . . . . . . . . . 482

34.10.2. Signals and Backgrounds . . . . . . . . . . 483

34.10.2.1. Charged-Current Quasi-Elastic Scattering andPions . . . . . . . . . . . . . . . . . . . . 483

34.10.2.2. Deep Inelastic Scattering . . . . . . . . 483

34.10.2.3. Neutral Currents . . . . . . . . . . . . 483

34.10.3. Instances of Neutrino Detector Technology . . . 483

34.10.3.1. Spark Chambers . . . . . . . . . . . . 483

34.10.3.2. Bubble Chambers . . . . . . . . . . . 483

34.10.3.3. Iron Tracking Calorimeters . . . . . . . 483

34.10.3.4. Cherenkov Detectors . . . . . . . . . . 484

34.10.3.5. Scintillation Detectors . . . . . . . . . . 484

34.10.3.6. Liquid Argon Time Projection Chambers . 484

34.10.3.7. Emulsion Detectors . . . . . . . . . . . 484

34.10.3.8. Hybrid Detectors . . . . . . . . . . . . 485

34.11. Superconducting magnets for collider detectors . . . 485

34.11.1. Solenoid Magnets . . . . . . . . . . . . . . 485

34.11.2. Properties of collider detector magnets . . . . 486

34.11.3. Toroidal magnets . . . . . . . . . . . . . . 487

34.12. Measurement of particle momenta in a uniform mag-netic field . . . . . . . . . . . . . . . . . . . . . 487

References . . . . . . . . . . . . . . . . . . . . . . 487

34.1. Introduction

This review summarizes the detector technologies employed ataccelerator particle physics experiments. Several of these detectorsare also used in a non-accelerator context and examples of suchapplications will be provided. The detector techniques which arespecific to non-accelerator particle physics experiments are thesubject of Chap. 35. More detailed discussions of detectors andtheir underlying physics can be found in books by Ferbel [1],Kleinknecht [2], Knoll [3], Green [4], Leroy & Rancoita [5], andGrupen [6].

In Table 34.1 are given typical resolutions and deadtimes of commoncharged particle detectors. The quoted numbers are usually based ontypical devices, and should be regarded only as rough approximationsfor new designs. The spatial resolution refers to the intrinsic detectorresolution, i.e. without multiple scattering. We note that analogdetector readout can provide better spatial resolution than digitalreadout by measuring the deposited charge in neighboring channels.Quoted ranges attempt to be representative of both possibilities.The time resolution is defined by how accurately the time at whicha particle crossed the detector can be determined. The deadtimeis the minimum separation in time between two resolved hits onthe same channel. Typical performance of calorimetry and particleidentification are provided in the relevant sections below.

Table 34.1: Typical resolutions and deadtimes of commoncharged particle detectors. Revised November 2011.

Intrinsinc Spatial Time Dead

Detector Type Resolution (rms) Resolution Time

Resistive plate chamber . 10 mm 1 ns (50 psa) —

Streamer chamber 300 µmb 2 µs 100 ms

Liquid argon drift [7] ∼175–450 µm ∼ 200 ns ∼ 2 µs

Scintillation tracker ∼100 µm 100 ps/nc 10 ns

Bubble chamber 10–150 µm 1 ms 50 msd

Proportional chamber 50–100 µme 2 ns 20-200 ns

Drift chamber 50–100 µm 2 nsf 20-100 ns

Micro-pattern gas detectors 30–40 µm < 10 ns 10-100 ns

Silicon strip pitch/(3 to 7)g few nsh . 50 nsh

Silicon pixel . 10 µm few nsh . 50 nsh

Emulsion 1 µm — —

a For multiple-gap RPCs.b 300 µm is for 1 mm pitch (wirespacing/

√12).

c n = index of refraction.d Multiple pulsing time.e Delay line cathode readout can give ±150 µm parallel to anode

wire.f For two chambers.g The highest resolution (“7”) is obtained for small-pitch detectors

(. 25 µm) with pulse-height-weighted center finding.h Limited by the readout electronics [8].

34. Detectors at accelerators 457

34.2. Photon detectors

Updated August 2011 by D. Chakraborty (Northern Illinois U) andT. Sumiyoshi (Tokyo Metro U).

Most detectors in high-energy, nuclear, and astrophysics relyon the detection of photons in or near the visible range,100nm . λ . 1000nm, or E ≈ a few eV. This range coversscintillation and Cherenkov radiation as well as the light detected inmany astronomical observations.

Generally, photodetection involves generating a detectable electricalsignal proportional to the (usually very small) number of incidentphotons. The process involves three distinct steps:

1. generation of a primary photoelectron or electron-hole (e-h) pair byan incident photon by the photoelectric or photoconductive effect,

2. amplification of the p.e. signal to detectable levels by one or moremultiplicative bombardment steps and/or an avalanche process(usually), and,

3. collection of the secondary electrons to form the electrical signal.

The important characteristics of a photodetector include thefollowing in statistical averages:

1. quantum efficiency (QE or ǫQ): the number of primary photo-electrons generated per incident photon (0 ≤ ǫQ ≤ 1; in siliconmore than one e-h pair per incident photon can be generated forλ <∼ 165 nm),

2. collection efficiency (CE or ǫC): the overall acceptance factor otherthan the generation of photoelectrons (0 ≤ ǫC ≤ 1),

3. gain (G): the number of electrons collected for each photoelectrongenerated,

4. dark current or dark noise: the electrical signal when there is nophoton,

5. energy resolution: electronic noise (ENC or Ne) and statisticalfluctuations in the amplification process compound the Poissondistribution of nγ photons from a given source:

σ(E)

〈E〉 =

√

fN

nγǫQǫC+

(

Ne

GnγǫQǫC

)2, (34.1)

where fN , or the excess noise factor (ENF), is the contribution tothe energy distribution variance due to amplification statistics [9],

6. dynamic range: the maximum signal available from the detector(this is usually expressed in units of the response to noise-equivalentpower, or NEP, which is the optical input power that produces asignal-to-noise ratio of 1),

7. time dependence of the response: this includes the transit time,which is the time between the arrival of the photon and theelectrical pulse, and the transit time spread, which contributes tothe pulse rise time and width, and

8. rate capability: inversely proportional to the time needed, after thearrival of one photon, to get ready to receive the next.

Table 34.2: Representative characteristics of some photodetectorscommonly used in particle physics. The time resolution of the deviceslisted here vary in the 10–2000 ps range.

Type λ ǫQ ǫC Gain Risetime Area 1-p.e noise HV Price

(nm) (ns) (mm2) (Hz) (V) (USD)

PMT∗ 115–1700 0.15–0.25 103–107 0.7–10 102–105 10–104 500–3000 100–5000

MCP∗ 100–650 0.01–0.10 103–107 0.15–0.3 102–104 0.1–200 500–3500 10–6000

HPD∗ 115–850 0.1–0.3 103–104 7 102–105 10–103 ∼2 × 104 ∼600

GPM∗ 115–500 0.15–0.3 103–106 O(0.1) O(10) 10–103 300–2000 O(10)

APD 300–1700 ∼0.7 10–108 O(1) 10–103 1–103 400–1400 O(100)

PPD 320–900 0.15–0.3 105–106 ∼ 1 1–10 O(106) 30–60 O(100)

VLPC 500–600 ∼0.9 ∼5 × 104 ∼ 10 1 O(104) ∼7 ∼1

∗These devices often come in multi-anode configurations. In suchcases, area, noise, and price are to be considered on a “perreadout-channel” basis.

The QE is a strong function of the photon wavelength (λ), and isusually quoted at maximum, together with a range of λ where theQE is comparable to its maximum. Spatial uniformity and linearitywith respect to the number of photons are highly desirable in aphotodetector’s response.

Optimization of these factors involves many trade-offs and varywidely between applications. For example, while a large gain isdesirable, attempts to increase the gain for a given device alsoincreases the ENF and after-pulsing (“echos” of the main pulse). Insolid-state devices, a higher QE often requires a compromise in thetiming properties. In other types, coverage of large areas by focusingincreases the transit time spread.

Other important considerations also are highly application-specific.These include the photon flux and wavelength range, the totalarea to be covered and the efficiency required, the volume availableto accommodate the detectors, characteristics of the environmentsuch as chemical composition, temperature, magnetic field, ambientbackground, as well as ambient radiation of different types and,mode of operation (continuous or triggered), bias (high-voltage)requirements, power consumption, calibration needs, aging, cost, andso on. Several technologies employing different phenomena for thethree steps described above, and many variants within each, offer awide range of solutions to choose from. The salient features of themain technologies and the common variants are described below.Some key characteristics are summarized in Table 34.2.

34.2.1. Vacuum photodetectors : Vacuum photodetectors canbe broadly subdivided into three types: photomultiplier tubes,microchannel plates, and hybrid photodetectors.

34.2.1.1. Photomultiplier tubes: A versatile class of photon detectors,vacuum photomultiplier tubes (PMT) has been employed by a vastmajority of all particle physics experiments to date [9]. Both“transmission-” and “reflection-type” PMT’s are widely used. In theformer, the photocathode material is deposited on the inside of atransparent window through which the photons enter, while in thelatter, the photocathode material rests on a separate surface thatthe incident photons strike. The cathode material has a low workfunction, chosen for the wavelength band of interest. When a photonhits the cathode and liberates an electron (the photoelectric effect),the latter is accelerated and guided by electric fields to impinge ona secondary-emission electrode, or dynode, which then emits a few(∼ 5) secondary electrons. The multiplication process is repeatedtypically 10 times in series to generate a sufficient number of electrons,which are collected at the anode for delivery to the external circuit.The total gain of a PMT depends on the applied high voltage V asG = AV kn, where k ≈ 0.7–0.8 (depending on the dynode material),n is the number of dynodes in the chain, and A a constant (whichalso depends on n). Typically, G is in the range of 105–106. Pulserisetimes are usually in the few nanosecond range. With e.g. two-leveldiscrimination the effective time resolution can be much better.


A large variety of PMT’s, including many just recently developed,covers a wide span of wavelength ranges from infrared (IR) to extremeultraviolet (XUV) [10]. They are categorized by the window materials,photocathode materials, dynode structures, anode configurations, etc.

Common window materials are borosilicate glass for IR to near-UV,fused quartz and sapphire (Al2O3) for UV, and MgF2 or LiF for XUV.The choice of photocathode materials include a variety of mostly Cs-and/or Sb-based compounds such as CsI, CsTe, bi-alkali (SbRbCs,SbKCs), multi-alkali (SbNa2KCs), GaAs(Cs), GaAsP, etc. Sensitivewavelengths and peak quantum efficiencies for these materials aresummarized in Table 34.3. Typical dynode structures used in PMT’sare circular cage, line focusing, box and grid, venetian blind, andfine mesh. In some cases, limited spatial resolution can be obtainedby using a mosaic of multiple anodes. Fast PMT’s with very largewindows—measuring up to 508 mm across—have been developedin recent years for detection of Cherenkov radiation in neutrinoexperiments such as Super-Kamiokande and KamLAND among manyothers. Specially prepared low-radioactivity glass is used to makethese PMT’s, and they are also able to withstand the high pressure ofthe surrounding liquid.

PMT’s are vulnerable to magnetic fields—sometimes even thegeomagnetic field causes large orientation-dependent gain changes. Ahigh-permeability metal shield is often necessary. However, proximity-focused PMT’s, e.g. the fine-mesh types, can be used even in ahigh magnetic field (≥ 1 T) if the electron drift direction is parallelto the field. CMS uses custom-made vacuum phototriodes (VPT)mounted on the back face of projective lead tungstate crystals todetect scintillation light in the endcap sections of its electromagneticcalorimeters, which are inside a 3.8 T superconducting solenoid. AVPT employs a single dynode (thus, G ≈ 10) placed close to thephotocathode, and a mesh anode plane between the two, to help itcope with the strong magnetic field, which is not too unfavorablyoriented with respect to the photodetector axis in the endcaps(within 25), but where the radiation level is too high for AvalanchePhotodiodes (APD’s) like those used in the barrel section.

34.2.1.2. Microchannel plates: A typical Microchannel plate (MCP)photodetector consists of one or more ∼2 mm thick glass plates withdensely packed O(10 µm)-diameter cylindrical holes, or “channels”,sitting between the transmission-type photocathode and anode planes,separated by O(1 mm) gaps. Instead of discrete dynodes, the innersurface of each cylindrical tube serves as a continuous dynode forthe entire cascade of multiplicative bombardments initiated by aphotoelectron. Gain fluctuations can be minimized by operating ina saturation mode, whence each channel is only capable of a binaryoutput, but the sum of all channel outputs remains proportional to thenumber of photons received so long as the photon flux is low enoughto ensure that the probability of a single channel receiving more thanone photon during a single time gate is negligible. MCP’s are thin,offer good spatial resolution, have excellent time resolution (∼20 ps),and can tolerate random magnetic fields up to 0.1 T and axial fieldsup to ∼ 1 T. However, they suffer from relatively long recoverytime per channel and short lifetime. MCP’s are widely employed asimage-intensifiers, although not so much in HEP or astrophysics.

34.2.1.3. Hybrid photon detectors: Hybrid photon detectors (HPD)combine the sensitivity of a vacuum PMT with the excellent spatialand energy resolutions of a Si sensor [11]. A single photoelectronejected from the photocathode is accelerated through a potentialdifference of ∼20 kV before it impinges on the silicon sensor/anode.The gain nearly equals the maximum number of e-h pairs that couldbe created from the entire kinetic energy of the accelerated electron:G ≈ eV/w, where e is the electronic charge, V is the applied potentialdifference, and w ≈ 3.7 eV is the mean energy required to create ane-h pair in Si at room temperature. Since the gain is achieved in asingle step, one might expect to have the excellent resolution of asimple Poisson statistic with large mean, but in fact it is even better,thanks to the Fano effect discussed in Sec. 34.7.

Low-noise electronics must be used to read out HPD’s if oneintends to take advantage of the low fluctuations in gain, e.g. whencounting small numbers of photons. HPD’s can have the same ǫQ ǫCand window geometries as PMT’s and can be segmented down to ∼50

µm. However, they require rather high biases and will not function ina magnetic field. The exception is proximity-focused devices (⇒ no(de)magnification) in an axial field. With time resolutions of ∼10 psand superior rate capability, proximity-focused HPD’s can be analternative to MCP’s. Current applications of HPD’s include the CMShadronic calorimeter and the RICH detector in LHCb. Large-sizeHPD’s with sophisticated focusing may be suitable for future waterCherenkov experiments.

Hybrid APD’s (HAPD’s) add an avalanche multiplication stepfollowing the electron bombardment to boost the gain by a factor of∼50. This affords a higher gain and/or lower electrical bias, but alsodegrades the signal definition.

Table 34.3: Properties of photocathode and window materialscommonly used in vacuum photodetectors [10].

Photocathode λ Window Peak ǫQ (λ/nm)

material (nm) material

CsI 115–200 MgF2 0.11 (140)

CsTe 115–320 MgF2 0.14 (240)

Bi-alkali 300–650 Borosilicate 0.27 (390)

160-650 Synthetic Silica 0.27 (390)

“Ultra Bi-alkali” 300–650 Borosilicate 0.43 (350)


Multi-alkali 300–850 Borosilicate 0.20 (360)


GaAs(Cs)∗ 160–930 Synthetic Silica 0.23 (280)

GaAsP(Cs) 300-750 Borosilicate 0.50 (500)

InP/InGaAsP† 350-1700 Borosilicate 0.01 (1100)

∗Reflection type photocathode is used. †Requires cooling to∼ −80C.

34.2.2. Gaseous photon detectors : In gaseous photomultipliers(GPM) a photoelectron in a suitable gas mixture initiates an avalanchein a high-field region, producing a large number of secondary impact-ionization electrons. In principle the charge multiplication andcollection processes are identical to those employed in gaseous trackingdetectors such as multiwire proportional chambers, micromesh gaseousdetectors (Micromegas), or gas electron multipliers (GEM). These arediscussed in Sec. 34.6.4.

The devices can be divided into two types depending on thephotocathode material. One type uses solid photocathode materialsmuch in the same way as PMT’s. Since it is resistant to gas mixturestypically used in tracking chambers, CsI is a common choice. In theother type, photoionization occurs on suitable molecules vaporizedand mixed in the drift volume. Most gases have photoionizationwork functions in excess of 10 eV, which would limit their sensitivityto wavelengths far too short. However, vapors of TMAE (tetrakisdimethyl-amine ethylene) or TEA (tri-ethyl-amine), which havesmaller work functions (5.3 eV for TMAE and 7.5 eV for TEA), aresuited for XUV photon detection [12]. Since devices like GEM’s offersub-mm spatial resolution, GPM’s are often used as position-sensitivephoton detectors. They can be made into flat panels to cover largeareas (O(1 m2)), can operate in high magnetic fields, and are relativelyinexpensive. Many of the ring imaging Cherenkov (RICH) detectorsto date have used GPM’s for the detection of Cherenkov light [13].Special care must be taken to suppress the photon-feedback processin GPM’s. It is also important to maintain high purity of the gas asminute traces of O2 can significantly degrade the detection efficiency.


34.2.3. Solid-state photon detectors : In a phase of rapiddevelopment, solid-state photodetectors are competing with vacuum-or gas-based devices for many existing applications and makingway for a multitude of new ones. Compared to traditional vacuum-and gaseous photodetectors, solid-state devices are more compact,lightweight, rugged, tolerant to magnetic fields, and often cheaper.They also allow fine pixelization, are easy to integrate into largesystems, and can operate at low electric potentials, while matching orexceeding most performance criteria. They are particularly well suitedfor detection of γ- and X-rays. Except for applications where coverageof very large areas or dynamic range is required, solid-state detectorsare proving to be the better choice. Some hybrid devices attempt tocombine the best features of different technologies while applicationsof nanotechnology are opening up exciting new possibilities.

Silicon photodiodes (PD) are widely used in high-energy physicsas particle detectors and in a great number of applications (includingsolar cells!) as light detectors. The structure is discussed in somedetail in Sec. 34.7. In its simplest form, the PD is a reverse-biasedp-n junction. Photons with energies above the indirect bandgapenergy (wavelengths shorter than about 1050 nm, depending on thetemperature) can create e-h pairs (the photoconductive effect), whichare collected on the p and n sides, respectively. Often, as in the PD’sused for crystal scintillator readout in CLEO, L3, Belle, BaBar, andGLAST, intrinsic silicon is doped to create a p-i-n structure. Thereverse bias increases the thickness of the depleted region; in the caseof these particular detectors, to full depletion at a depth of about100 µm. Increasing the depletion depth decreases the capacitance(and hence electronic noise) and extends the red response. Quantumefficiency can exceed 90%, but falls toward the red because of theincreasing absorption length of light in silicon. The absorption lengthreaches 100 µm at 985 nm. However, since G = 1, amplification isnecessary. Optimal low-noise amplifiers are slow, but, even so, noiselimits the minimum detectable signal in room-temperature devices toseveral hundred photons.

Very large arrays containing O(107) of O(10 µm2)-sized photodiodespixelizing a plane are widely used to photograph all sorts of thingsfrom everyday subjects at visible wavelengths to crystal structureswith X-rays and astronomical objects from infrared to UV. To limitthe number of readout channels, these are made into charge-coupleddevices (CCD), where pixel-to-pixel signal transfer takes place overthousands of synchronous cycles with sequential output through shiftregisters [14]. Thus, high spatial resolution is achieved at the expenseof speed and timing precision. Custom-made CCD’s have virtuallyreplaced photographic plates and other imagers for astronomy andin spacecraft. Typical QE’s exceed 90% over much of the visiblespectrum, and “thick” CCD’s have useful QE up to λ = 1 µm. ActivePixel Sensor (APS) arrays with a preamplifier on each pixel andCMOS processing afford higher speeds, but are challenged at longerwavelengths. Much R&D is underway to overcome the limitations ofboth CCD and CMOS imagers.

In APD’s, an exponential cascade of impact ionizations initiatedby the original photogenerated e-h pair under a large reverse-biasvoltage leads to an avalanche breakdown [15]. As a result, detectableelectrical response can be obtained from low-intensity optical signalsdown to single photons. Excellent junction uniformity is critical, anda guard ring is generally used as a protection against edge breakdown.Well-designed APD’s, such as those used in CMS’ crystal-basedelectromagnetic calorimeter, have achieved ǫQ ǫC ≈ 0.7 with sub-nsresponse time. The sensitive wavelength window and gain depend onthe semiconductor used. The gain is typically 10–200 in linear and upto 108 in Geiger mode of operation. Stability and close monitoring ofthe operating temperature are important for linear-mode operation,and substantial cooling is often necessary. Position-sensitive APD’suse time information at multiple anodes to calculate the hit position.

One of the most promising recent developments in the field is that ofdevices consisting of large arrays (O(103)) of tiny APD’s packed overa small area (O(1 mm2)) and operated in a limited Geiger mode [16].Among different names used for this class of photodetectors, “PPD”(for “Pixelized Photon Detector”) is most widely accepted (formerly“SiPM”). Although each cell only offers a binary output, linearitywith respect to the number of photons is achieved by summing the

cell outputs in the same way as with a MCP in saturation mode(see above). PPD’s are being adopted as the preferred solution forvarious purposes including medical imaging, e.g. positron emissiontomography (PET). These compact, rugged, and economical devicesallow auto-calibration through decent separation of photoelectronpeaks and offer gains of O(106) at a moderate bias voltage (∼50 V).However, the single-photoelectron noise of a PPD, being the logical“or” of O(103) Geiger APD’s, is rather large: O(1 MHz/mm2) atroom temperature. PPD’s are particularly well-suited for applicationswhere triggered pulses of several photons are expected over a smallarea, e.g. fiber-guided scintillation light. Intense R&D is expectedto lower the noise level and improve radiation hardness, resulting incoverage of larger areas and wider applications. Attempts are beingmade to combine the fabrication of the sensors and the front-endelectronics (ASIC) in the same process with the goal of making PPD’sand other finely pixelized solid-state photodetectors extremely easy touse.

Of late, much R&D has been directed to p-i-n diode arrays basedon thin polycrystalline diamond films formed by chemical vapordeposition (CVD) on a hot substrate (∼1000 K) from a hydrocarbon-containing gas mixture under low pressure (∼100 mbar). Thesedevices have maximum sensitivity in the extreme- to moderate-UVregion [17]. Many desirable characteristics, including high toleranceto radiation and temperature fluctuations, low dark noise, blindnessto most of the solar radiation spectrum, and relatively low cost makethem ideal for space-based UV/XUV astronomy, measurement ofsynchrotron radiation, and luminosity monitoring at (future) leptoncollider(s).

Visible-light photon counters (VLPC) utilize the formation of animpurity band only 50 meV below the conduction band in As-doped Sito generate strong (G ≈ 5 × 104) yet sharp response to single photonswith ǫQ ≈ 0.9 [18]. The smallness of the band gap considerablyreduces the gain dispersion. Only a very small bias (∼7 V) isneeded, but high sensitivity to infrared photons requires cooling below10 K. The dark noise increases sharply and exponentially with bothtemperature and bias. The Run 2 DØ detector used 86000 VLPC’sto read the optical signal from its scintillating-fiber tracker andscintillator-strip preshower detectors.

34.3. Organic scintillators

Revised August 2011 by Kurtis F. Johnson (FSU).

Organic scintillators are broadly classed into three types, crystalline,liquid, and plastic, all of which utilize the ionization produced bycharged particles (see Sec. 33.2 of this Review) to generate opticalphotons, usually in the blue to green wavelength regions [19]. Plasticscintillators are by far the most widely used, liquid organic scintillatoris finding increased use, and crystal organic scintillators are practicallyunused in high-energy physics. Plastic scintillator densities range from1.03 to 1.20 g cm−3. Typical photon yields are about 1 photon per100 eV of energy deposit [20]. A one-cm-thick scintillator traversedby a minimum-ionizing particle will therefore yield ≈ 2× 104 photons.The resulting photoelectron signal will depend on the collection andtransport efficiency of the optical package and the quantum efficiencyof the photodetector.

Organic scintillator does not respond linearly to the ionizationdensity. Very dense ionization columns emit less light than expectedon the basis of dE/dx for minimum-ionizing particles. A widelyused semi-empirical model by Birks posits that recombination andquenching effects between the excited molecules reduce the lightyield [21]. These effects are more pronounced the greater the densityof the excited molecules. Birks’ formula is

dL

dx= L0

dE/dx

1 + kB dE/dx, (34.2)

where L is the luminescence, L0 is the luminescence at lowspecific ionization density, and kB is Birks’ constant, which must bedetermined for each scintillator by measurement. Decay times are inthe ns range; rise times are much faster. The high light yield and fastresponse time allow the possibility of sub-ns timing resolution [22].


The fraction of light emitted during the decay “tail” can dependon the exciting particle. This allows pulse shape discrimination as atechnique to carry out particle identification. Because of the hydrogencontent (carbon to hydrogen ratio ≈ 1) plastic scintillator is sensitiveto proton recoils from neutrons. Ease of fabrication into desiredshapes and low cost has made plastic scintillator a common detectorelement. In the form of scintillating fiber it has found widespread usein tracking and calorimetry [23].

Demand for large volume detectors has lead to increased use ofliquid organic scintillator, which has the same scintillation mechanismas plastic scintillator, due to its cost advantage. The containmentvessel defines the detector shape; photodetectors or waveshifters maybe immersed in the liquid.

34.3.1. Scintillation mechanism :

A charged particle traversing matter leaves behind it a wakeof excited molecules. Certain types of molecules, however, willrelease a small fraction (≈ 3%) of this energy as optical photons.This process, scintillation, is especially marked in those organicsubstances which contain aromatic rings, such as polystyrene (PS)and polyvinyltoluene (PVT). Liquids which scintillate include toluene,xylene and pseudocumene.

In fluorescence, the initial excitation takes place via the absorptionof a photon, and de-excitation by emission of a longer wavelengthphoton. Fluors are used as “waveshifters” to shift scintillation light toa more convenient wavelength. Occurring in complex molecules, theabsorption and emission are spread out over a wide band of photonenergies, and have some overlap, that is, there is some fraction of theemitted light which can be re-absorbed [24]. This “self-absorption”is undesirable for detector applications because it causes a shortenedattenuation length. The wavelength difference between the majorabsorption and emission peaks is called the Stokes’ shift. It is usuallythe case that the greater the Stokes’ shift, the smaller the selfabsorption thus, a large Stokes’ shift is a desirable property for a fluor.

Ionization excitation of base plastic

Forster energy transfer

γ

γ

base plastic

primary fluor (~1% wt/wt )

secondary fluor (~0.05% wt/wt )

photodetector

emit UV, ~340 nm

absorb blue photon

absorb UV photon

emit blue, ~400 nm

1 m

10−4m

10−8m

Figure 34.1: Cartoon of scintillation “ladder” depicting theoperating mechanism of organic scintillator. Approximate fluorconcentrations and energy transfer distances for the separatesub-processes are shown.

The plastic scintillators used in high-energy physics are binaryor ternary solutions of selected fluors in a plastic base containingaromatic rings. (See the appendix in Ref. 25 for a comprehensive listof components.) Virtually all plastic scintillators contain as a baseeither PVT or PS. PVT-based scintillator can be up to 50% brighter.

Ionization in the plastic base produces UV photons with shortattenuation length (several mm). Longer attenuation lengths areobtained by dissolving a “primary” fluor in high concentration (1%by weight) into the base, which is selected to efficiently re-radiateabsorbed energy at wavelengths where the base is more transparent(see Fig. 34.1).

The primary fluor has a second important function. The decay timeof the scintillator base material can be quite long – in pure polystyreneit is 16 ns, for example. The addition of the primary fluor in highconcentration can shorten the decay time by an order of magnitudeand increase the total light yield. At the concentrations used (1% and

greater), the average distance between a fluor molecule and an excitedbase unit is around 100 A, much less than a wavelength of light. Atthese distances the predominant mode of energy transfer from base tofluor is not the radiation of a photon, but a resonant dipole-dipoleinteraction, first described by Foerster, which strongly couples thebase and fluor [26]. The strong coupling sharply increases the speedand the light yield of the plastic scintillators.

Unfortunately, a fluor which fulfills other requirements is usuallynot completely adequate with respect to emission wavelength orattenuation length, so it is necessary to add yet another waveshifter(the “secondary” fluor), at fractional percent levels, and occasionallya third (not shown in Fig. 34.1).

External wavelength shifters are widely used to aid light collectionin complex geometries. Scintillation light is captured by a lightpipecomprising a wave-shifting fluor dissolved in a nonscintillating base.The wavelength shifter must be insensitive to ionizing radiation andCherenkov light. A typical wavelength shifter uses an acrylic basebecause of its good optical qualities, a single fluor to shift the lightemerging from the plastic scintillator to the blue-green, and containsultra-violet absorbing additives to deaden response to Cherenkov light.

34.3.2. Caveats and cautions :

Plastic scintillators are reliable, robust, and convenient. However,they possess quirks to which the experimenter must be alert. Exposureto solvent vapors, high temperatures, mechanical flexing, irradiation,or rough handling will aggravate the process. A particularly fragileregion is the surface which can “craze” develop microcracks whichdegrade its transmission of light by total internal reflection. Crazing isparticularly likely where oils, solvents, or fingerprints have contactedthe surface.

They have a long-lived luminescence which does not follow asimple exponential decay. Intensities at the 10−4 level of the initialfluorescence can persist for hundreds of ns [19,27].

They will decrease their light yield with increasing partial pressureof oxygen. This can be a 10% effect in an artificial atmosphere [28].It is not excluded that other gases may have similar quenching effects.

Their light yield may be changed by a magnetic field. The effectis very nonlinear and apparently not all types of plastic scintillatorsare so affected. Increases of ≈ 3% at 0.45 T have been reported [29].Data are sketchy and mechanisms are not understood.

Irradiation of plastic scintillators creates color centers which absorblight more strongly in the UV and blue than at longer wavelengths.This poorly understood effect appears as a reduction both of light yieldand attenuation length. Radiation damage depends not only on theintegrated dose, but on the dose rate, atmosphere, and temperature,before, during and after irradiation, as well as the materials propertiesof the base such as glass transition temperature, polymer chain length,etc. Annealing also occurs, accelerated by the diffusion of atmosphericoxygen and elevated temperatures. The phenomena are complex,unpredictable, and not well understood [30]. Since color centers areless disruptive at longer wavelengths, the most reliable method ofmitigating radiation damage is to shift emissions at every step to thelongest practical wavelengths, e.g., utilize fluors with large Stokes’shifts (aka the “Better red than dead” strategy).

34.3.3. Scintillating and wavelength-shifting fibers :

The clad optical fiber comprising scintillator and wavelength shifter(WLS) is particularly useful [31]. Since the initial demonstrationof the scintillating fiber (SCIFI) calorimeter [32], SCIFI techniqueshave become mainstream [33]. SCIFI calorimeters are fast, dense,radiation hard, and can have leadglass-like resolution. SCIFI trackerscan handle high rates and are radiation tolerant, but the low photonyield at the end of a long fiber (see below) forces the use of sensitivephotodetectors. WLS scintillator readout of a calorimeter allows avery high level of hermeticity since the solid angle blocked by the fiberon its way to the photodetector is very small. The sensitive regionof scintillating fibers can be controlled by splicing them onto clear(non-scintillating/non-WLS) fibers.

A typical configuration would be fibers with a core of polystyrene-based scintillator or WLS (index of refraction n = 1.59), surrounded


by a cladding of PMMA (n = 1.49) a few microns thick, or, foradded light capture, with another cladding of fluorinated PMMA withn = 1.42, for an overall diameter of 0.5 to 1 mm. The fiber is drawnfrom a boule and great care is taken during production to ensure thatthe intersurface between the core and the cladding has the highestpossible uniformity and quality, so that the signal transmission viatotal internal reflection has a low loss. The fraction of generated lightwhich is transported down the optical pipe is denoted the capturefraction and is about 6% for the single-clad fiber and 10% for thedouble-clad fiber. The number of photons from the fiber available atthe photodetector is always smaller than desired, and increasing thelight yield has proven difficult. A minimum-ionizing particle traversinga high-quality 1 mm diameter fiber perpendicular to its axis willproduce fewer than 2000 photons, of which about 200 are captured.Attenuation may eliminate 95% of these photons in a large collidertracker.

A scintillating or WLS fiber is often characterized by its attenuationlength, over which the signal is attenuated to 1/e of its originalvalue. Many factors determine the attenuation length, including theimportance of re-absorption of emitted photons by the polymer baseor dissolved fluors, the level of crystallinity of the base polymer, andthe quality of the total internal reflection boundary [34]. Attenuationlengths of several meters are obtained by high quality fibers. However,it should be understood that the attenuation length is not the solemeasure of fiber quality. Among other things, it is not constant withdistance from the excitation source and it is wavelength dependent.

34.4. Inorganic scintillators

Revised November 2015 by R.-Y. Zhu (California Institute ofTechnology) and C.L. Woody (BNL).

Inorganic crystals form a class of scintillating materials with muchhigher densities than organic plastic scintillators (typically ∼ 4–8g/cm3) with a variety of different properties for use as scintillationdetectors. Due to their high density and high effective atomic number,they can be used in applications where high stopping power or ahigh conversion efficiency for electrons or photons is required. Theseinclude total absorption electromagnetic calorimeters (see Sec. 34.9.1),which consist of a totally active absorber (as opposed to a samplingcalorimeter), as well as serving as gamma ray detectors over a widerange of energies. Many of these crystals also have very high lightoutput, and can therefore provide excellent energy resolution down tovery low energies (∼ few hundred keV).

Some crystals are intrinsic scintillators in which the luminescence isproduced by a part of the crystal lattice itself. However, other crystalsrequire the addition of a dopant, typically fluorescent ions such asthallium (Tl) or cerium (Ce) which is responsible for producing thescintillation light. However, in both cases, the scintillation mechanismis the same. Energy is deposited in the crystal by ionization, eitherdirectly by charged particles, or by the conversion of photons intoelectrons or positrons which subsequently produce ionization. Thisenergy is transferred to the luminescent centers which then radiatescintillation photons. The light yield L in terms of the number ofscintillation photons produced per MeV of energy deposit in thecrystal can be expressed as [35]

L = 106 S · Q/(β · Eg), (34.3)

where β · Eg is is the energy required to create an e-h pair expressedas a multiple of the band gap energy Eg (eV), S is the efficiencyof energy transfer to the luminescent center and Q is the quantumefficiency of the luminescent center. The values of β, S and Q arecrystal dependent and are the main factors in determining the intrinsiclight yield of the scintillator. The decay time of the scintillator ismainly dominated by the decay time of the luminescent center.

Table 34.4 lists the basic properties of some commonly usedinorganic crystals. NaI(Tl) is one of the most common and widelyused scintillators, with an emission that is well matched to a bialkaliphotomultiplier tube, but it is highly hygroscopic and difficult to workwith, and has a rather low density. CsI(Tl) and CsI(Na) have highlight yield, low cost, and are mechanically robust (high plasticity and

resistance to cracking). However, they need careful surface treatmentand are slightly and highly hygroscopic respectively. Pure CsI hasidentical mechanical properties as CsI(Tl), but faster emission atshorter wavelength and a much lower light output. BaF2 has a fastcomponent with a sub-nanosecond decay time, and is the fastestknown scintillator. However, it also has a slow component with amuch longer decay time (∼ 630 ns). Bismuth gemanate (Bi4Ge3O12

or BGO) has a high density, and consequently a short radiation lengthX0 and Moliere radius RM . Similar to CsI(Tl), BGO’s emission iswell-matched to the spectral sensitivity of photodiodes, and it is easyto handle and not hygroscopic. Lead tungstate (PbWO4 or PWO) hasa very high density, with a very short X0 and RM , but its intrinsiclight yield is rather low.

Cerium doped lutetium oxyorthosilicate (Lu2SiO5:Ce, orLSO:Ce) [36] and cerium doped lutetium-yttrium oxyorthosili-cate (Lu2(1−x)Y2xSiO5, LYSO:Ce) [37] are dense crystal scintillatorswhich have a high light yield and a fast decay time. Only theproperties of LSO:Ce are listed in Table 34.4 since the propertiesof LYSO:Ce are similar to that of LSO:Ce except a slightly lowerdensity than LSO:Ce depending on the yttrium fraction in LYSO:Ce.This material is also featured with excellent radiation hardness [38],so is expected to be used where extraordinary radiation hardness isrequired.

Also listed in Table 34.4 are other fluoride crystals such as PbF2 asa Cherenkov material and CeF3, which have been shown to provideexcellent energy resolution in calorimeter applications. Table 34.4also includes cerium doped lanthanum tri-halides, such as LaBr3 [39]and CeBr3 [40], which are brighter and faster than LSO:Ce, butthey are highly hygroscopic and have a lower density. The FWHMenergy resolution measured for these materials coupled to a PMT withbi-alkali photocathode for 0.662 MeV γ-rays from a 137Cs source isabout 3%, and has recently been improved to 2% by co-doping withcerium and strontium [41], which is the best among all inorganiccrystal scintillators. For this reason, LaBr3 and CeBr3 are expected tobe used in applications where a good energy resolution for low energyphotons are required, such as homeland security.

Beside the crystals listed in Table 34.4, a number of new crystals arebeing developed that may have potential applications in high energyor nuclear physics. Of particular interest is the family of yttriumand lutetium perovskites and garnet, which include YAP (YAlO3:Ce),LuAP (LuAlO3:Ce), YAG (Y3Al5O12:Ce) and LuAG (Lu3Al5O12:Ce)and their mixed compositions. These have been shown to be linearover a large energy range [42], and have the potential for providinggood intrinsic energy resolution.

Aiming at the best jet-mass resolution inorganic scintillators arebeing investigated for HEP calorimeters with dual readout for bothCherenkov and scintillation light to be used at future linear colliders.These materials may be used for an electromagnetic calorimeter [43]or a homogeneous hadronic calorimetry (HHCAL) detector concept,including both electromagnetic and hadronic parts [44]. Because ofthe unprecedented volume (70 to 100 m3) foreseen for the HHCALdetector concept the materials must be (1) dense (to minimize theleakage) and (2) cost-effective. It should also be UV transparent(for effective collection of the Cherenkov light) and allow for a cleardiscrimination between the Cherenkov and scintillation light. Thepreferred scintillation light is thus at a longer wavelength, and notnecessarily bright or fast. Dense crystals, scintillating glasses andceramics offer a very attractive implementation for this detectorconcept [45].

The fast scintillation light provides timing information aboutelectromagnetic interactions and showers, which may be used tomitigate pile-up effects and/or for particle identification since thetime development of electromagnetic and hadronic showers, as wellas minimum ionizing particles, are different. The timing informationis primarily determined by the scintillator rise time and decay time,and the number of photons produced. For fast timing, it is importantto have a large number of photons emitted in the initial part of thescintillation pulse, e.g. in the first ns, since one is often measuringthe arrival time of the particle in the crystal using the leading edgeof the light pulse. A good example of this is BaF2, which has ∼ 10%of its light in its fast component with a decay time of < 1 ns. The


light propagation can spread out the arrival time of the scintillationphotons at the photodetector due to time dispersion [46]. The timeresponse of the photodetector also plays a major role in achievinggood time resolution with fast scintillating crystals.

Table 34.4 gives the light output of other crystals relative to NaI(Tl)and their dependence to the temperature variations measured for 1.5X0 cube crystal samples with a Tyvek paper wrapping and a full endface coupled to a photodetector [47]. The quantum efficiencies of thephotodetector is taken out to facilitate a direct comparison of crystal’slight output. However, the useful signal produced by a scintillatoris usually quoted in terms of the number of photoelectrons perMeV produced by a given photodetector. The relationship betweenthe number of photons/MeV produced (L) and photoelectrons/MeVdetected (Np.e./MeV) involves the factors for the light collectionefficiency (LC) and the quantum efficiency (QE) of the photodetector:

Np.e./MeV = L · LC · QE. (34.4)

LC depends on the size and shape of the crystal, and includeseffects such as the transmission of scintillation light within the crystal(i.e., the bulk attenuation length of the material), scattering fromwithin the crystal, reflections and scattering from the crystal surfaces,and re-bouncing back into the crystal by wrapping materials. Thesefactors can vary considerably depending on the sample, but can be inthe range of ∼10–60%. The internal light transmission depends on theintrinsic properties of the material, e.g. the density and type of thescattering centers and defects that can produce internal absorptionwithin the crystal, and can be highly affected by factors such asradiation damage, as discussed below.

The quantum efficiency depends on the type of photodetectorused to detect the scintillation light, which is typically ∼15–30% forphotomultiplier tubes and ∼70% for silicon photodiodes for visiblewavelengths. The quantum efficiency of the detector is usually highlywavelength dependent and should be matched to the particular crystalof interest to give the highest quantum yield at the wavelength

Table 34.4: Properties of several inorganic crystals. Most of thenotation is defined in Sec. 6 of this Review.

Parameter: ρ MP X∗0 R∗

M dE∗/dx λ∗I τdecay λmax n Relative Hygro- d(LY)/dT

output† scopic?Units: g/cm3 C cm cm MeV/cm cm ns nm %/C‡

NaI(Tl) 3.67 651 2.59 4.13 4.8 42.9 245 410 1.85 100 yes −0.2

BGO 7.13 1050 1.12 2.23 9.0 22.8 300 480 2.15 21 no −0.9

BaF2 4.89 1280 2.03 3.10 6.5 30.7 650s 300s 1.50 36s no −1.9s

0.9f 220f 4.1f 0.1f

CsI(Tl) 4.51 621 1.86 3.57 5.6 39.3 1220 550 1.79 165 slight 0.4

CsI(Na) 4.51 621 1.86 3.57 5.6 39.3 690 420 1.84 88 yes 0.4

CsI(pure) 4.51 621 1.86 3.57 5.6 39.3 30s 310 1.95 3.6s slight −1.4

6f 1.1f

PbWO4 8.30 1123 0.89 2.00 10.1 20.7 30s 425s 2.20 0.3s no −2.5

10f 420f 0.077f

LSO(Ce) 7.40 2050 1.14 2.07 9.6 20.9 40 402 1.82 85 no −0.2

PbF2 7.77 824 0.93 2.21 9.4 21.0 - - - Cherenkov no -

CeF3 6.16 1460 1.70 2.41 8.42 23.2 30 340 1.62 7.3 no 0

LaBr3(Ce) 5.29 783 1.88 2.85 6.90 30.4 20 356 1.9 180 yes 0.2

CeBr3 5.23 722 1.96 2.97 6.65 31.5 17 371 1.9 165 yes −0.1

∗ Numerical values calculated using formulae in this review. Refractive index at the wavelength of the emission maximum.† Relative light output measured for samples of 1.5 X0 cube with aTyvek paper wrapping and a full end face coupled to a photodetector.The quantum efficiencies of the photodetector are taken out.‡ Variation of light yield with temperature evaluated at the roomtemperature.f = fast component, s = slow component

corresponding to the peak of the scintillation emission. Fig. 34.2 showsthe quantum efficiencies of two photodetectors, a Hamamatsu R2059PMT with bi-alkali cathode and quartz window and a HamamatsuS8664 avalanche photodiode (APD) as a function of wavelength. Alsoshown in the figure are emission spectra of three crystal scintillators,BGO, LSO:Ce/LYSO:Ce and CsI(Tl), and the numerical valuesof the emission weighted quantum efficiency. The area under eachemission spectrum is proportional to crystal’s light yield, as shownin Table 34.4, where the quantum efficiencies of the photodetectorhas been taken out. Results with different photodetectors can besignificantly different. For example, the response of CsI(Tl) relativeto NaI(Tl) with a standard photomultiplier tube with a bi-alkaliphoto-cathode, e.g. Hamamatsu R2059, would be 45 rather than 165because of the photomultiplier’s low quantum efficiency at longerwavelengths. For scintillators which emit in the UV, a detector with aquartz window should be used.

For very low energy applications (typically below 1 MeV), non-proportionality of the scintillation light yield may be important. Ithas been known for a long time that the conversion factor betweenthe energy deposited in a crystal scintillator and the number ofphotons produced is not constant. It is also known that the energyresolution measured by all crystal scintillators for low energy γ-rays issignificantly worse than the contribution from photo-electron statisticsalone, indicating an intrinsic contribution from the scintillator itself.Precision measurement using low energy electron beam shows thatthis non-proportionality is crystal dependent [48]. Recent study onthis issue also shows that this effect is also sample dependent evenfor the same crystal [49]. Further work is therefore needed to fullyunderstand this subject.

One important issue related to the application of a crystalscintillator is its radiation hardness. Stability of its light output, orthe ability to track and monitor the variation of its light output in aradiation environment, is required for high resolution and precisioncalibration [50]. All known crystal scintillators suffer from ionizationdose induced radiation damage [51], where a common damage


phenomenon is the appearance of radiation induced absorption causedby the formation of color centers originated from the impuritiesor point defects in the crystal. This radiation induced absorptionreduces the light attenuation length in the crystal, and hence itslight output. For crystals with high defect density, a severe reductionof light attenuation length may cause a distortion of the lightresponse uniformity, leading to a degradation of the energy resolution.Additional radiation damage effects may include a reduced intrinsicscintillation light yield (damage to the luminescent centers) and anincreased phosphorescence (afterglow). For crystals to be used in ahigh precision calorimeter in a radiation environment, its scintillationmechanism must not be damaged and its light attenuation length inthe expected radiation environment must be long enough so that itslight response uniformity, and thus its energy resolution, does notchange.

7

Figure 34.2: The quantum efficiencies of two photodetectors,a Hamamatsu R2059 PMT with bi-alkali cathode and aHamamatsu S8664 avalanche photodiode (APD), are shownas a function of wavelength. Also shown in the figure areemission spectra of three crystal scintillators, BGO, LSO andCsI(Tl), and the numerical values of the emission weightedquantum efficiencies. The area under each emission spectrum isproportional to crystal’s light yield.

While radiation damage induced by ionization dose is wellunderstood [52], investigation is on-going to understand radiationdamage caused by hadrons, including both charged hadrons andneutrons. Two additional fundamental processes may cause defects byhadrons: displacement damage and nuclear breakup. While chargedhadrons can produce all three types of damage (and it’s often difficultto separate them), neutrons can produce only the last two, andelectrons and photons only produce ionization damage. Studies onhadron induced radiation damage to lead tungstate [53] show aproton-specific damage component caused by fragments from fissioninduced in lead and tungsten by particles in the hadronic shower. Thefragments cause a severe, local damage to the crystalline lattice due totheir extremely high energy loss over a short distance [53]. Studieson neutron-specific damage in lead tungstate [54] up to 4×1019 n/cm2

show no neutron-specific damage in PWO [55].

Most of the crystals listed in Table 34.4 have been used in highenergy or nuclear physics experiments when the ultimate energyresolution for electrons and photons is desired. Examples are theCrystal Ball NaI(Tl) calorimeter at SPEAR, the L3 BGO calorimeterat LEP, the CLEO CsI(Tl) calorimeter at CESR, the KTeV CsIcalorimeter at the Tevatron, the BaBar, BELLE and BES II CsI(Tl)calorimeters at PEP-II, KEK and BEPC III. Because of their highdensity and relative low cost, PWO calorimeters are used by CMS andALICE at LHC, by CLAS and PrimEx at CEBAF and by PANDA atGSI, and PbF2 calorimeters are used by the A4 experiment at MAINZ

and by the g-2 experiment at Fermilab. A LYSO:Ce calorimeter isbeing constructed by the COMET experiment at J-PARC.

34.5. Cherenkov detectors

Revised August 2015 by B.N. Ratcliff (SLAC).

Although devices using Cherenkov radiation are often thought of asonly particle identification (PID) detectors, in practice they are usedover a much broader range of applications including; (1) fast particlecounters; (2) hadronic PID; and (3) tracking detectors performingcomplete event reconstruction. Examples of applications from eachcategory include; (1) the Quartic fast timing counter designed tomeasure small angle scatters at the LHC [56]; (2) the hadronicPID detectors at the B factory detectors—DIRC in BaBar [57] andthe aerogel threshold Cherenkov in Belle [58]; and (3) large waterCherenkov counters such as Super-Kamiokande [59]. Cherenkovcounters contain two main elements; (1) a radiator through whichthe charged particle passes, and (2) a photodetector. As Cherenkovradiation is a weak source of photons, light collection and detectionmust be as efficient as possible. The refractive index n and theparticle’s path length through the radiator L appear in the Cherenkovrelations allowing the tuning of these quantities for particularapplications.

Cherenkov detectors utilize one or more of the properties ofCherenkov radiation discussed in the Passages of Particles throughMatter section (Sec. 33 of this Review): the prompt emission of alight pulse; the existence of a velocity threshold for radiation; andthe dependence of the Cherenkov cone half-angle θc and the numberof emitted photons on the velocity of the particle and the refractiveindex of the medium.

The number of photoelectrons (Np.e.) detected in a given device is

Np.e. = Lα2z2

re mec2

∫

ǫ(E) sin2 θc(E)dE , (34.5)

where ǫ(E) is the efficiency for collecting the Cherenkov light andtransducing it into photoelectrons, and α2/(re mec

2) = 370 cm−1eV−1.

The quantities ǫ and θc are functions of the photon energy E. Asthe typical energy dependent variation of the index of refraction ismodest, a quantity called the Cherenkov detector quality factor N0 canbe defined as

N0 =α2z2

re mec2

∫

ǫ dE , (34.6)

so that, taking z = 1 (the usual case in high-energy physics),

Np.e. ≈ LN0〈sin2 θc〉 . (34.7)

This definition of the quality factor N0 is not universal, nor,indeed, very useful for those common situations where ǫ factorizes asǫ = ǫcollǫdet with the geometrical photon collection efficiency (ǫcoll)varying substantially for different tracks while the photon detectorefficiency (ǫdet) remains nearly track independent. In this case, itcan be useful to explicitly remove (ǫcoll) from the definition of N0.A typical value of N0 for a photomultiplier (PMT) detection systemworking in the visible and near UV, and collecting most of theCherenkov light, is about 100 cm−1. Practical counters, utilizinga variety of different photodetectors, have values ranging betweenabout 30 and 180 cm−1. Radiators can be chosen from a varietyof transparent materials (Sec. 33 of this Review and Table 6.1). Inaddition to refractive index, the choice requires consideration of factorssuch as material density, radiation length and radiation hardness,transmission bandwidth, absorption length, chromatic dispersion,optical workability (for solids), availability, and cost. When themomenta of particles to be identified is high, the refractive index mustbe set close to one, so that the photon yield per unit length is lowand a long particle path in the radiator is required. Recently, the gapin refractive index that has traditionally existed between gases andliquid or solid materials has been partially closed with transparentsilica aerogels with indices that range between about 1.007 and 1.13.

Cherenkov counters may be classified as either imaging or threshold

types, depending on whether they do or do not make use of Cherenkov


angle (θc) information. Imaging counters may be used to trackparticles as well as identify them. The recent development of very fastphotodetectors such as micro-channel plate PMTs (MCP PMT) (seeSec. 34.2 of this Review) also potentially allows very fast Cherenkovbased time of flight (TOF) detectors of either class [60]. The tracktiming resolution of imaging detectors can be extremely good as itscales approximately as 1√

Np.e..

Threshold Cherenkov detectors [61], in their simplest form, makea yes/no decision based on whether the particle is above orbelow the Cherenkov threshold velocity βt = 1/n. A straightforwardenhancement of such detectors uses the number of observedphotoelectrons (or a calibrated pulse height) to discriminate betweenspecies or to set probabilities for each particle species [62]. Thisstrategy can increase the momentum range of particle separation bya modest amount (to a momentum some 20% above the thresholdmomentum of the heavier particle in a typical case).

Careful designs give 〈ǫcoll〉& 90%. For a photomultiplier with atypical bialkali cathode,

∫

ǫdetdE ≈ 0.27 eV, so that

Np.e./L ≈ 90 cm−1 〈sin2 θc〉 (i.e., N0 = 90 cm−1) . (34.8)

Suppose, for example, that n is chosen so that the threshold for speciesa is pt; that is, at this momentum species a has velocity βa = 1/n. Asecond, lighter, species b with the same momentum has velocity βb, socos θc = βa/βb, and

Np.e./L ≈ 90 cm−1 m2a − m2

b

p2t + m2

a

. (34.9)

For K/π separation at p = pt = 1(5) GeV/c, Np.e./L ≈ 16(0.8) cm−1

for π’s and (by design) 0 for K’s.

For limited path lengths Np.e. will usually be small. The overallefficiency of the device is controlled by Poisson fluctuations, whichcan be especially critical for separation of species where one particletype is dominant. Moreover, the effective number of photoelectrons isoften less than the average number calculated above due to additionalequivalent noise from the photodetector (see the discussion of theexcess noise factor in Sec. 34.2 of this Review). It is common todesign for at least 10 photoelectrons for the high velocity particlein order to obtain a robust counter. As rejection of the particlethat is below threshold depends on not seeing a signal, electronicand other background noise, especially overlapping tracks, can beimportant. Physics sources of light production for the below thresholdparticle, such as decay to an above threshold particle, scintillationlight, or the production of delta rays in the radiator, often limitthe separation attainable, and need to be carefully considered. Welldesigned, modern multi-channel counters, such as the ACC at Belle[58], can attain adequate particle separation performance over asubstantial momentum range.

Imaging counters make the most powerful use of the informationavailable by measuring the ring-correlated angles of emission of theindividual Cherenkov photons. They typically provide positive IDinformation both for the “wanted” and the “unwanted” particles, thusreducing mis-identification substantially. Since low-energy photondetectors can measure only the position (and, perhaps, a precisedetection time) of the individual Cherenkov photons (not the anglesdirectly), the photons must be “imaged” onto a detector so that theirangles can be derived [63]. Typically the optics map the Cherenkovcone onto (a portion of) a distorted “circle” at the photodetector.Though the imaging process is directly analogous to familiar imagingtechniques used in telescopes and other optical instruments, there isa somewhat bewildering variety of methods used in a wide varietyof counter types with different names. Some of the imaging methodsused include (1) focusing by a lens or mirror; (2) proximity focusing(i.e., focusing by limiting the emission region of the radiation); and(3) focusing through an aperture (a pinhole). In addition, the promptCherenkov emission coupled with the speed of some modern photondetectors allows the use of (4) time imaging, a method which islittle used in conventional imaging technology, and may allow someseparation with particle TOF. Finally, (5) correlated tracking (and

event reconstruction) can be performed in large water counters bycombining the individual space position and time of each photontogether with the constraint that Cherenkov photons are emitted fromeach track at the same polar angle (Sec. 35.3.1 of this Review).

In a simple model of an imaging PID counter, the fractional erroron the particle velocity (δβ) is given by

δβ =σβ

β= tan θcσ(θc) , (34.10)

where

σ(θc) =〈σ(θi)〉√

Np.e.⊕ C , (34.11)

and 〈σ(θi)〉 is the average single photoelectron resolution, as definedby the optics, detector resolution and the intrinsic chromaticityspread of the radiator index of refraction averaged over the photondetection bandwidth. C combines a number of other contributions toresolution including, (1) correlated terms such as tracking, alignment,and multiple scattering, (2) hit ambiguities, (3) background hits fromrandom sources, and (4) hits coming from other tracks. The actualseparation performance is also limited by physics effects such as decaysin flight and particle interactions in the material of the detector. Inmany practical cases, the performance is limited by these effects.

For a β ≈ 1 particle of momentum (p) well above threshold enteringa radiator with index of refraction (n), the number of σ separation(Nσ) between particles of mass m1 and m2 is approximately

Nσ ≈ |m21 − m2

2|2p2σ(θc)

√n2 − 1

. (34.12)

In practical counters, the angular resolution term σ(θc) variesbetween about 0.1 and 5 mrad depending on the size, radiator, andphotodetector type of the particular counter. The range of momentaover which a particular counter can separate particle species extendsfrom the point at which the number of photons emitted becomessufficient for the counter to operate efficiently as a threshold device(∼20% above the threshold for the lighter species) to the value inthe imaging region given by the equation above. For example, forσ(θc) = 2mrad, a fused silica radiator(n = 1.474), or a fluorocarbongas radiator (C5F12, n = 1.0017), would separate π/K’s from thethreshold region starting around 0.15(3) GeV/c through the imagingregion up to about 4.2(18) GeV/c at better than 3σ.

Many different imaging counters have been built during the last sev-eral decades [60]. Among the earliest examples of this class of countersare the very limited acceptance Differential Cherenkov detectors,designed for particle selection in high momentum beam lines. Thesedevices use optical focusing and/or geometrical masking to selectparticles having velocities in a specified region. With careful design, avelocity resolution of σβ/β ≈ 10−4–10−5 can be obtained [61].

Practical multi-track Ring-Imaging Cherenkov detectors (generi-cally called RICH counters) are a more recent development. RICHcounters are sometimes further classified by ‘generations’ that differbased on historical timing, performance, design, and photodetectiontechniques.

Prototypical examples of first generation RICH counters are thoseused in the DELPHI and SLD detectors at the LEP and SLC Z factorye+e− colliders [60]. They have both liquid (C6F14, n = 1.276)and gas (C5F12, n = 1.0017) radiators, the former being proximityimaged with the latter using mirrors. The phototransducers are aTPC/wire-chamber combination. They are made sensitive to photonsby doping the TPC gas (usually, ethane/methane) with ∼ 0.05%TMAE (tetrakis(dimethylamino)ethylene). Great attention to detailis required, (1) to avoid absorbing the UV photons to which TMAEis sensitive, (2) to avoid absorbing the single photoelectrons as theydrift in the long TPC, and (3) to keep the chemically active TMAEvapor from interacting with materials in the system. In spite of theirunforgiving operational characteristics, these counters attained goode/π/K/p separation over wide momentum ranges (from about 0.25to 20 GeV/c) during several years of operation at LEP and SLC.Related but smaller acceptance devices include the OMEGA RICH


at the CERN SPS, and the RICH in the balloon-borne CAPRICEdetector [60].

Later generation counters [60] generally operate at much higherrates, with more detection channels, than the first generation detectorsjust described. They also utilize faster, more forgiving photondetectors, covering different photon detection bandwidths. Radiatorchoices have broadened to include materials such as lithium fluoride,fused silica, and aerogel. Vacuum based photodetection systems (e.g.,single or multi anode PMTs, MCP PMTs, or hybrid photodiodes(HPD)) have become increasingly common (see Sec. 34.2 of thisReview). They handle high rates, and can be used with a wide choiceof radiators. Examples include (1) the SELEX RICH at Fermilab,which mirror focuses the Cherenkov photons from a neon radiatoronto a camera array made of ∼ 2000 PMTs to separate hadrons over awide momentum range (to well above 200 GeV/c for heavy hadrons);(2) the HERMES RICH at HERA, which mirror focuses photons fromC4F10(n = 1.00137) and aerogel(n = 1.0304) radiators within thesame volume onto a PMT camera array to separate hadrons in themomentum range from 2 to 15 GeV/c; and (3) the LHCb detectornow running at the LHC. It uses two separate counters readout byhybrid PMTs. One volume, like HERMES, contains two radiators(aerogel and C4F10) while the second volume contains CF4. Photonsare mirror focused onto detector arrays of HPDs to cover a π/Kseparation momentum range between 1 and 150 GeV/c. This devicewill be upgraded to deal with the higher luminosities provided byLHC after 2018 by modifying the optics and removing the aerogelradiator of the upstream RICH and replacing the Hybrid PMTs withmulti-anode PMTs (MaPMTs).

Other fast detection systems that use solid cesium iodide (CsI)photocathodes or triethylamine (TEA) doping in proportionalchambers are useful with certain radiator types and geometries.Examples include (1) the CLEO-III RICH at CESR that uses a LiFradiator with TEA doped proportional chambers; (2) the ALICEdetector at the LHC that uses proximity focused liquid (C6F14

radiators and solid CSI photocathodes (similar photodectors havebeen used for several years by the HADES and COMPASS detectors),and the hadron blind detector (HBD) in the PHENIX detector atRHIC that couples a low index CF4 radiator to a photodetectorbased on electron multiplier (GEM) chambers with reflective CSIphotocathodes [60].

A DIRC (Detection [of] Internally Reflected Cherenkov [light])is a distinctive, compact RICH subtype first used in the BaBardetector [57,60]. A DIRC “inverts” the usual RICH principle foruse of light from the radiator by collecting and imaging the totalinternally reflected light rather than the transmitted light. It utilizesthe optical material of the radiator in two ways, simultaneously;first as a Cherenkov radiator, and second, as a light pipe. Themagnitudes of the photon angles are preserved during transport bythe flat, rectangular cross section radiators, allowing the photons tobe efficiently transported to a detector outside the path of the particlewhere they may be imaged in up to three independent dimensions (theusual two in space and, due to the long photon paths lengths, one intime). Because the index of refraction in the radiator is large (∼ 1.48for fused silica), light collection efficiency is good, but the momentumrange with good π/K separation is rather low. The BaBar DIRCrange extends up to ∼ 4 GeV/c. It is plausible, but challenging,to extend it up to about 10 GeV/c with an improved design. NewDIRC detectors are being developed that take advantage of the new,very fast, pixelated photodetectors becoming available, such as flatpanel MaPMTs and MCP PMTs. They typically utilize either timeimaging or mirror focused optics, or both, leading not only to aprecision measurement of the Cherenkov angle, but in some cases,to a precise measurement of the particle TOF, and/or to correctionof the chromatic dispersion in the radiator. Examples [60] include(1) the time of propagation (TOP) counter being fabricated for theBELLE-II upgrade at KEKB emphasizing precision timing for bothCherenkov imaging and TOF, which is scheduled for installation in2016; (2) the full scale 3-dimensional imaging FDIRC prototype usingthe BaBar DIRC radiators which was designed for the SuperB detectorat the Italian SuperB collider and uses precision timing not only forimproving the angle reconstruction and TOF precision, but also to

correct the chromatic dispersion; (3) the DIRCs being developed forthe PANDA detector at FAIR that use elegant focusing optics andfast timing; and (4) the TORCH proposal being developed for anLHCb upgrade after 2019 which uses DIRC imaging with fast photondetectors to provide particle separation via particle TOF over a pathlength of 9.5m.

34.6. Gaseous detectors

34.6.1. Energy loss and charge transport in gases : RevisedMarch 2010 by F. Sauli (CERN) and M. Titov (CEA Saclay).

Gas-filled detectors localize the ionization produced by chargedparticles, generally after charge multiplication. The statistics ofionization processes having asymmetries in the ionization trails, affectthe coordinate determination deduced from the measurement of drifttime, or of the center of gravity of the collected charge. For thin gaslayers, the width of the energy loss distribution can be larger thanits average, requiring multiple sample or truncated mean analysis toachieve good particle identification. In the truncated mean methodfor calculating 〈dE/dx〉, the ionization measurements along the tracklength are broken into many samples and then a fixed fraction ofhigh-side (and sometimes also low-side) values are rejected [64].

The energy loss of charged particles and photons in matter isdiscussed in Sec. 33. Table 34.5 provides values of relevant parametersin some commonly used gases at NTP (normal temperature, 20 C,and pressure, 1 atm) for unit-charge minimum-ionizing particles(MIPs) [65–71]. Values often differ, depending on the source, sothose in the table should be taken only as approximate. For differentconditions and for mixtures, and neglecting internal energy transferprocesses (e.g., Penning effect), one can scale the density, NP , and NT

with temperature and pressure assuming a perfect gas law.

Table 34.5: Properties of noble and molecular gases at normaltemperature and pressure (NTP: 20 C, one atm). EX , EI : firstexcitation, ionization energy; WI : average energy per ion pair;dE/dx|min, NP , NT : differential energy loss, primary and totalnumber of electron-ion pairs per cm, for unit charge minimumionizing particles.

Gas Density, Ex EI WI dE/dx|min NP NT

mg cm−3 eV eV eV keVcm−1 cm−1 cm−1

He 0.179 19.8 24.6 41.3 0.32 3.5 8

Ne 0.839 16.7 21.6 37 1.45 13 40

Ar 1.66 11.6 15.7 26 2.53 25 97

Xe 5.495 8.4 12.1 22 6.87 41 312

CH4 0.667 8.8 12.6 30 1.61 28 54

C2H6 1.26 8.2 11.5 26 2.91 48 112

iC4H10 2.49 6.5 10.6 26 5.67 90 220

CO2 1.84 7.0 13.8 34 3.35 35 100

CF4 3.78 10.0 16.0 54 6.38 63 120

When an ionizing particle passes through the gas it createselectron-ion pairs, but often the ejected electrons have sufficientenergy to further ionize the medium. As shown in Table 34.5, thetotal number of electron-ion pairs (NT ) is usually a few times largerthan the number of primaries (NP ).

The probability for a released electron to have an energy E or largerfollows an approximate 1/E2 dependence (Rutherford law), shown inFig. 34.3 for Ar/CH4 at NTP (dotted line, left scale). More detailedestimates taking into account the electronic structure of the mediumare shown in the figure, for three values of the particle velocityfactor βγ [66]. The dot-dashed line provides, on the right scale, thepractical range of electrons (including scattering) of energy E. As anexample, about 0.6% of released electrons have 1 keV or more energy,substantially increasing the ionization loss rate. The practical rangeof 1 keV electrons in argon (dot-dashed line, right scale) is 70 µm andthis can contribute to the error in the coordinate determination.


Figure 34.3: Probability of single collisions in which releasedelectrons have an energy E or larger (left scale) and practicalrange of electrons in Ar/CH4 (P10) at NTP (dot-dashed curve,right scale) [66].

The number of electron-ion pairs per primary ionization, or clustersize, has an exponentially decreasing probability; for argon, there isabout 1% probability for primary clusters to contain ten or moreelectron-ion pairs [67].

Once released in the gas, and under the influence of an appliedelectric field, electrons and ions drift in opposite directions and diffusetowards the electrodes. The scattering cross section is determinedby the details of atomic and molecular structure. Therefore, thedrift velocity and diffusion of electrons depend very strongly on thenature of the gas, specifically on the inelastic cross-section involvingthe rotational and vibrational levels of molecules. In noble gases,the inelastic cross section is zero below excitation and ionizationthresholds. Large drift velocities are achieved by adding polyatomicgases (usually CH4, CO2, or CF4) having large inelastic cross sectionsat moderate energies, which results in “cooling” electrons into theenergy range of the Ramsauer-Townsend minimum (at ∼ 0.5 eV)of the elastic cross-section of argon. The reduction in both thetotal electron scattering cross-section and the electron energy resultsin a large increase of electron drift velocity (for a compilation ofelectron-molecule cross sections see Ref. 68). Another principal roleof the polyatomic gas is to absorb the ultraviolet photons emittedby the excited noble gas atoms. Extensive collections of experimentaldata [69] and theoretical calculations based on transport theory [70]permit estimates of drift and diffusion properties in pure gases andtheir mixtures. In a simple approximation, gas kinetic theory providesthe drift velocity v as a function of the mean collision time τ andthe electric field E: v = eEτ/me (Townsend’s expression). Values ofdrift velocity and diffusion for some commonly used gases at NTP aregiven in Fig. 34.4 and Fig. 34.5. These have been computed with theMAGBOLTZ program [71]. For different conditions, the horizontalaxis must be scaled inversely with the gas density. Standard deviationsfor longitudinal (σL) and transverse diffusion (σT ) are given for onecm of drift, and scale with the the square root of the drift distance.Since the collection time is inversely proportional to the drift velocity,diffusion is less in gases such as CF4 that have high drift velocities. Inthe presence of an external magnetic field, the Lorentz force acting onelectrons between collisions deflects the drifting electrons and modifiesthe drift properties. The electron trajectories, velocities and diffusionparameters can be computed with MAGBOLTZ. A simple theory, thefriction force model, provides an expression for the vector drift velocityv as a function of electric and magnetic field vectors E and B, of theLarmor frequency ω = eB/me, and of the mean collision time τ :

v =e

me

τ

1 + ω2τ2

(

E +ωτ

B(E ×B) +

ω2τ2

B2(E · B)B

)

(34.13)

To a good approximation, and for moderate fields, one can assumethat the energy of the electrons is not affected by B, and use for τ

the values deduced from the drift velocity at B = 0 (the Townsendexpression). For E perpendicular to B, the drift angle to the relative tothe electric field vector is tan θB = ωτ and v = (E/B)(ωτ/

√1 + ω2τ2).

For parallel electric and magnetic fields, drift velocity and longitudinaldiffusion are not affected, while the transverse diffusion can bestrongly reduced: σT (B) = σT (B = 0)/

√1 + ω2τ2. The dotted line in

Fig. 34.5 represents σT for the classic Ar/CH4 (90:10) mixture at 4 T.Large values of ωτ ∼ 20 at 5T are consistent with the measurementof diffusion coefficient in Ar/CF4/iC4H10 (95:3:2). This reduction isexploited in time projection chambers (Sec. 34.6.5) to improve spatialresolution.

Figure 34.4: Computed electron drift velocity as a function ofelectric field in several gases at NTP and B = 0 [71].

In mixtures containing electronegative molecules, such as O2 orH2O, electrons can be captured to form negative ions. Capture cross-sections are strongly energy-dependent, and therefore the captureprobability is a function of applied field. For example, the electronis attached to the oxygen molecule at energies below 1 eV. Thethree-body electron attachment coefficients may differ greatly for thesame additive in different mixtures. As an example, at moderatefields (up to 1 kV/cm) the addition of 0.1% of oxygen to an Ar/CO2

mixture results in an electron capture probability about twenty timeslarger than the same addition to Ar/CH4.

Carbon tetrafluoride is not electronegative at low and moderatefields, making its use attractive as drift gas due to its very lowdiffusion. However, CF4 has a large electron capture cross section atfields above ∼ 8 kV/cm, before reaching avalanche field strengths.Depending on detector geometry, some signal reduction and resolutionloss can be expected using this gas.

If the electric field is increased sufficiently, electrons gain enoughenergy between collisions to ionize molecules. Above a gas-dependentthreshold, the mean free path for ionization, λi, decreases exponentiallywith the field; its inverse, α = 1/λi, is the first Townsend coefficient.In wire chambers, most of the increase of avalanche particle densityoccurs very close to the anode wires, and a simple electrostaticconsideration shows that the largest fraction of the detected signalis due to the motion of positive ions receding from the wires. Theelectron component, although very fast, contributes very little to thesignal. This determines the characteristic shape of the detected signalsin the proportional mode: a fast rise followed by a gradual increase.The slow component, the so-called “ion tail” that limits the timeresolution of the detector, is usually removed by differentiation of thesignal. In uniform fields, N0 initial electrons multiply over a length xforming an electron avalanche of size N = N0 eαx; N/N0 is the gainof the detector. Fig. 34.6 shows examples of Townsend coefficients forseveral gas mixtures, computed with MAGBOLTZ [71].

Positive ions released by the primary ionization or produced inthe avalanches drift and diffuse under the influence of the electricfield. Negative ions may also be produced by electron attachment togas molecules. The drift velocity of ions in the fields encountered in


Figure 34.5: Electron longitudinal diffusion (σL) (dashed lines)and transverse diffusion (σT ) (full lines) for 1 cm of drift at NTPand B = 0. The dotted line shows σT for the P10 mixture at4T [71].

Figure 34.6: Computed first Townsend coefficient α as afunction of electric field in several gases at NTP [71].

gaseous detectors (up to few kV/cm) is typically about three ordersof magnitude less than for electrons. The ion mobility µ, the ratio ofdrift velocity to electric field, is constant for a given ion type up tovery high fields. Values of mobility at NTP for ions in their own andother gases are given in Table 34.6 [72]. For different temperaturesand pressures, the mobility can be scaled inversely with the densityassuming an ideal gas law. For mixtures, due to a very effective chargetransfer mechanism, only ions with the lowest ionization potentialsurvive after a short path in the gas. Both the lateral and transversediffusion of ions are proportional to the square root of the drift time,with a coefficient that depends on temperature but not on the ionmass. Accumulation of ions in the gas drift volume may induce fielddistortions (see Sec. 34.6.5).

Table 34.6: Mobility of ions in gases at NTP [72].

Gas Ion Mobility µ

(cm2 V−1 s−1)

He He+ 10.4

Ne Ne+ 4.7

Ar Ar+ 1.54

Ar/CH4 CH+4 1.87

Ar/CO2 CO+2 1.72

CH4 CH+4 2.26

CO2 CO+2 1.09

34.6.2. Multi-Wire Proportional and Drift Chambers : Re-vised March 2010 by Fabio Sauli (CERN) and Maxim Titov (CEASaclay).

Single-wire counters that detect the ionization produced in agas by a charged particle, followed by charge multiplication andcollection around a thin wire have been used for decades. Good energyresolution is obtained in the proportional amplification mode, whilevery large saturated pulses can be detected in the streamer and Geigermodes [3].

Multiwire proportional chambers (MWPCs) [73,74], introduced inthe late ’60’s, detect, localize and measure energy deposit by chargedparticles over large areas. A mesh of parallel anode wires at a suitablepotential, inserted between two cathodes, acts almost as a set ofindependent proportional counters (see Fig. 34.7a). Electrons releasedin the gas volume drift towards the anodes and produce avalanches inthe increasing field. Analytic expressions for the electric field can befound in many textbooks. The fields close to the wires E(r), in thedrift region ED, and the capacitance C per unit length of anode wireare approximately given by

E(r) =CV0

2πǫ0

1

rED =

CV0

2ǫ0sC =

2πǫ0π(ℓ/s) − ln(2πa/s)

, (34.14)

where r is the distance from the center of the anode, s the wirespacing, ℓ and V0 the distance and potential difference between anodeand cathode, and a the anode wire radius.

Because of electrostatic forces, anode wires are in equilibrium onlyfor a perfect geometry. Small deviations result in forces displacing thewires alternatively below and above the symmetry plane, sometimeswith catastrophic results. These displacement forces are countered bythe mechanical tension of the wire, up to a maximum unsupportedstable length, LM [64], above which the wire deforms:

LM =s

CV0

√

4πǫ0TM (34.15)

The maximum tension TM depends on the wire diameter and modulusof elasticity. Table 34.7 gives approximate values for tungsten andthe corresponding maximum stable wire length under reasonableassumptions for the operating voltage (V0 = 5 kV) [75]. Internalsupports and spacers can be used in the construction of longer detectorsto overcome limits on the wire length imposed by Eq. (34.15).

Table 34.7: Maximum tension TM and stable unsupportedlength LM for tungsten wires with spacing s, operated atV0 = 5 kV. No safety factor is included.

Wire diameter (µm) TM (newton) s (mm) LM (cm)

10 0.16 1 25

20 0.65 2 85

Detection of charge on the wires over a predefined thresholdprovides the transverse coordinate to the wire with an accuracycomparable to that of the wire spacing. The coordinate along eachwire can be obtained by measuring the ratio of collected charge atthe two ends of resistive wires. Making use of the charge profileinduced on segmented cathodes, the so-called center-of gravity (COG)method, permits localization of tracks to sub-mm accuracy. Due tothe statistics of energy loss and asymmetric ionization clusters, theposition accuracy is ∼ 50 µm rms for tracks perpendicular to thewire plane, but degrades to ∼ 250µmat 30 to the normal [76]. Theintrinsic bi-dimensional characteristic of the COG readout has foundnumerous applications in medical imaging.

Drift chambers, developed in the early ’70’s, can be used to estimatethe longitudinal position of a track by exploiting the arrival time ofelectrons at the anodes if the time of interaction is known [77]. Thedistance between anode wires is usually several cm, allowing coverageof large areas at reduced cost. In the original design, a thicker wire


−0.15

−0.10

−0.05

0.00

0.05

0.10

x-axis [cm] −0.2−0.3 −0.1 0.0 0.1 0.2 0.3

−0.10

−0.05

0.00

0.05

0.10

0.15

y-ax

is [

cm]

y-ax

is [

cm]

(a) Multiwire proportional chamber

(b) Drift chamber

Figure 34.7: Electric field lines and equipotentials in (a) amultiwire proportional chamber and (b) a drift chamber.

(the field wire) at the proper voltage, placed between the anodewires, reduces the field at the mid-point between anodes and improvescharge collection (Fig. 34.7b). In some drift chamber designs, andwith the help of suitable voltages applied to field-shaping electrodes,the electric field structure is adjusted to improve the linearity ofspace-to-drift-time relation, resulting in better spatial resolution [78].

Drift chambers can reach a longitudinal spatial resolution fromtiming measurement of order 100 µm (rms) or better for minimumionizing particles, depending on the geometry and operating conditions.However, a degradation of resolution is observed [79] due to primaryionization statistics for tracks close to the anode wires, caused by thespread in arrival time of the nearest ionization clusters. The effect canbe reduced by operating the detector at higher pressures. Samplingthe drift time on rows of anodes led to the concept of multiple arrayssuch as the multi-drift module [80] and the JET chamber [81]. Ameasurement of drift time, together with the recording of chargesharing from the two ends of the anode wires provides the coordinatesof segments of tracks. The total charge gives information on thedifferential energy loss and is exploited for particle identification. Thetime projection chamber (TPC) [82] combines a measurement of drifttime and charge induction on cathodes, to obtain excellent trackingfor high multiplicity topologies occurring at moderate rates (seeSec. 34.6.5). In all cases, a good knowledge of electron drift velocityand diffusion properties is required. This has to be combined withthe knowledge of the electric fields in the structures, computed withcommercial or custom-developed software [71,83]. For an overviewof detectors exploiting the drift time for coordinate measurement seeRefs. 6 and 64.

Multiwire and drift chambers have been operated with a varietyof gas fillings and operating modes, depending on experimentalrequirements. The so-called “Magic Gas,” a mixture of argon,isobutane and Freon [74], permits very high and saturated gains(∼ 106). This gas mixture was used in early wire chambers, but wasfound to be susceptible to severe aging processes. With present-dayelectronics, proportional gains around 104 are sufficient for detectionof minimum ionizing particles, and noble gases with moderate amountsof polyatomic gases, such as methane or carbon dioxide, are used.

Although very powerful in terms of performance, multi-wirestructures have reliability problems when used in harsh or hard-to-access environments, since a single broken wire can disable the entiredetector. Introduced in the ’80’s, straw and drift tube systems makeuse of large arrays of wire counters encased in individual enclosures,each acting as an independent wire counter [84]. Techniques forlow-cost mass production of these detectors have been developed forlarge experiments, such as the Transition Radiation Tracker and theDrift Tubes arrays for CERN’s LHC experiments [85].

34.6.3. High Rate Effects : Revised March 2010 by Fabio Sauli(CERN) and Maxim Titov (CEA Saclay).

The production of positive ions in the avalanches and their slowdrift before neutralization result in a rate-dependent accumulation ofpositive charge in the detector. This may result in significant fielddistortion, gain reduction and degradation of spatial resolution. Asshown in Fig. 34.8 [86], the proportional gain drops above a chargeproduction rate around 109 electrons per second and mm of wire,independently of the avalanche size. For a proportional gain of 104

and 100 electrons per track, this corresponds to a particle flux of103 s−1mm−1 (1 kHz/mm2 for 1 mm wire spacing).

Figure 34.8: Charge rate dependence of normalized gas gainG/G0 (relative to zero counting rate) in proportional thin-wiredetectors [86]. Q is the total charge in single avalanche; N isthe particle rate per wire length.

At high radiation fluxes, a fast degradation of detectors due to theformation of polymers deposits (aging) is often observed. The processhas been extensively investigated, often with conflicting results.Several causes have been identified, including organic pollutants andsilicone oils. Addition of small amounts of water in many (but notall) cases has been shown to extend the lifetime of the detectors.Addition of fluorinated gases (e.g., CF4) or oxygen may result in anetching action that can overcome polymer formation, or even eliminatealready existing deposits. However, the issue of long-term survival ofgas detectors with these gases is controversial [87]. Under optimumoperating conditions, a total collected charge of a few coulombs per cmof wire can usually be reached before noticeable degradation occurs.This corresponds, for one mm spacing and at a gain of 104, to a totalparticle flux of ∼ 1014 MIPs/cm2.

34.6.4. Micro-Pattern Gas Detectors : Revised March 2010 byFabio Sauli (CERN) and Maxim Titov (CEA Saclay)

Despite various improvements, position-sensitive detectors basedon wire structures are limited by basic diffusion processes andspace charge effects to localization accuracies of 50–100µm [88].Modern photolithographic technology led to the development of novelMicro-Pattern Gas Detector (MPGD) concepts [89], revolutionizingcell size limitations for many gas detector applications. By using pitchsize of a few hundred µm, an order of magnitude improvement ingranularity over wire chambers, these detectors offer intrinsic high ratecapability (> 106 Hz/mm2), excellent spatial resolution (∼ 30 µm),multi-particle resolution (∼ 500 µm), and single photo-electron timeresolution in the ns range.

The Micro-Strip Gas Chamber (MSGC), invented in 1988, wasthe first of the micro-structure gas chambers [90]. It consists ofa set of tiny parallel metal strips laid on a thin resistive support,alternatively connected as anodes and cathodes. Owing to the smallanode-to-cathode distance (∼ 100 µm), the fast collection of positiveions reduces space charge build-up, and provides a greatly increasedrate capability. Unfortunately, the fragile electrode structure of theMSGC turned out to be easily destroyed by discharges induced by


heavily ionizing particles [91]. Nevertheless, detailed studies of theirproperties, and in particular, on the radiation-induced processesleading to discharge breakdown, led to the development of themore powerful devices: GEM and Micromegas. These have improvedreliability and radiation hardness. The absence of space-charge effectsin GEM detectors at the highest rates reached so far and the finegranularity of MPGDs improve the maximum rate capability by morethan two orders of magnitude (Fig. 34.9) [78,92]. Even larger ratecapability has been reported for Micromegas [93].

Figure 34.9: Normalized gas gain as a function of particle ratefor MWPC [78] and GEM [92].

140 µm

50 µm

Figure 34.10: Schematic view and typical dimensions of thehole structure in the GEM amplification cell. Electric field lines(solid) and equipotentials (dashed) are shown.

The Gas Electron Multiplier (GEM) detector consists of athin-foil copper-insulator-copper sandwich chemically perforated toobtain a high density of holes in which avalanches occur [94]. Thehole diameter is typically between 25 µm and 150 µm, while thecorresponding distance between holes varies between 50 µm and200 µm. The central insulator is usually (in the original design)the polymer Kapton, with a thickness of 50 µm. Application of apotential difference between the two sides of the GEM generates theelectric fields indicated in Fig. 34.10. Each hole acts as an independentproportional counter. Electrons released by the primary ionizationparticle in the upper conversion region (above the GEM foil) driftinto the holes, where charge multiplication occurs in the high electricfield (50–70 kV/cm). Most of avalanche electrons are transferred

HV1

HV2Micromesh

100

µm

Anode plane

e−

E2

50-70 kV/cm

Particle

Drift gap

Amplificationgap

Figure 34.11: Schematic drawing of the Micromegas detector.

into the gap below the GEM. Several GEM foils can be cascaded,allowing the multi-layer GEM detectors to operate at overall gas gainabove 104 in the presence of highly ionizing particles, while stronglyreducing the risk of discharges. This is a major advantage of the GEMtechnology [95]. Localization can then be performed by collectingthe charge on a patterned one- or two-dimensional readout board ofarbitrary pattern, placed below the last GEM.

The micro-mesh gaseous structure (Micromegas) is a thin parallel-plate avalanche counter, as shown in Fig. 34.11 [96]. It consists ofa drift region and a narrow multiplication gap (25–150 µm) betweena thin metal grid (micromesh) and the readout electrode (strips orpads of conductor printed on an insulator board). Electrons fromthe primary ionization drift through the holes of the mesh into thenarrow multiplication gap, where they are amplified. The electricfield is homogeneous both in the drift (electric field ∼ 1 kV/cm)and amplification (50–70 kV/cm) gaps. In the narrow multiplicationregion, gain variations due to small variations of the amplificationgap are approximately compensated by an inverse variation of theamplification coefficient, resulting in a more uniform gain. The smallamplification gap produces a narrow avalanche, giving rise to excellentspatial resolution: 12 µm accuracy, limited by the micro-mesh pitch,has been achieved for MIPs, as well as very good time resolution andenergy resolution (∼ 12% FWHM with 6 keV x rays) [97].

The performance and robustness of GEM and Micromegas haveencouraged their use in high-energy and nuclear physics, UV andvisible photon detection, astroparticle and neutrino physics, neutrondetection and medical physics. Most structures were originallyoptimized for high-rate particle tracking in nuclear and high-energyphysics experiments. COMPASS, a high-luminosity experiment atCERN, pioneered the use of large-area (∼ 40 × 40 cm2) GEM andMicromegas detectors close to the beam line with particle rates of25 kHz/mm2. Both technologies achieved a tracking efficiency of closeto 100% at gas gains of about 104, a spatial resolution of 70–100 µmand a time resolution of ∼ 10 ns. GEM detectors are also used fortriggering in the LHCb Muon System and for tracking in the TOTEMTelescopes. Both GEM and Micromegas devices are foreseen for theupgrade of the LHC experiments and for one of the readout optionsfor the Time Projection Chamber (TPC) at the International LinearCollider (ILC). The development of new fabrication techniques—“bulk” Micromegas technology [98] and single-mask GEMs [99] —is abig step toward industrial production of large-size MPGDs. In someapplications requiring very large-area coverage with moderate spatialresolution, coarse macro-patterned detectors, such as Thick GEMs(THGEM) [100] or patterned resistive-plate devices [101] might offereconomically interesting solutions.

Sensitive and low-noise electronics enlarge the range of the MPGDapplications. Recently, the GEM and Micromegas detectors wereread out by high-granularity (∼ 50 µm pitch) CMOS chips assembleddirectly below the GEM or Micromegas amplification structures [102].These detectors use the bump-bonding pads of a pixel chip as anintegrated charge collecting anode. With this arrangement signals are


induced at the input gate of a charge-sensitive preamplifier (top metallayer of the CMOS chip). Every pixel is then directly connected to theamplification and digitization circuits, integrated in the underlyingactive layers of the CMOS technology, yielding timing and chargemeasurements as well as precise spatial information in 3D.

The operation of a MPGD with a Timepix CMOS chip hasdemonstrated the possibility of reconstructing 3D-space points ofindividual primary electron clusters with ∼ 30µm spatial resolutionand event-time resolution with nanosecond precision. This hasbecome indispensable for tracking and triggering and also fordiscriminating between ionizing tracks and photon conversions. TheGEM, in conjunction with a CMOS ASIC,* can directly view theabsorption process of a few keV x-ray quanta and simultaneouslyreconstruct the direction of emission, which is sensitive to the x-raypolarization. Thanks to these developments, a micro-pattern devicewith finely segmented CMOS readout can serve as a high-precision“electronic bubble chamber.” This may open new opportunities forx-ray polarimeters, detection of weakly interacting massive particles(WIMPs) and axions, Compton telescopes, and 3D imaging of nuclearrecoils.

An elegant solution for the construction of the Micromegas withpixel readout is the integration of the amplification grid and CMOSchip by means of an advanced “wafer post-processing” technology [103].This novel concept is called “Ingrid” (see Fig. 34.12). With thistechnique, the structure of a thin (1 µm) aluminum grid is fabricatedon top of an array of insulating pillars. which stands ∼ 50µm abovethe CMOS chip. The sub-µm precision of the grid dimensions andavalanche gap size results in a uniform gas gain. The grid hole size,pitch and pattern can be easily adapted to match the geometry of anypixel readout chip.

Figure 34.12: Photo of the Micromegas “Ingrid” detector.The grid holes can be accurately aligned with readout pixels ofCMOS chip. The insulating pillars are centered between the gridholes, thus avoiding dead regions.

Recent developments in radiation hardness research with state-of-the-art MPGDs are reviewed in Ref. 104. Earlier aging studies ofGEM and Micromegas concepts revealed that they might be evenless vulnerable to radiation-induced performance degradation thanstandard silicon microstrip detectors.

The RD51 collaboration was established in 2008 to further advancetechnological developments of micro-pattern detectors and associatedelectronic-readout systems for applications in basic and appliedresearch [105].

* Application Specific Integrated Circuit

Inner wall and field cage

Outer wall

E, Bdirections

Front endcards

Beamdirection

Central cathode

Central cathode HV

Figure 34.14: One of the 3 TPC modules for the near detectorof the T2K experiment [107]. The size is 2 × 2 × 0.8m3.Micromegas devices are used for gas amplification and readout.

34.6.5. Time-projection chambers : Written August 2015 byC. Lippmann (GSI Helmholtzzentrum fur Schwerionenforschung,Darmstadt, Germany)

The Time Projection Chamber (TPC) concept was invented byDavid Nygren in the late 1970’s [82]. It consists of a cylindricalor square field cage filled with a detection medium that is usuallya gas or a liquid. Charged particles produce tracks of ionizationelectrons that drift in a uniform electric field towards a position-sensitive amplification stage which provides a 2D projection of theparticle trajectories. The third coordinate can be calculated from thearrival times of the drifted electrons. The start for this drift timemeasurement is usually derived from an external detector, e.g. a fastinteraction trigger detector.

This section focuses on the gas-filled TPCs that are typically usedin particle or nuclear physics experiments at accelerators due to theirlow material budget. For neutrino physics (Sec. 34.10) or for detectingrare events (Sec. 35.4), on the contrary, usually high density and largeactive mass are required, and a liquid detection medium is favored.

The TPC enables full 3D measurements of charged particle tracks,which gives it a distinct advantage over other tracking detector designswhich record information only in two-dimensional detector planesand have less overall segmentation. This advantage is often exploitedfor pattern recognition in events with large numbers of particles,e.g. heavy-ion collisions. Two examples of modern large-volumegaseous TPCs are shown in Fig. 34.13 and Fig. 34.14.

Figure 34.13: Schematic view of the ALICE TPC [106]. Thedrift volume with 5 m diameter is divided into two halves, eachproviding 2.5m drift length.


Identification of the charged particles crossing the TPC is possibleby simultaneously measuring their momentum and specific energydeposit through ionisation (dE/dx). The momentum, as well as thecharge sign, are calculated from a helix fit to the particle trajectoryin the presence of a magnetic field (typically parallel to the driftfield). For this application, precise spatial measurements in the planetransverse to the magnetic field are most important. The specificenergy deposit is estimated from many charge measurements along theparticle trajectory (e.g. one measurement per anode wire or per row ofreadout pads). As the charge collected per readout segment dependson the track angle and on the ambient conditions, the measuredvalues are corrected for the effective length of the track segmentsand for variations of the gas temperature and pressure. The mostprobable value of the corrected signal amplitudes provides the bestestimator for the specific energy deposit (see Sec. 33.2.3); it is usuallyapproximated by the truncated mean, i.e. the average of the 50%-70%smallest values. The resulting particle identification performance isillustrated in Fig. 34.15, for the ALICE TPC.

Momentum (GeV/c)

1−10 1 10

π

μ

e

K p d t ALICE performance

= 13 TeVspp,

B = 0.2 T

En

erg

y d

ep

osit p

er

un

it le

ng

th (

ke

V/c

m)

10

8

6

5

4

3

2

20

30

Figure 34.15: Energy deposit versus momentum measured inthe ALICE TPC [108].

The dependence of the achievable energy resolution on the numberof measurements N , on the thickness of the sampling layers t, and onthe gas pressure P can be estimated using an empirical formula [109]:

σdE/dx = 0.41 N−0.43(t P )−0.32. (34.16)

Typical values at nominal pressure are σdE/dx = 4.5 to 7.5%, witht = 0.4 to 1.5 cm and N = 40 up to more than 300. Due to the highgas pressure of 8.5 bar, the resolution achieved with the PEP-4/9 TPCwas an unprecedented 3% [110].

The greatest challenges for a large TPC are due to the length ofthe drift of up to several meters. In particular, it can make the devicesensitive to small distortions in the electric field. Such distortionscan arise from a number of sources, e.g. imperfections in the fieldcage construction or the presence of ions in the drift volume. Theelectron drift in a TPC in the presence of a magnetic field is definedby Eq. (34.13). The E ×B term of Eq. (34.13) vanishes for perfectlyaligned electric and magnetic fields, which can however be difficult toachieve in practice. Furthermore, the electron drift depends on the ωτfactor, which is defined by the chosen gas mixture and magnetic fieldstrength. The electrons will tend to follow the magnetic field linesfor ωτ > 1 or the electric field lines for ωτ < 1. The former modeof operation makes the TPC less sensitive to non-uniformities of theelectric field, which is usually desirable.

The drift of the ionization electrons is superposed with a randomdiffusion motion which degrades their position information. Theultimate resolution of a single position measurement is limited toaround

σx =σD

√L√

n, (34.17)

where σD is the transverse diffusion coefficient for 1 cm drift, L is thedrift length in cm and n is the effective number of electrons collected.

Without a magnetic field, σD,B=0

√L is typically a few mm after a

drift of L = 100 cm. However, in a strong magnetic field parallel tothe drift field, a large value of ωτ can significantly reduce diffusion:

σD,B>0

σD,B=0=

1√1 + ω2τ2

. (34.18)

This factor can reach values of up to 10. In practice, the finalresolution limit due to diffusion will typically be around σx = 100 µm.

The drift and diffusion of electrons depend strongly on the natureof the gas that is used. The optimal gas mixture varies accordingto the environment in which the TPC will operate. In all cases, theoxygen concentration must be kept very low (few ten parts per millionin a large TPC) in order to avoid electron loss through attachment.Ideally, the drift velocity should depend only weakly on the electricfield at the nominal operating condition. The classic Ar/CH4 (90:10)mixture, known as P10, has a drift velocity maximum of 5 cm/µsat an electric field of only 125V/cm (Fig. 34.4). In this regime,the electron arrival time is not affected by small variations in theambient conditions. Moreover, low electric fields simplify the designand operation of the field cage. The mixture has a large transversediffusion at B = 0, but this can be reduced significantly in a strongmagnetic field due to the relatively large value of ωτ .

For certain applications, organic gases like CH4 are not desirable,since they may cause aging. An alternative is to replace CH4 withCO2. An Ar/CO2 (90:10) mixture features a low transverse diffusionat all magnetic field strengths, but does not provide a saturated driftvelocity for the typical electric fields used in TPCs (up to a few100V/cm), so it is quite sensitive to the ambient conditions. Freonadmixtures like CF4 can be an attractive option for a TPC as well,since the resulting gas mixtures provide high drift velocities at lowelectric fields. However, the use of CF4 always needs to be thoroughlyvalidated for compatibility with all materials of the detector and thegas system.

Historically, the amplification stages used in gaseous TPCs havebeen planes of anode wires operated in proportional mode. Theperformance is limited by effects related to the feature size of a fewmm (wire spacing). Since near the wires the electric and magneticfields are not parallel, the incoming ionisation electrons are displacedin the direction of the wires (“wire E ×B effect”), which degrades theresolution. The smaller feature sizes of Micro-Pattern Gas Detectors(MPGDs) like GEMs and Micromegas lead to many advantages ascompared to wire planes (see Sec. 34.6.4). In particular, E ×B effectsin the amplification stage are much smaller. Moreover, the signalinduction process in MPGDs leads to a very narrow pad response,allowing for a much finer segmentation and improving the separationof two nearby tracks. Combinations of MPGDs with silicon sensorshave resulted in the highest granularity readout systems so far (seeSec. 34.6.4). These devices make it possible to count the numberof ionization clusters along the length of a track, which can, inprinciple, improve the particle identification capability. However, thebig challenge for such a system is the huge number of read-outchannels for a TPC of a typical size.

The accumulation of the positive ions created by the ionizationfrom the particle tracks can lead to time-dependent distortions ofthe drift field. Due to their small drift velocity, ions from manyevents may coexist in the drift volume. To reduce the effect of sucha build-up of space charge, Argon can be replaced by Neon as themain component of the gas mixture. Neon features a lower numberof ionisation electrons per unit of track length (see Table 34.5) and ahigher ion mobility (see Table 34.6).

Of much greater concern are the ions produced in the gasamplification stage. In order to prevent them from entering the driftvolume, large TPCs built until now usually have a gating grid. Thegating grid can be switched to transparent mode (usually in thepresence of an interaction trigger) to allow the ionization electronsto pass into the amplification region. After all electrons have reachedthe amplification region, it is usually closed such that it is renderedopaque to electrons and ions.

Alternatively, new readout schemes are being developed usingMPGDs. These can be optimized in a way that they release many


fewer positive ions than wire planes operating at the same effectivegain. This is an exciting possibility for future TPCs.

34.6.6. Transition radiation detectors (TRD’s) : Revised Au-gust 2013 by P. Nevski (BNL) and A. Romaniouk (Moscow Eng. &Phys. Inst.)

Transition radiation (TR) x-rays are produced when a highlyrelativistic particle (γ >∼ 103) crosses a refractive index interface, asdiscussed in Sec. 33.7. The x-rays, ranging from a few keV to a fewdozen keV or more, are emitted at a characteristic angle 1/γ fromthe particle trajectory. Since the TR yield is about 1% per boundarycrossing, radiation from multiple surface crossings is used in practicaldetectors. In the simplest concept, a detector module might consistof low-Z foils followed by a high-Z active layer made of proportionalcounters filled with a Xe-rich gas mixture. The atomic numberconsiderations follow from the dominant photoelectric absorption crosssection per atom going roughly as Z n/E3

x, where n varies between 4and 5 over the region of interest, and the x-ray energy is Ex.* Tominimize self-absorption, materials such as polypropylene, Mylar,carbon, and (rarely) lithium are used as radiators. The TR signal inthe active regions is in most cases superimposed upon the particleionization losses, which are proportional to Z.

The TR intensity for a single boundary crossing always increaseswith γ, but, for multiple boundary crossings, interference leadsto saturation above a Lorentz factor γ sat = 0.6 ω1

√ℓ1ℓ2/c [111],

where ω1 is the radiator material plasma frequency, ℓ1 is itsthickness, and ℓ2 the spacing. In most of the detectors used inparticle physics the radiator parameters are chosen to provideγ sat ≈ 2000. Those detectors normally work as threshold devices,ensuring the best electron/pion separation in the momentum range1 GeV/c <∼ p <∼ 150 GeV/c.

One can distinguish two design concepts—“thick” and “thin”detectors:

1. The radiator, optimized for a minimum total radiation lengthat maximum TR yield and total TR absorption, consists of fewhundred foils (for instance 300 20 µm thick polypropylene foils).Most of the TR photons are absorbed in the radiator itself. Tomaximise the number of TR photons reaching the detector, partof the radiator far from the active layers is often made of thickerfoils, which shifts the x-ray spectrum to higher energies. Thedetector thickness, about 2-4 cm for Xe-filled gas chambers, isoptimized to absorb the incoming x-ray spectrum. A classicaldetector is composed of several similar modules which respondnearly independently. Such detectors were used in the UA2, NA34and other experiments [112], and are being used in the ALICEexperiment [113], [114].

2. In other TRD concepts a fine granular radiator/detector structureexploits the soft part of the TR spectrum more efficiently andthereby may act also as an integral part of the tracking detector.This can be achieved, for instance, by distributing small-diameterstraw-tube detectors uniformly or in thin layers throughout theradiator material (foils or fibers). Even with a relatively thinradiator stack, radiation below 5 keV is mostly lost in the radiatorsthemselves. However for photon energies above this value, theabsorption is reduced and the radiation can be registered by severalconsecutive detector layers, thus creating a strong TR build-upeffect. This approach allows to realise TRD as an integral part ofthe tracking detector. Descriptions of detectors using this approachcan be found in both accelerator and space experiments [113,114].For example, in the ATLAS TR tracker (TRT), charged particlescross about 35 effective straw tube layers embedded in the radiatormaterial [113]. The effective thickness of the Xe gas per straw isabout 2.2 mm and the average number of foils per straw is about40 with an effective foil thickness of about 18 µm.

Both TR photon absorption and the TR build-up significantly affectthe detector performance. Although the values mentioned above are

* Photon absorption coefficients for the elements (via a NIST link),and dE/dx|min and plasma energies for many materials are given inpdg.lbl.gov/AtomicNuclearProperties.

typical for most of the plastic radiators used with Xe-based detectors,they vary significantly depending on the detector parameters: radiatormaterial, thickness and spacing, the geometry and position of thesensitive chambers, etc. Thus careful simulations are usually neededto build a detector optimized for a particular application. For TRDsimulation stand-alone codes based on GEANT3 program wereusually used (P.Nevski in [113]) . TR simulation is now available inGEANT4 [118]. The most recent version of it (starting from release9.5) shows a reasonable agreement with data (S. Furletov in [114]and [115]) .

0.01

0.1

0.001

10 20 50 200100

NA34 (HELIOS)C.Fabjan et al.R 806A. Bungener et al.ZEUS

KEKUA2H.Butt et al.D0M.Holder et al.H.WeidkampH.Grassler et al.

ATLAS

NOMAD

AMS

Total detector length (cm)

Pion

eff

icie

ncy

ALICEPAMELA

..

..

Figure 34.16: Pion efficiency measured (or predicted) fordifferent TRDs as a function of the detector length for a fixedelectron efficiency of 90%. The plot is taken from [112]. Resultsfrom more recent detectors are added from [113] and [114].

The discrimination between electrons and pions can be based onthe charge deposition measured in each detection module, on thenumber of clusters – energy depositions observed above an optimalthreshold (usually it is 5–7 keV ), or on more sophisticated methodssuch as analyzing the pulse shape as a function of time. The totalenergy measurement technique is more suitable for thick gas volumes,which absorb most of the TR radiation and where the ionizationloss fluctuations are small. The cluster-counting method worksbetter for detectors with thin gas layers, where the fluctuations of theionization losses are big. Cluster-counting replaces the Landau-Vavilovdistribution of background ionization energy losses with the Poissonstatistics of δ-electrons, responsible for the distribution tails. Thelatter distribution is narrower than the Landau-Vavilov distribution.In practice, most of the experiments use a likelihood method, whichexploits detailed knowledge of the detector response for differentparticles and gives the best separation. The more parameters thatare considered, the better separation power. The recent results ofthe TRD in the AMS experiment is a good example. In the realexperiment the rejection power is better by almost one order ofmagnitude than that obtained in the beam test if stringent criteriafor track selection are applied (see T. Kirn et al. in [114]) . Anotherexample is a neural network method used by the ALICE TRD (ALICEpoint in Fig. 34.16) which gives another factor of 2–3 in rejecton powerwith respect to the likelihood method [116]) .

The major factor in the performance of any TRD is its overalllength. This is illustrated in Fig. 34.16, which shows, for a variety ofdetectors, the pion efficiency at a fixed electron efficiency of 90% asa function of the overall detector length. TRD performance dependson particle energy and in this figure the experimental data, covering arange of particle energies from 1 GeV to 40 GeV, are rescaled to anenergy of 10 GeV when possible. Phenomenologically, the rejectionpower against pions increases as 5 · 10L/38, where the range of validityis L ≈ 20–100 cm. Apart from the beam energy variations, theobserved scattering of the points in the plot reflects how effectivelythe detector space is used and how well the exact response to different


particles is taken into account in the analysis. For instance, theATLAS TRT was built as a compromise between TR and trackingrequirements; that is why the test-beam prototype result (lowerpoint) is better than the real TRT performance at the LHC shownin Fig. 34.16 for different regions in the detector (in agreement withMC).

In most cases, recent TRDs combine particle identification withcharged-track measurement in the same detector [113,114,117]. Thisis particularly important for collider experiments, where the availablespace for the inner detector is very limited. For a modest increaseof the radiation length due to the radiator (∼4% X0), a significantenhancement of the electron identification was obtained in the caseof the ATLAS TRT. The combination of the two detector functionsprovides a powerful tool for electron identification even at very highparticle densities.

In addition to the enhancement of the electron identification, oneof the most important roles of the TRDs in the collider experimentsis their participation in different trigger and data analysis algorithms.The ALICE experiment [114] is a good example of the use of theTRD in a First Level Trigger. In the ATLAS experiment, the TRTinformation is used in the High Level Trigger (HLT) algorithms.With continuous increase of instantaneous luminosity, the electrontrigger output rate becomes so high, that a significant increase of thecalorimeter energy threshold is required to keep it at an acceptablelevel. For luminosities above 2 · 1034cm−2s−1 at the LHC this willaffect the trigger efficiency of very important physics channels (e.g.W → eν inclusive decay). Even a very soft TR cut at HLT level,which preserves high electron efficiency (98%), allows to maintaina high trigger efficiency and its purity for physics events with asingle electron in a final state. TRT also plays a crucial role in thestudies where an electron suppression is required (e.g. hadronic modeof τ–decays). TR information is a completely independent tool forelectron identification and allows to study systematic uncertainties ofother electron reconstruction methods.

Electron identification is not the only TRD application. RecentTRDs for particle astrophysics are designed to directly measure theLorentz factor of high-energy nuclei by using the quadratic dependenceof the TR yield on nuclear charge; see Cherry and Muller papersin [113]. The radiator configuration (ℓ1, ℓ2) is tuned to extend theTR yield rise up to γ <∼ 105 using the more energetic part of the TRspectrum (up to 100 keV). Large density radiator materials (such asAl) are the best for this purpose. Direct absorption of the TR-photonsof these energies with thin detectors becomes problematic and TRdetection methods based on Compton scattering have been proposedto use (M. Cherry in [113], [114]) .

In all cases to-date, the radiator properties have been the mainlimiting factor for the TRDs, and for future progress in this field, itis highly important to develop effective and compact radiators. Bynow, all traditional materials have been studied extensively, so newtechnologies must be invented. The properties of all radiators aredefined by one basic parameter which is the plasma frequency of theradiator material – ω1 ∼ 1/me (see Eq. (33.48)). In semiconductormaterials, a quantum mechanical treatment of the electron binding tothe lattice leads to a small effective electron mass and correspondinglyto large values of ω1. All semiconductor materials have large Z andmay not be good candidates as TR radiators, but new materials,such as graphene, may offer similar features at much lower Z (M.Cherry in [114]) . It might even be possible to produce graphene-basedradiators with the required ω1 value. One should take into accountthat TR cutoff energy – Ec ∼ ω1γ and 95% of TR energy belongsto an interval of 0.1Ec to Ec. For large ω1 the detector must have alarger thickness to absorb x-rays in this range. It would be importantto control ω1 during radiator production and use it as a free parameterin the detector optimization process.

Si-microstrip tracking detectors operating in a magnetic field canalso be used for TR detection, even though the dE/dx losses in Siare much larger than the absorbed TR energy. The excellent spatialresolution of the Si detectors provides separation of the TR photonsand dE/dx losses at relatively modest distances between radiator anddetector. Simulations made on the basis of the beam-test data resultshas shown that in a magnetic field of 2 T and for the geometry of

the ATLAS Si-tracker proposed for sLHC, a rejection factor of > 30can be obtained for an electron efficiency above 90% over a particlemomentum range 2-30 GeV/c (Brigida et al. in [113] and [114]) . Newdetector techniques for TRDs are also under development and amongthem one should mention GasPixel detectors which allow to obtaina space point accuracy of < 30 µm and exploit all details of theparticle tracks to highlight individual TR clusters in the gas (F. Harjeset al. in [114]) . Thin films of heavy scintillators (V.V Berdnikovet al.

in [114]) might be very attractive in a combination with new radiatorsmentioned above.

34.6.7. Resistive-plate chambers : Written July 2015 by G.Aielli (U. Roma Tor Vergata).

The resistive-plate chamber (RPC) is a gaseous detector developedby R. Santonico and R. Cardarelli in the early 1980’s [119] *.Although its first purpose was to provide a competitive alternativeto large scintillator counters, it was quickly recognized that it hadrelevant potential as a timing tracker due to the high space-timelocalization of the discharge. The RPC, as sketched in Fig. 34.17, is alarge planar capacitor with two parallel high bulk resistivity electrodeplates (109–1013 Ω·cm) separated by a set of insulating spacers. Thespacers define a gap in the range from a few millimeters down to0.1 mm with a precision of a few ∼ µm. The gap is filled with asuitable atmospheric-pressure gas mixture which serves as a targetfor ionizing radiation. Primary ionization for sub-millimeter gas gapscan be insufficient, thus multiple gaps can be combined to ensure anacceptable detection efficiency [121].

Induced negative

signal on Y strip

Induced positive

signal on X strip

Insulating foil

HV contact

Graphite layer

Low density filler 3 mm

Copper ground plane

Resistive electrode 2 mm

Gas 2 mmspacerFrameHV

Figure 34.17: Schematic cross section of a generic single gapRPC.

The electrodes are most commonly made of high pressure phenolic-melaminic laminate (HPL), improperly referred to as ”bakelite”,or glass. A moderate electrode resistivity (∼ 105 Ω/¤) establishesa uniform electric field of several kV/mm across the gap, whichinitiates an electron avalanche following primary ionization. Theabove resistivity is low enough to ensure uniformity of the electricfield, yet still transparent to fast signal transients from avalanches.This field configuration allows an excellent space-time localizationof the signal. Due to the high electrode resistivity in RPCs, theelectrode time constant is much longer than discharge processes.Therefore only the locally-stored electrostatic energy contributes tothe discharge, which prevents the formation of sparks and leaves therest of the detector field unaffected. The gas-facing surface of HPLelectrodes are commonly coated with a resistive varnish (e.g. ∼ µmlayer of polymerized linseed oil) to achieve the necessary resistivityas well as to protect the electrode from discharge damage. As withother gaseous detectors, the gas mixture is optimized for each specificapplication. In general it needs to contain a component to quenchUV photons, thus avoiding discharge propagation. An electronegativecomponent controls the avalanche growth in case of very highelectric fields [122,123]. To first order, each primary ionization inan RPC is exponentially amplified according to its distance from theanode. Therefore RPC signals span a large dynamic range, unlikegaseous detectors where ionization and amplification occur in separateregions (e.g. wire chambers or MPGDs). For increasingly strongerfields, the avalanche exponential growth progressively saturates tolinear [124], and finally reaches a strongly-saturated ”streamer”transition which exhausts all the locally-available energy [125]. Thesignal induced by the fast movement of the avalanche electrons is

* The RPC was based on earlier work on a spark counter with onemetallic and one high-resistivity plate [120].


isotropically distributed with respect to the field direction and presentwith equal but opposite amplitude on the two electrodes. A setof metallic readout electrodes (e.g. pads or strips) placed behindthe resistive electrodes detect the charge pulse. This feature allowsfor 2D localization of the signal with uniform spatial resolution.Sensitivity to high-frequency electron avalanche signals over largeRPC areas requires a correspondingly adequate Faraday cage andreadout structure design. In particular, the front end electronics mustbe time-sensitive with a fast response and low noise, although theserequirements are usually in competition [126].

34.6.7.1. RPC types and applications: RPCs are generally classifiedin two categories depending on the gas gap structure: single gapRPCs (described above) and multiple gap RPCs (typically referredas mRPCs or timing RPCs). While they are both based on the sameprinciple they have different construction techniques, performance andlimitations, making them suitable for different applications. Due to itssimplicity and robustness, the single gap RPC is ideal for covering verylarge surfaces. Typical detector systems can have sensitive surfaceareas up to ∼104 m2, with single module areas of a few m2, and aspace-time resolution down to ∼0.4 ns × 100 µm [127,128]. Typicalapplications are in muon systems (e.g. the muon trigger systems ofthe LHC experiments) or ground and underground based cosmic raysand neutrino arrays [129]. Moreover, single gap RPCs have recentlyfound an application in tracking calorimetry [130]. The mRPC allowsfor smaller gas gap thicknesses while still maintaining a sufficientgaseous target. Th most common version [131] consists of a stackof floating glass electrodes separated by monofilament (i.e. fishing)line, sandwiched between two external electrodes which provide thehigh-voltage bias. The floating glass electrodes assume a potentialdetermined by the avalanche processes occurring between them.mRPCs have been largely used in TOF systems and in applicationssuch as timing PET.

34.6.7.2. Time and space resolution: The RPC field configurationgenerates an avalanche which is strongly correlated in space and timeto the original ionizing event. Space-time uncertainties generally arisefrom the statistical fluctuations of the ionization and multiplicationprocesses, and from the characteristics of the readout and front-endelectronics. The intrinsic signal latency is commonly in the ns range,making the RPC suitable for applications where a low latency isessential. A higher time resolution and shorter signal duration iscorrelated with a thinner gas gap, although a higher electric fieldis required for sufficient avalanche development [131,132]. Typicaltiming performances are from around 1 ns with a 2 mm gas gap, downto 20 ps for a stack of several 0.1 mm gaps [133]. The mechanicaldelicacy of sub-mm gap structures currently limit this technique tosmall detector areas. Digital strip readouts are commonly used, withspatial resolution determined by the strip pitch and the cluster size(∼0.5 cm). Recent developments toward higher spatial resolutionsare mostly based on charge centroid techniques, benefiting fromthe availability of low-cost high-performance readout electronics.The present state of the art detectors have a combined space-timeresolution of ∼50 ps × 40 µm [134].

34.6.7.3. Rate capability and ageing: RPC rate capability is limitedby the voltage drop on resistive electrodes, ∆V = Va−Vgas = I ·R [135].Here Va is the applied voltage, Vgas is the effective voltage on thegas, R = ρ · d/S is the total electrode resistance and I is the workingcurrent. Expressing I as the particle flux Φ times an average chargeper avalanche 〈Q〉 gives ∆V/Φ = ρ · d · 〈Q〉. A large I not onlylimits the rate capability but also affects the long term performanceof the detector. Discharges deplete the conductive properties ofHPL electrodes [136]. In the presence of fluorocarbons and water,discharges generate hydrofluoric acid (HF) which damages internaldetector surfaces, particularly glass electrodes [137]. HF damagecan be mitigated by preventing water vapor contamination and bysufficient flushing of the gas gap. Operating in the streamer regimeputs low requirements on the front end electronics sensitivity, butgenerally limits the counting rate capability to ∼100 Hz/cm2 andrequires stability over a large gain range. Higher rate operation canbe achieved by reducing gas gain in favor of electronic amplification.Increasing electronegative gases, such as C2H2F4 and SF6 [123], shifts

the streamer transition to higher gains. With these techniques, stableperformance at high rates (e.g. 10 kHz/cm2) has been achieved forlarge area single gap RPCs [126]. Additional techniques rely on thenatural redundancy and small gain of multiple gap structures [138]and electrodes made with lower resistivity materials [139].

34.7. Semiconductor detectors

Updated November 2013 by H. Spieler.

Semiconductor detectors provide a unique combination of energyand position resolution. In collider detectors they are most widelyused as position sensing devices and photodetectors (Sec. 34.2).Integrated circuit technology allows the formation of high-densitymicron-scale electrodes on large (15–20 cm diameter) wafers, providingexcellent position resolution. Furthermore, the density of silicon andits small ionization energy yield adequate signals with active layersonly 100–300 µm thick, so the signals are also fast (typically tensof ns). The high energy resolution is a key parameter in x-ray,gamma, and charged particle spectroscopy, e.g., in neutrinoless doublebeta decay searches. Silicon and germanium are the most commonlyused materials, but gallium-arsenide, CdTe, CdZnTe, and othermaterials are also useful. CdZnTe provides a higher stopping powerand the ratio of Cd to Zn concentrations changes the bandgap. Gedetectors are commonly operated at liquid nitrogen temperature toreduce the bias current, which depends exponentially on temperature.Semiconductor detectors depend crucially on low-noise electronics (seeSec. 34.8), so the detection sensitivity is determined by signal chargeand capacitance. For a comprehensive discussion of semiconductordetectors and electronics see Ref. 140 or the tutorial websitehttp://www-physics.lbl.gov/ spieler.

34.7.1. Materials Requirements :

Semiconductor detectors are essentially solid state ionizationchambers. Absorbed energy forms electron-hole pairs, i.e., negativeand positive charge carriers, which under an applied electric fieldmove towards their respective collection electrodes, where they inducea signal current. The energy required to form an electron-hole pairis proportional to the bandgap. In tracking detectors the energy lossin the detector should be minimal, whereas for energy spectroscopythe stopping power should be maximized, so for gamma rays high-Zmaterials are desirable.

Measurements on silicon photodiodes [141] show that for photonenergies below 4 eV one electron-hole (e-h) pair is formed per incidentphoton. The mean energy Ei required to produce an e-h pair peaks at4.4 eV for a photon energy around 6 eV. Above ∼1.5 keV it assumesa constant value, 3.67 eV at room temperature. It is larger than thebandgap energy because momentum conservation requires excitationof lattice vibrations (phonons). For minimum-ionizing particles, themost probable charge deposition in a 300 µm thick silicon detector isabout 3.5 fC (22000 electrons). Other typical ionization energies are2.96 eV in Ge, 4.2 eV in GaAs, and 4.43 eV in CdTe.

Since both electronic and lattice excitations are involved, thevariance in the number of charge carriers N = E/Ei produced byan absorbed energy E is reduced by the Fano factor F (about0.1 in Si and Ge). Thus, σN =

√FN and the energy resolution

σE/E =√

FEi/E. However, the measured signal fluctuations areusually dominated by electronic noise or energy loss fluctuations inthe detector. The electronic noise contributions depend on the pulseshaping in the signal processing electronics, so the choice of theshaping time is critical (see Sec. 34.8).

A smaller bandgap would produce a larger signal and improveenergy resolution, but the intrinsic resistance of the material is critical.Thermal excitation, given by the Fermi-Dirac distribution, promoteselectrons into the conduction band, so the thermally excited carrierconcentration increases exponentially with decreasing bandgaps. Inpure Si the carrier concentration is ∼1010cm−3 at 300K, correspondingto a resistivity ρ ≈ 400 kΩ cm. In reality, crystal imperfections andminute impurity concentrations limit Si carrier concentrations to∼ 1011 cm−3 at 300K, corresponding to a resistivity ρ ≈ 40 kΩ cm.In practice, resistivities up to 20 kΩ cm are available, with massproduction ranging from 5 to 10 kΩ cm. Signal currents at keV scale


energies are of order µA. However, for a resistivity of 104 Ωcm a300 µm thick sensor with 1 cm2 area would have a resistance of300 Ω , so 30 V would lead to a current flow of 100 mA and a powerdissipation of 3 W. On the other hand, high-quality single crystalsof Si and Ge can be grown economically with suitably large volumes,so to mitigate the effect of resistivity one resorts to reverse-biaseddiode structures. Although this reduces the bias current relative to aresistive material, the thermally excited leakage current can still beexcessive at room temperature, so Ge diodes are typically operated atliquid nitrogen temperature (77K).

A major effort is to find high-Z materials with a bandgap thatis sufficiently high to allow room-temperature operation while stillproviding good energy resolution. Compound semiconductors, e.g.,CdZnTe, can allow this, but typically suffer from charge collectionproblems, characterized by the product µτ of mobility and carrierlifetime. In Si and Ge µτ > 1 cm2 V−1 for both electrons and holes,whereas in compound semiconductors it is in the range 10−3–10−8.Since for holes µτ is typically an order of magnitude smaller thanfor electrons, detector configurations where the electron contributionto the charge signal dominates—e.g., strip or pixel structures—canprovide better performance.

34.7.2. Detector Configurations :

A p-n junction operated at reverse bias forms a sensitive regiondepleted of mobile charge and sets up an electric field that sweepscharge liberated by radiation to the electrodes. Detectors typically usean asymmetric structure, e.g., a highly doped p electrode and a lightlydoped n region, so that the depletion region extends predominantlyinto the lightly doped volume.

In a planar device the thickness of the depleted region is

W =√

2ǫ (V + Vbi)/Ne =√

2ρµǫ(V + Vbi) , (34.19)

where V = external bias voltage

Vbi = “built-in” voltage (≈ 0.5 V for resistivities typically usedin Si detectors)

N = doping concentration

e = electronic charge

ǫ = dielectric constant = 11.9 ǫ0 ≈ 1 pF/cm in Si

ρ = resistivity (typically 1–10 kΩ cm in Si)

µ = charge carrier mobility

= 1350 cm2 V−1 s−1 for electrons in Si

= 450 cm2 V−1 s−1 for holes in Si

In Si

W = 0.5 [µm/√

Ω-cm · V] ×√

ρ(V + Vbi) for n-type Si, and

W = 0.3 [µm/√

Ω-cm · V] ×√

ρ(V + Vbi) for p-type Si.

The conductive p and n regions together with the depleted volumeform a capacitor with the capacitance per unit area

C = ǫ/W ≈ 1 [pF/cm] /W in Si. (34.20)

In strip and pixel detectors the capacitance is dominated by thefringing capacitance to neighboring electrodes. For example, thestrip-to-strip Si fringing capacitance is ∼ 1–1.5 pF cm−1 of striplength at a strip pitch of 25–50 µm.

Large volume (∼ 102–103 cm3) Ge detectors are commonlyconfigured as coaxial detectors, e.g., a cylindrical n-type crystal with5–10 cm diameter and 10 cm length with an inner 5–10mm diametern+ electrode and an outer p+ layer forming the diode junction. Gecan be grown with very low impurity levels, 109–1010 cm−3 (HPGe),so these large volumes can be depleted with several kV.

34.7.3. Signal Formation :

The signal pulse shape depends on the instantaneous carriervelocity v(x) = µE(x) and the electrode geometry, which determinesthe distribution of induced charge (e.g., see Ref. 140, pp. 71–83).Charge collection time decreases with increasing bias voltage, and canbe reduced further by operating the detector with “overbias,” i.e., abias voltage exceeding the value required to fully deplete the device.Note that in partial depletion the electric field goes to zero, whereasgoing beyond full depletion adds a constantly distributed field. Thecollection time is limited by velocity saturation at high fields (inSi approaching 107 cm/s at E > 104 V/cm); at an average field of104 V/cm the collection time is about 15 ps/µm for electrons and30 ps/µm for holes. In typical fully-depleted detectors 300 µm thick,electrons are collected within about 10 ns, and holes within about25 ns.

Position resolution is limited by transverse diffusion during chargecollection (typically 5 µm for 300 µm thickness) and by knock-onelectrons. Resolutions of 2–4 µm (rms) have been obtained in beamtests. In magnetic fields, the Lorentz drift deflects the electron andhole trajectories and the detector must be tilted to reduce spatialspreading (see “Hall effect” in semiconductor textbooks).

Electrodes can be in the form of cm-scale pads, strips, or µm-scalepixels. Various readout structures have been developed for pixels, e.g.,CCDs, DEPFETs, monolithic pixel devices that integrate sensor andelectronics (MAPS), and hybrid pixel devices that utilize separatesensors and readout ICs connected by two-dimensional arrays of solderbumps. For an overview and further discussion see Ref. 140.

In gamma ray spectroscopy (Eγ >102 keV) Compton scatteringdominates, so for a significant fraction of events the incident gammaenergy is not completely absorbed, i.e., the Compton scatteredphoton escapes from the detector and the energy deposited by theCompton electron is only a fraction of the total. Distinguishingmulti-interaction events, e.g., multiple Compton scatters with afinal photoelectric absorption, from single Compton scatters allowsbackground suppression. Since the individual interactions take placein different parts of the detector volume, these events can bedistinguished by segmenting the outer electrode of a coaxial detectorand analyzing the current pulse shapes. The different collection timescan be made more distinguishable by using “point” electrodes, wheremost of the signal is induced when charges are close to the electrode,similarly to strip or pixel detectors. Charge clusters arriving fromdifferent positions in the detector will arrive at different times andproduce current pulses whose major components are separated in time.Point electrodes also reduce the electrode capacitance, which reduceselectronic noise, but careful design is necessary to avoid low-fieldregions in the detector volume.

34.7.4. Radiation Damage : Radiation damage occurs throughtwo basic mechanisms:

1. Bulk damage due to displacement of atoms from their latticesites. This leads to increased leakage current, carrier trapping,and build-up of space charge that changes the required operatingvoltage. Displacement damage depends on the nonionizing energyloss and the energy imparted to the recoil atoms, which caninitiate a chain of subsequent displacements, i.e., damage clusters.Hence, it is critical to consider both particle type and energy.

2. Surface damage due to charge build-up in surface layers, whichleads to increased surface leakage currents. In strip detectors theinter-strip isolation is affected. The effects of charge build-up arestrongly dependent on the device structure and on fabricationdetails. Since the damage is proportional to the absorbed energy(when ionization dominates), the dose can be specified in rad (orGray) independent of particle type.

The increase in reverse bias current due to bulk damage is∆Ir = αΦ per unit volume, where Φ is the particle fluence and α thedamage coefficient (α ≈ 3×10−17 A/cm for minimum ionizing protonsand pions after long-term annealing; α ≈ 2 × 10−17 A/cm for 1 MeV


neutrons). The reverse bias current depends strongly on temperature

IR(T2)

IR(T1)=

(

T2

T1

)2

exp

[

− E

2k

(

T1 − T2

T1T2

)]

, (34.21)

where E = 1.2 eV, so rather modest cooling can reduce the currentsubstantially (∼ 6-fold current reduction in cooling from roomtemperature to 0C).

Displacement damage forms acceptor-like states. These trapelectrons, building up a negative space charge, which in turn requiresan increase in the applied voltage to sweep signal charge through thedetector thickness. This has the same effect as a change in resistivity,i.e., the required voltage drops initially with fluence, until the positiveand negative space charge balance and very little voltage is required tocollect all signal charge. At larger fluences the negative space chargedominates, and the required operating voltage increases (V ∝ N).The safe limit on operating voltage ultimately limits the detectorlifetime. Strip detectors specifically designed for high voltages havebeen extensively operated at bias voltages >500V. Since the effectof radiation damage depends on the electronic activity of defects,various techniques have been applied to neutralize the damage sites.For example, additional doping with oxygen can increase the allowablecharged hadron fluence roughly three-fold [142]. Detectors withcolumnar electrodes normal to the surface can also extend operationallifetime [143]. The increase in leakage current with fluence, on theother hand, appears to be unaffected by resistivity and whether thematerial is n or p-type. At fluences beyond 1015 cm−2 decreasedcarrier lifetime becomes critical [144,145].

Strip and pixel detectors have remained functional at fluencesbeyond 1015 cm−2 for minimum ionizing protons. At this damagelevel, charge loss due to recombination and trapping becomessignificant and the high signal-to-noise ratio obtainable with low-capacitance pixel structures extends detector lifetime. The highermobility of electrons makes them less sensitive to carrier lifetimethan holes, so detector configurations that emphasize the electroncontribution to the charge signal are advantageous, e.g., n+ stripsor pixels on a p- or n-substrate. The occupancy of the defect chargestates is strongly temperature dependent; competing processes canincrease or decrease the required operating voltage. It is critical tochoose the operating temperature judiciously (−10 to 0C in typicalcollider detectors) and limit warm-up periods during maintenance.For a more detailed summary see Ref. 146 and and the web-sites of theROSE and RD50 collaborations at http://RD48.web.cern.ch/rd48

and http://RD50.web.cern.ch/rd50. Materials engineering, e.g.,introducing oxygen interstitials, can improve certain aspects and isunder investigation. At high fluences diamond is an alternative, butoperates as an insulator rather than a reverse-biased diode.

Currently, the lifetime of detector systems is still limited bythe detectors; in the electronics use of standard “deep submicron”CMOS fabrication processes with appropriately designed circuitry hasincreased the radiation resistance to fluences > 1015 cm−2 of minimumionizing protons or pions. For a comprehensive discussion of radiationeffects see Ref. 147.

34.8. Low-noise electronics

Revised November 2013 by H. Spieler.

Many detectors rely critically on low-noise electronics, either toimprove energy resolution or to allow a low detection threshold. Atypical detector front-end is shown in Fig. 34.18.

The detector is represented by a capacitance Cd, a relevant modelfor most detectors. Bias voltage is applied through resistor Rb and thesignal is coupled to the preamplifier through a blocking capacitor Cc.The series resistance Rs represents the sum of all resistances presentin the input signal path, e.g. the electrode resistance, any inputprotection networks, and parasitic resistances in the input transistor.The preamplifier provides gain and feeds a pulse shaper, which tailorsthe overall frequency response to optimize signal-to-noise ratio whilelimiting the duration of the signal pulse to accommodate the signalpulse rate. Even if not explicitly stated, all amplifiers provide someform of pulse shaping due to their limited frequency response.

OUTPUTDETECTOR

BIASRESISTOR

Rb

Cc Rs

Cb

Cd

DETECTOR BIAS

PULSE SHAPERPREAMPLIFIER

Figure 34.18: Typical detector front-end circuit.

The equivalent circuit for the noise analysis (Fig. 34.19) includesboth current and voltage noise sources. The leakage current of asemiconductor detector, for example, fluctuates due to continuouselectron emission statistics. The statistical fluctuations in the chargemeasurement will scale with the square root of the total number ofrecorded charges, so this noise contribution increases with the widthof the shaped output pulse. This “shot noise” ind is represented by acurrent noise generator in parallel with the detector. Resistors exhibitnoise due to thermal velocity fluctuations of the charge carriers. Thisyields a constant noise power density vs. frequency, so increasing thebandwidth of the shaped output pulse, i.e. reducing the shaping time,will increase the noise. This noise source can be modeled either as avoltage or current generator. Generally, resistors shunting the inputact as noise current sources and resistors in series with the input actas noise voltage sources (which is why some in the detector communityrefer to current and voltage noise as “parallel” and “series” noise).Since the bias resistor effectively shunts the input, as the capacitor Cb

passes current fluctuations to ground, it acts as a current generatorinb and its noise current has the same effect as the shot noise currentfrom the detector. Any other shunt resistances can be incorporatedin the same way. Conversely, the series resistor Rs acts as a voltagegenerator. The electronic noise of the amplifier is described fully by acombination of voltage and current sources at its input, shown as ena

and ina.

DETECTOR

Cd

BIASRESISTOR

SERIESRESISTOR

AMPLIFIER +PULSE SHAPER

Rb

Rs

i

i i

e

e

nd

nb na

ns

na

Figure 34.19: Equivalent circuit for noise analysis.

Shot noise and thermal noise have a “white” frequency distribution,i.e. the spectral power densities dPn/df ∝ di2n/df ∝ de2

n/df areconstant with the magnitudes

i2nd = 2eId ,

i2nb =4kT

Rb,

e2ns = 4kTRs , (34.22)

where e is the electronic charge, Id the detector bias current, k theBoltzmann constant and T the temperature. Typical amplifier noiseparameters ena and ina are of order nV/

√Hz and pA/

√Hz. Trapping

and detrapping processes in resistors, dielectrics and semiconductorscan introduce additional fluctuations whose noise power frequentlyexhibits a 1/f spectrum. The spectral density of the 1/f noise voltageis

e2nf =

Af

f, (34.23)

where the noise coefficient Af is device specific and of order

10−10–10−12 V2.


A fraction of the noise current flows through the detectorcapacitance, resulting in a frequency-dependent noise voltagein/(ωCd), which is added to the noise voltage in the input circuit.Thus, the current noise contribution increases with lowering frequency,so its contribution increases with shaping pulse width. Since theindividual noise contributions are random and uncorrelated, theyadd in quadrature. The total noise at the output of the pulseshaper is obtained by integrating over the full bandwidth ofthe system. Superimposed on repetitive detector signal pulses ofconstant magnitude, purely random noise produces a Gaussian signaldistribution.

Since radiation detectors typically convert the deposited energyinto charge, the system’s noise level is conveniently expressed as anequivalent noise charge Qn, which is equal to the detector signalthat yields a signal-to-noise ratio of one. The equivalent noise chargeis commonly expressed in Coulombs, the corresponding number ofelectrons, or the equivalent deposited energy (eV). For a capacitivesensor

Q2n = i2nFiTS + e2

nFvC2

TS+ Fvf AfC2 , (34.24)

where C is the sum of all capacitances shunting the input, Fi, Fv,and Fvf depend on the shape of the pulse determined by the shaperand Ts is a characteristic time, for example, the peaking time of asemi-gaussian pulse or the sampling interval in a correlated doublesampler. The form factors Fi, Fv are easily calculated

Fi =1

2TS

∫

∞

−∞

[W (t)]2 dt , Fv =TS

2

∫

∞

−∞

[

dW (t)

dt

]2

dt , (34.25)

where for time-invariant pulse-shaping W (t) is simply the system’simpulse response (the output signal seen on an oscilloscope) for ashort input pulse with the peak output signal normalized to unity.For more details see Refs. 148 and 149.

A pulse shaper formed by a single differentiator and integrator withequal time constants has Fi = Fv = 0.9 and Fvf = 4, independentof the shaping time constant. The overall noise bandwidth, however,depends on the time constant, i.e. the characteristic time Ts. Thecontribution from noise currents increases with shaping time, i.e., pulseduration, whereas the voltage noise decreases with increasing shapingtime, i.e. reduced bandwidth. Noise with a 1/f spectrum dependsonly on the ratio of upper to lower cutoff frequencies (integratorto differentiator time constants), so for a given shaper topologythe 1/f contribution to Qn is independent of Ts. Furthermore, thecontribution of noise voltage sources to Qn increases with detectorcapacitance. Pulse shapers can be designed to reduce the effectof current noise, e.g., mitigate radiation damage. Increasing pulsesymmetry tends to decrease Fi and increase Fv (e.g., to 0.45 and 1.0for a shaper with one CR differentiator and four cascaded integrators).For the circuit shown in Fig. 34.19,

Q2n =

(

2eId + 4kT/Rb + i2na

)

FiTS

+(

4kTRs + e2na

)

FvC2d/TS + FvfAfC2

d .(34.26)

As the characteristic time TS is changed, the total noise goesthrough a minimum, where the current and voltage contributions areequal. Fig. 34.20 shows a typical example. At short shaping times thevoltage noise dominates, whereas at long shaping times the currentnoise takes over. The noise minimum is flattened by the presenceof 1/f noise. Increasing the detector capacitance will increase thevoltage noise and shift the noise minimum to longer shaping times.

For quick estimates, one can use the following equation, whichassumes an FET amplifier (negligible ina) and a simple CR–RCshaper with time constants τ (equal to the peaking time):

(Qn/e)2 = 12

[

1

nA · ns

]

Idτ + 6 × 105[

kΩ

ns

]

τ

Rb

+ 3.6 × 104

[

ns

(pF)2(nV)2/Hz

]

e2n

C2

τ.

(34.27)

Equ

ival

ent n

oise

cha

rge

(e)

10000

5000

2000

1000

100

500

200

10.10.01 10 100Shaping time (µs)

1/f noise

Current n

oise Voltage noise

Total

Total

Increasing V noise

Figure 34.20: Equivalent noise charge vs shaping time.Changing the voltage or current noise contribution shifts thenoise minimum. Increased voltage noise is shown as an example.

Noise is improved by reducing the detector capacitance andleakage current, judiciously selecting all resistances in the inputcircuit, and choosing the optimum shaping time constant. Anothernoise contribution to consider is that noise cross-couples from theneighboring front-ends in strip and pixel detectors through theinter-electrode capacitance.

The noise parameters of the amplifier depend primarily on theinput device. In field effect transistors, the noise current contributionis very small, so reducing the detector leakage current and increasingthe bias resistance will allow long shaping times with correspondinglylower noise. In bipolar transistors, the base current sets a lower boundon the noise current, so these devices are best at short shaping times.In special cases where the noise of a transistor scales with geometry,i.e., decreasing noise voltage with increasing input capacitance, thelowest noise is obtained when the input capacitance of the transistoris equal to the detector capacitance, albeit at the expense of powerdissipation. Capacitive matching is useful with field-effect transistors,but not bipolar transistors. In bipolar transistors, the minimumobtainable noise is independent of shaping time, but only at theoptimum collector current IC , which does depend on shaping time.

Q2n,min = 4kT

C√βDC

√

FiFv at Ic =kT

eC

√

βDC

√

Fv

Fi

1

TS, (34.28)

where βDC is the DC current gain. For a CR–RC shaper andβDC = 100,

Qn,min/e ≈ 250√

C/pF . (34.29)

Practical noise levels range from ∼ 1e for CCD’s at long shapingtimes to ∼ 104 e in high-capacitance liquid argon calorimeters. Siliconstrip detectors typically operate at ∼ 103 electrons, whereas pixeldetectors with fast readout provide noise of several hundred electrons.

In timing measurements, the slope-to-noise ratio must be optimized,rather than the signal-to-noise ratio alone, so the rise time tr of thepulse is important. The “jitter” σt of the timing distribution is

σt =σn

(dS/dt)ST

≈ trS/N

, (34.30)

where σn is the rms noise and the derivative of the signal dS/dt isevaluated at the trigger level ST . To increase dS/dt without incurringexcessive noise, the amplifier bandwidth should match the rise-timeof the detector signal. The 10 to 90% rise time of an amplifier withbandwidth fU is 0.35/fU . For example, an oscilloscope with 350 MHzbandwidth has a 1 ns rise time. When amplifiers are cascaded, whichis invariably necessary, the individual rise times add in quadrature.

tr ≈√

t2r1 + t2r2 + ... + t2rn . (34.31)


Increasing signal-to-noise ratio also improves time resolution, sominimizing the total capacitance at the input is also important.At high signal-to-noise ratios, the time jitter can be much smallerthan the rise time. The timing distribution may shift with signallevel (“walk”), but this can be corrected by various means, either inhardware or software [8].

The basic principles discussed above apply to both analog anddigital signal processing. In digital signal processing the pulse shapershown in Fig. 34.18 is replaced by an analog to digital converter(ADC) followed by a digital processor that determines the pulse shape.Digital signal processing allows great flexibility in implementingfiltering functions. The software can be changed readily to adapt to awide variety of operating conditions and it is possible to implementfilters that are impractical or even impossible using analog circuitry.However, this comes at the expense of increased circuit complexityand increased demands on the ADC compared to analog shaping.

If the sampling rate of the ADC is too low, high frequencycomponents will be transferred to lower frequencies (“aliasing”).The sampling rate of the ADC must be high enough to capturethe maximum frequency component of the input signal. Apartfrom missing information on the fast components of the pulse,undersampling introduces spurious artifacts. If the frequency range ofthe input signal is much greater, the noise at the higher frequencieswill be transferred to lower frequencies and increase the noise level inthe frequency range of pulses formed in the subsequent digital shaper.The Nyquist criterion states that the sampling frequency must be atleast twice the maximum relevant input frequency. This requires thatthe bandwith of the circuitry preceding the ADC must be limited.The most reliable technique is to insert a low-pass filter.

The digitization process also introduces inherent noise, sincethe voltage range ∆V corresponding to a minimum bit introducesquasi-random fluctuations relative to the exact amplitude

σn =∆V√

12. (34.32)

When the Nyquist condition is fulfilled the noise bandwidth ∆fn isspread nearly uniformly and extends to 1/2 the sampling frequencyfS , so the spectral noise density

en =σn√∆fn

=∆V√

12· 1√

fS/2=

∆V√6fS

. (34.33)

Sampling at a higher frequency spreads the total noise over alarger frequency range, so oversampling can be used to increase theeffective resolution. In practice, this quantization noise is increasedby differential nonlinearity. Furthermore, the equivalent input noise ofADCs is often rather high, so the overall gain of the stages precedingthe ADC must be sufficiently large for the preamplifier input noise tooverride.

When implemented properly, digital signal processing providessignificant advantages in systems where the shape of detector signalpulses changes greatly, for example in large semiconductor detectorsfor gamma rays or in gaseous detectors (e.g. TPCs) where theduration of the current pulse varies with drift time, which can rangeover orders of magnitude. Where is analog signal processing best(most efficient)? In systems that require fast time response the highpower requirements of high-speed ADCs are prohibitive. Systems thatare not sensitive to pulse shape can use fixed shaper constants andrather simple filters, which can be either continuous or sampled. Inhigh density systems that require small circuit area and low power(e.g. strip and pixel detectors), analog filtering often yields therequired response and tends to be most efficient.

It is important to consider that additional noise is often introducedby external electronics, e.g. power supplies and digital systems.External noise can couple to the input. Often the “commongrounding” allows additional noise current to couple to the currentloop connecting the detector to the preamp. Recognizing additionalnoise sources and minimizing cross-coupling to the detector currentloop is often important. Understanding basic physics and its practicaleffects is important in forming a broad view of the detector system

and recognizing potential problems (e.g. modified data), rather thanmerely following standard recipes.

For a more detailed introduction to detector signal processingand electronics see Ref. 140 or the tutorial website http://www-

physics.lbl.gov/ spieler.

34.9. Calorimeters

A calorimeter is designed to measure a particle’s (or jet’s) energyand direction for an (ideally) contained electromagnetic (EM) orhadronic shower. The characteristic interaction distance for anelectromagnetic interaction is the radiation length X0, which rangesfrom 13.8 g cm−2 in iron to 6.0 g cm−2 in uranium.* Similarly, thecharacteristic nuclear interaction length λI varies from 132.1 g cm−2

(Fe) to 209 g cm−2 (U).† In either case, a calorimeter must be manyinteraction lengths deep, where “many” is determined by physical size,cost, and other factors. EM calorimeters tend to be 15–30 X0 deep,while hadronic calorimeters are usually compromised at 5–8 λI . Inreal experiments there is likely to be an EM calorimeter in front of thehadronic section, which in turn has less sampling density in the back,so the hadronic cascade occurs in a succession of different structures.

20 30 50 70 9040 60 80 100Z

10

0

20

30

40

50

1

0

2

3

4

5

ΛI/

ρ (

cm)

ΛI

X0/

ρ (

cm)

X0

CuFe Ru Pd W Au Pb U

Figure 34.21: Nuclear interaction length λI/ρ (circles) andradiation length X0/ρ (+’s) in cm for the chemical elementswith Z > 20 and λI < 50 cm.

In all cases there is a premium on small λI/ρ and X0/ρ (bothwith units of length). These quantities are shown for Z > 20 forthe chemical elements in Fig. 34.21. For the hadronic case, metallicabsorbers in the W–Au region are best, followed by U. The Ru–Pdregion elements are rare and expensive. Lead is a bad choice. Givencost considerations, Fe and Cu might be appropriate choices. For EMcalorimeters high Z is preferred, and lead is not a bad choice.

These considerations are for sampling calorimeters consisting ofmetallic absorber sandwiched or (threaded) with an active materialwhich generates signal. The active medium may be a scintillator, anionizing noble liquid, a gas chamber, a semiconductor, or a Cherenkovradiator. The average interaction length is thus greater than that ofthe absorber alone, sometimes substantially so.

There are also homogeneous calorimeters, in which the entirevolume is sensitive, i.e., contributes signal. Homogeneous calorimeters(so far usually electromagnetic) may be built with inorganic heavy(high density, high 〈Z〉) scintillating crystals, or non-scintillatingCherenkov radiators such as lead glass and lead fluoride. Scintillationlight and/or ionization in noble liquids can be detected. Nuclearinteraction lengths in inorganic crystals range from 17.8 cm (LuAlO3)to 42.2 cm (NaI). Popular choices have been BGO with λI = 22.3 cmand X0 = 1.12 cm, and PbWO4 (20.3 cm and 0.89 cm). Properties ofthese and other commonly used inorganic crystal scintillators can befound in Table 34.4.

* X0 = 120 g cm−2 Z−2/3 to better than 5% for Z > 23.† λI = 37.8 g cm−2 A0.312 to within 0.8% for Z > 15.

See pdg.lbl.gov/AtomicNuclearProperties for actual values.


34.9.1. Electromagnetic calorimeters :

Revised September 2015 by R.-Y. Zhu (California Institute ofTechnology).

The development of electromagnetic showers is discussed in thesection on “Passage of Particles Through Matter” (Sec. 33 of thisReview). Formulae are given which approximately describe averageshowers, but since the physics of electromagnetic showers is wellunderstood, detailed and reliable Monte Carlo simulation is possible.EGS4 [150] and GEANT [151] have emerged as the standards.

There are homogeneous and sampling electromagnetic calorimeters.In a homogeneous calorimeter the entire volume is sensitive, i.e.,contributes signal. Homogeneous electromagnetic calorimeters maybe built with inorganic heavy (high-Z) scintillating crystals such asBaF2, BGO, CsI, LYSO, NaI and PWO, non-scintillating Cherenkovradiators such as lead glass and lead fluoride (PbF2), or ionizing nobleliquids. Properties of commonly used inorganic crystal scintillatorscan be found in Table 34.4. A sampling calorimeter consists of anactive medium which generates signal and a passive medium whichfunctions as an absorber. The active medium may be a scintillator, anionizing noble liquid, a semiconductor, or a gas chamber. The passivemedium is usually a material of high density, such as lead, tungsten,iron, copper, or depleted uranium.

The energy resolution σE/E of a calorimeter can be parameterizedas a/

√E⊕b⊕c/E, where ⊕ represents addition in quadrature and E is

in GeV. The stochastic term a represents statistics-related fluctuationssuch as intrinsic shower fluctuations, photoelectron statistics, deadmaterial at the front of the calorimeter, and sampling fluctuations.For a fixed number of radiation lengths, the stochastic term a for asampling calorimeter is expected to be proportional to

√

t/f , where tis plate thickness and f is sampling fraction [152,153]. While a is ata few percent level for a homogeneous calorimeter, it is typically 10%for sampling calorimeters.

The main contributions to the systematic, or constant, term bare detector non-uniformity and calibration uncertainty. In the caseof the hadronic cascades discussed below, non-compensation alsocontributes to the constant term. One additional contribution tothe constant term for calorimeters built for modern high-energyphysics experiments, operated in a high-beam intensity environment,is radiation damage of the active medium. This can be mitigatedby developing radiation-hard active media [51], by reducing thesignal path length [52] and by frequent in situ calibration andmonitoring [50,153]. With effort, the constant term b can be reducedto below one percent. The term c is due to electronic noise summedover readout channels within a few Moliere radii. The best energyresolution for electromagnetic shower measurement is obtained in totalabsorption homogeneous calorimeters, e.g. calorimeters built withheavy crystal scintillators. These are used when ultimate performanceis pursued.

The position resolution depends on the effective Moliere radiusand the transverse granularity of the calorimeter. Like the energyresolution, it can be factored as a/

√E ⊕ b, where a is a few to 20 mm

and b can be as small as a fraction of mm for a dense calorimeterwith fine granularity. Electromagnetic calorimeters may also providedirection measurement for electrons and photons. This is importantfor photon-related physics when there are uncertainties in event origin,since photons do not leave information in the particle tracking system.Typical photon angular resolution is about 45 mrad/

√E, which can

be provided by implementing longitudinal segmentation [154] for asampling calorimeter or by adding a preshower detector [155] for ahomogeneous calorimeter without longitudinal segmentation.

Novel technologies have been developed for electromagneticcalorimetry. New heavy crystal scintillators, such as PWO andLYSO:Ce (see Sec. 34.4), have attracted much attention. In somecases, such as PWO, it has received broad applications in high-energyand nuclear physics experiments. The “spaghetti” structure has beendeveloped for sampling calorimetry with scintillating fibers as thesensitive medium. The “shashlik” structure has been developed forsampling calorimetry with wavelength shifting fibers functioning asboth the converter and transporter for light generated in the sensitivemedium. The “accordion” structure has been developed for sampling

calorimetry with ionizing noble liquid as the sensitive medium.

Table 34.8 provides a brief description of typical electromagneticcalorimeters built recently for high-energy physics experiments. Alsolisted in this table are calorimeter depths in radiation lengths (X0) andthe achieved energy resolution. Whenever possible, the performance ofcalorimeters in situ is quoted, which is usually in good agreement withprototype test beam results as well as EGS or GEANT simulations,provided that all systematic effects are properly included. Detailedreferences on detector design and performance can be found inAppendix C of reference [153] and Proceedings of the InternationalConference series on Calorimetry in High Energy Physics.

Table 34.8: Resolution of typical electromagnetic calorimeters.E is in GeV.

Technology (Experiment) Depth Energy resolution Date

NaI(Tl) (Crystal Ball) 20X0 2.7%/E1/4 1983

Bi4Ge3O12 (BGO) (L3) 22X0 2%/√

E ⊕ 0.7% 1993

CsI (KTeV) 27X0 2%/√

E ⊕ 0.45% 1996

CsI(Tl) (BaBar) 16–18X0 2.3%/E1/4 ⊕ 1.4% 1999

CsI(Tl) (BELLE) 16X0 1.7% for Eγ > 3.5 GeV 1998

PbWO4 (PWO) (CMS) 25X0 3%/√

E ⊕ 0.5% ⊕ 0.2/E 1997

Lead glass (OPAL) 20.5X0 5%/√

E 1990

Liquid Kr (NA48) 27X0 3.2%/√

E⊕ 0.42% ⊕ 0.09/E 1998

Scintillator/depleted U 20–30X0 18%/√

E 1988

(ZEUS)

Scintillator/Pb (CDF) 18X0 13.5%/√

E 1988

Scintillator fiber/Pb 15X0 5.7%/√

E ⊕ 0.6% 1995

spaghetti (KLOE)

Liquid Ar/Pb (NA31) 27X0 7.5%/√

E ⊕ 0.5%⊕ 0.1/E 1988

Liquid Ar/Pb (SLD) 21X0 8%/√

E 1993

Liquid Ar/Pb (H1) 20–30X0 12%/√

E ⊕ 1% 1998

Liquid Ar/depl. U (DØ) 20.5X0 16%/√

E ⊕ 0.3% ⊕ 0.3/E 1993

Liquid Ar/Pb accordion 25X0 10%/√

E ⊕ 0.4% ⊕ 0.3/E 1996

(ATLAS)

34.9.2. Hadronic calorimeters : [1–5,153]

Revised September 2013 by D. E. Groom (LBNL).

Hadronic calorimetry is considerably more difficult than EMcalorimetry. For the same cascade containment fraction discussed inthe previous section, the calorimeter would need to be ∼30 timesdeeper. Electromagnetic energy deposit from the decay of a smallnumber of π0’s are usually detected with greater efficiency thanare the hadronic parts of the cascade, themselves subject to largefluctuations in neutron production, undetectable energy loss to nucleardisassociation, and other effects.

Most large hadron calorimeters are parts of large 4π detectors atcolliding beam facilities. At present these are sampling calorimeters:plates of absorber (Fe, Pb, Cu, or occasionally U or W) alternatingwith plastic scintillators (plates, tiles, bars), liquid argon (LAr), orgaseous detectors. The ionization is measured directly, as in LArcalorimeters, or via scintillation light observed by photodetectors(usually PMT’s or silicon photodiodes). Wavelength-shifting fibers areoften used to solve difficult problems of geometry and light collectionuniformity. Silicon sensors are being studied for ILC detectors; inthis case e-h pairs are collected. There are as many variants of theseschemes as there are calorimeters, including variations in geometryof the absorber and sensors, e.g., scintillating fibers threading anabsorber [156], and the “accordion” LAr detector [157]. Thelatter has zig-zag absorber plates to minimize channeling effects; the


calorimeter is hermitic (no cracks), and plates are oriented so thatcascades cross the same plate repeatedly. Another departure fromthe traditional sandwich structure is the LAr-tube design shown inFig. 34.22(a) [158].

(a) (b)

W (Cu) absorber

LAr filledtubes

Hadrons z

rφ

scintillatortile

waveshifter fiber

PMT

Hadrons

Figure 34.22: (a) ATLAS forward hadronic calorimeter struc-ture (FCal2, 3) [158]. Tubes containing LAr are embedded in amainly tungsten matrix. (b) ATLAS central calorimeter wedge;iron with plastic scintillator tile with wavelength-shifting fiberreadout [159].

A relatively new variant in hadron calorimetry is the detectionof Cerenkov light. Such a calorimeter is sensitive to relativistic e±’sin the EM showers plus a few relativistic pions. An example is theradiation-hard forward calorimeter in CMS, with iron absorber andquartz fiber readout by PMT’s [160].

Ideally the calorimeter is segmented in φ and θ (or η =− ln tan(θ/2)). Fine segmentation, while desirable, is limited by cost,readout complexity, practical geometry, and the transverse size ofthe cascades—but see Ref. 161. An example, a wedge of the ATLAScentral barrel calorimeter, is shown in Fig. 34.22(b) [159].

Much of the following discussion assumes an idealized calorimeter,with the same structure throughout and without leakage. “Real”calorimeters usually have an EM detector in front and a coarse“catcher” in the back. Complete containment is generally impractical.

In an inelastic hadronic collision a significant fraction fem of theenergy is removed from further hadronic interaction by the productionof secondary π0’s and η’s, whose decay photons generate high-energyelectromagnetic (EM) showers. Charged secondaries (π±, p, . . . )deposit energy via ionization and excitation, but also interact withnuclei, producing spallation protons and neutrons, evaporationneutrons, and spallation products. The charged collision productsproduce detectable ionization, as do the showering γ-rays from theprompt de-excitation of highly excited nuclei. The recoiling nucleigenerate little or no detectable signal. The neutrons lose kineticenergy in elastic collisions, thermalize on a time scale of several µs,and are captured, with the production of more γ-rays—usually outsidethe acceptance gate of the electronics. Between endothermic spallationlosses, nuclear recoils, and late neutron capture, a significant fractionof the hadronic energy (20%–40%, depending on the absorber andenergy of the incident particle) is used to overcome nuclear bindingenergies and is therefore lost or “invisible.”

In contrast to EM showers, hadronic cascade processes arecharacterized by the production of relatively few high-energy particles.The lost energy and fem are highly variable from event to event. Untilthere is event-by-event knowledge of both the EM fraction and theinvisible energy loss, the energy resolution of a hadron calorimeter willremain significantly worse than that of its EM counterpart.

The efficiency e with which EM deposit is detected varies fromevent to event, but because of the large multiplicity in EM showersthe variation is small. In contrast, because a variable fraction ofthe hadronic energy deposit is detectable, the efficiency h withwhich hadronic energy is detected is subject to considerably largerfluctuations. It thus makes sense to consider the ratio h/e as astochastic variable.

Most energy deposit is by very low-energy electrons and chargedhadrons. Because so many generations are involved in a high-energycascade, the hadron spectra in a given material are essentiallyindependent of energy except for overall normalization [163]. For thisreason 〈h/e〉 is a robust concept, independently of hadron energy andspecies.

If the detection efficiency for the EM sector is e and that for thehadronic sector is h, then the ratio of the mean response to a pionrelative to that for an electron is

〈π/e〉 = 〈fem〉 + 〈fh〉〈h/e〉∗ = 1 − (1 − 〈h/e〉)〈fh〉 (34.34)

It has been shown by a simple induction argument and verified byexperiment, that the decrease in the average value of the hadronicenergy fraction 〈fh〉 = 1 − 〈fem〉 as the projectile energy E increasesis fairly well described by the power law [162,163]

〈fh〉 ≈ (E/E0)m−1 (for E > E0) , (34.35)

at least up to a few hundred GeV. The exponent m dependslogarithmically on the mean multiplicity and the mean fractional lossto π0 production in a single interaction. It is in the range 0.80–0.87.E0, roughly the energy for the onset of inelastic collisions, is 1 GeV ora little less for incident pions [162]. Both m and E0 must be obtainedexperimentally for a given calorimeter configuration.

Only the product (1 − 〈h/e〉)E1−m0 can be obtained by measuring

〈π/e〉 as a function of energy. Since 1 − m is small and E0 ≈ 1 GeVfor pion-induced cascades, this fact is usually ignored and 〈h/e〉 isreported.

In a hadron-nucleus collision a large fraction of the incident energyis carried by a “leading particle” with the same quark contentas the incident hadron. If the projectile is a charged pion, theleading particle is usually a pion, which can be neutral and hencecontributes to the EM sector. This is not true for incident protons.The result is an increased mean hadronic fraction for incident protons:E0 ≈ 2.6 GeV [162–165].

By definition, 0 ≤ fem ≤ 1. Its variance σ2fem

changes only

slowly with energy, but perforce 〈fem〉 → 1 as the projectile energyincreases. An empirical power law (unrelated to Eq. (34.34)) ofthe form σfem = (E/E1)

1−ℓ (where ℓ < 1) describes the energydependence of the variance adequately and has the right asymptoticproperties [153]. For 〈h/e〉 6= 1 (noncompensation), fluctuations infem significantly contribute to or even dominate the resolution. Sincethe fem distribution has a high-energy tail, the calorimeter response isnon-Gaussian with a high-energy tail if 〈h/e〉 < 1. Noncompensationthus seriously degrades resolution and produces a nonlinear response.

It is clearly desirable to compensate the response, i.e., to design thecalorimeter such that 〈h/e〉 = 1. This is possible only with a samplingcalorimeter, where several variables can be chosen or tuned:

1. Decrease the EM sensitivity. EM cross sections increase withZ,† and most of the energy in an EM shower is deposited bylow-energy electrons. A disproportionate fraction of the EM energyis thus deposited in the higher-Z absorber. Lower-Z cladding, suchas the steel cladding on ZEUS U plates, preferentially absorbslow-energy γ’s in EM showers and thus also lowers the electronicresponse. G10 signal boards in the DØ calorimeters and G10 nextto slicon readout detectors has the same effect. The degree ofEM signal suppression can be somewhat controlled by tuning thesensor/absorber thickness ratio.

2. Increase the hadronic sensitivity. The abundant neutrons producedin the cascade have large n-p elastic scattering cross sections, sothat low-energy scattered protons are produced in hydrogenoussampling materials such as butane-filled proportional countersor plastic scintillator. (The maximal fractional energy loss whena neutron scatters from a nucleus with mass number A is

∗ Technically, we should write 〈fh(h/e)〉, but we approximate it as〈fh〉〈h/e〉 to facilitate the rest of the discussion.

† The asymptotic pair-production cross section scales roughly as Z0.75,and |dE/dx| slowly decreases with increasing Z.


4A/(1 + A)2.) The down side in the scintillator case is that thesignal from a highly-ionizing stopping proton can be reduced by asmuch as 90% by recombination and quenching parameterized byBirks’ Law (Eq. (34.2)).

3. Fabjan and Willis proposed that the additional signal generated inthe aftermath of fission in 238U absorber plates should compensatenuclear fluctuations [166]. The production of fission fragmentsdue to fast n capture was later observed [167]. However, whilea very large amount of energy is released, it is mostly carriedby low-velocity, very highly ionizing fission fragments whichproduce very little observable signal because of recombination andquenching. But in fact much of the compensation observed withthe ZEUS 238U/scintillator calorimeter was mainly the result ofmethods 1 and 2 above.

Motivated very much by the work of Brau, Gabriel, Bruckmann,and Wigmans [168], several groups built calorimeters which were verynearly compensating. The degree of compensation was sensitive tothe acceptance gate width, and so could be somewhat further tuned.These included

a) HELIOS with 2.5 mm thick scintillator plates sandwiched between2 mm thick 238U plates (one of several structures); σ/E = 0.34/

√E

was obtained,

b) ZEUS, 2.6 cm thick scintillator plates between 3.3 mm 238U plates;σ/E = 0.35/

√E,

c) a ZEUS prototype with 10 mm Pb plates and 2.5 mm scintillatorsheets; σ/E = 0.44/

√E, and

d) DØ, where the sandwich cell consists of a 4–6 mm thick 238U plate,2.3 mm LAr, a G-10 signal board, and another 2.3 mm LAr gap;σ/E ≈ 0.45/

√E.

Given geometrical and cost constraints, the calorimeters used inmodern collider detectors are not compensating: 〈h/e〉 ≈ 0.7, for theATLAS central barrel calorimeter, is typical.

0.0 0.2 0.4 0.6 0.8 1.0S/E

0.0

0.2

0.4

0.6

0.8

1.0

C/E

100 GeV MC

Incident γIncident π−

fem = 0

fem = 1

h/e S

h/e C

1 − h/e C

1 − h/e S

Slope ξ =

Figure 34.23: Dotplot of Monte Carlo C (Cherenkov) vs S(scintillator) signals for individual events in a dual readoutcalorimeter. Hadronic (π−) induced events are shown in blue,and scatter about the indicated event locus. Electromagneticevents cluster about (C,S) = (0,0). In this case worse resolution(fewer p.e.’s) was assumed for the Cherenkov events, leading tothe “elliptical” distribution.

A more versatile approach to compensation is provided by adual-readout calorimeter, in which the signal is sensed by two readoutsystems with highly contrasting 〈h/e〉. Although the concept is morethan two decades old [169], it was only recently been implemented bythe DREAM collaboration [170]. The test beam calorimeter consistedof copper tubes, each filled with scintillator and quartz fibers. If thetwo signals C and S (quartz and scintillator) are both normalized toelectron response, then for each event Eq. (34.34) takes the form

C = E[fem + 〈h/e〉|C(1 − fem)]

S = E[fem + 〈h/e〉|S(1 − fem)] (34.36)

for the Cherenkov and scintillator responses. On a dotplot of C/E vsS/E, events scatter about a line-segment locus described in Fig. 34.23.With increasing energy the distribution moves upward along the locusand becomes tighter. Equations 34.36 are linear in 1/E and fem,and are easily solved to obtain estimators of the corrected energyand fem for each event. Both are subject to resolution effects, butcontributions due to fluctuations in fem are eliminated. The solutionfor the corrected energy is given by [163]:

E =ξS − C

ξ − 1, where ξ =

1 − 〈h/e〉|C1 − 〈h/e〉|S

(34.37)

ξ is the energy-independent slope of the event locus on a plot of Cvs S. It can be found either from the fitted slope or by measuringπ/e as a function of E. Because we have no knowledge of h/e on anevent-by-event basis, it has been replaced by 〈h/e〉 in Eq. (34.37).ξ must be as far from unity as possible to optimize resolution,which means in practical terms that the scintillator readout of thecalorimeter must be as compensating as possible.

Although the usually-dominant contribution of the fem distributionto the resolution can be minimized by compensation or the use of dualcalorimetry, there remain significant contributions to the resolution:

1. Incomplete corrections for leakage, differences in light collectionefficiency, and electronics calibration.

2. Readout transducer shot noise (usually photoelectron statistics),plus electronic noise.

3. Sampling fluctuations. Only a small part of the energy deposittakes place in the scintillator or other sensor, and that fractionis subject to large fluctuations. This can be as high as 40%/

√E

(lead/scintillator). It is even greater in the Fe/scint case becauseof the very small sampling fraction (if the calorimeter is to becompensating), and substantially lower in a U/scint calorimeter. Itis obviously zero for a homogeneous calorimeter.

4. Intrinisic fluctuations. The many ways ionization can be producedin a hadronic shower have different detection efficiencies andare subject to stochastic fluctuations. In particular, a very largefraction of the hadronic energy (∼20% for Fe/scint, ∼40% forU/scint) is “invisible,” going into nuclear dissociation, thermalizedneutrons, etc. The lost fraction depends on readout—it will begreater for a Cherenkov readout, less for an organic scintillatorreadout.

Except in a sampling calorimeter especially designed for thepurpose, sampling and intrinsic resolution contributions cannot beseparated. This may have been best studied by Drews et al. [171],who used a calorimeter in which even- and odd-numbered scintillatorswere separately read out. Sums and differences of the variances wereused to separate sampling and intrinsic contributions.

The fractional energy resolution can be represented by

σ

E=

a1(E)√E

⊕∣

∣

∣

∣

1 −⟨

h

e

⟩∣

∣

∣

∣

(

E

E1

)1−ℓ

(34.38)

The coefficient a1 is expected to have mild energy dependence fora number of reasons. For example, the sampling variance is (π/e)Erather than E. The term (E/E1)

1−ℓ is the parametrization of σfem

discussed above. Usually a plot of (σ/E)2 vs 1/E ia well-described bya straight line (constant a1) with a finite intercept—the square of theright term in Eq. (34.38), is called “the constant term.” Precise datashow the slight downturn [156].

After the first interaction of the incident hadron, the averagelongitudinal distribution rises to a smooth peak. The peak positionincreases slowly with energy. The distribution becomes nearlyexponential after several interaction lengths. Examples from theCDHS magnetized iron-scintillator sandwich calorimeter test beamcalibration runs [172] are shown in Fig. 34.24. Proton-inducedcascades are somewhat shorter and broader than pion-inducedcascades [165]. A gamma distribution fairly well describes thelongitudinal development of an EM shower, as discussed in Sec. 33.5.Following this logic, Bock et al. suggested that the profile of a hadroniccascade could be fitted by the sum of two Γ distributions, one with


a characteristic length X0 and the other with length λI [173]. Fitsto this 4-parameter function are commonly used, e.g., by the ATLASTilecal collaboration [165]. If the interaction point is not known (theusual case), the distribution must be convoluted with an exponentialin the interaction length of the incident particle. Adragna et al. givean analytic form for the convoluted function [165].

0 2 4 6 8 101 3 5 7 9

Depth (nuclear interaction lengths)

1

10

100

3

30

300

Sca

led

mea

n nu

mbe

r of

par

ticle

s in

cou

nter

CDHS: 15 GeV 30 GeV 50 GeV 75 GeV100 GeV140 GeV

Figure 34.24: Mean profiles of π+ (mostly) induced cascadesin the CDHS neutrino detector [172]. Corresponding results forthe ATLAS tile calorimeter can be found in Ref. 165.

The transverse energy deposit is characterized by a central coredominated by EM cascades, together with a wide “skirt” produced bywide-angle hadronic interactions [174].

The CALICE collaboration has tested a “tracking” calorimeter(AHCAL) with highly granular scintillator readout [161]. Since theposition of the first interaction is observed, the average longitudinaland radial shower distributions are obtained.

While the average distributions might be useful in designing acalorimeter, they have little meaning for individual events, whosedistributions are extremely variable because of the small number ofparticles involved early in the cascade.

Particle identification, primarily e-π discrimination, is accomplishedin most calorimeters by depth development. An EM shower is mostlycontained in 15X0 while a hadronic shower takes about 4λI . Inhigh-A absorbers such as Pb, X0/λI ∼ 0.03. In a fiber calorimeter,such as the RD52 dual-readout calorimeter [175], e-π discriminationis achieved by differences in the Cerenkov and scintillation signals,lateral spread, and timing differences, ultimately achieving about500:1 discrimination.

34.9.3. Free electron drift velocities in liquid ionization cham-bers :

Written August 2009 by W. Walkowiak (U. Siegen)

Drift velocities of free electrons in LAr [176] are given as a functionof electric field strength for different temperatures of the medium inFig. 34.25. The drift velocites in LAr have been measured using adouble-gridded drift chamber with electrons produced by a laser pulseon a gold-plated cathode. The average temperature gradient of thedrift velocity of the free electrons in LAr is described [176] by

∆vd

∆T vd= (−1.72 ± 0.08) %/K.

Earlier measurements [177–180] used different techniques and showsystematic deviations of the drift velocities for free electrons whichcannot be explained by the temperature dependence mentioned above.

Drift velocities of free electrons in LXe [178] as a function ofelectric field strength are also displayed in Fig. 34.25. The driftvelocity saturates for |E | > 3 kV/cm, and decreases with increasingtemperature for LXe as well as measured e.g. by [181].

E (kV/cm)

Vd

(m

m/µ

s) 87.0 K 89.8 K 93.9 K

163.0 K

97.0 K

LAr

LAr + 0.5% CH4

LXe

Miller et al. (1968)

Shibamura et al. (1976)Walkowiak (2000)

0 2 4 6 8 10 12 140

1

2

3

4

5

6

7

8

Figure 34.25: Drift velocity of free electrons as a function ofelectric field strength for LAr [176], LAr + 0.5% CH4 [178]and LXe [177]. The average temperatures of the liquids areindicated. Results of a fit to an empirical function [182] aresuperimposed. In case of LAr at 91 K the error band for theglobal fit [176] including statistical and systematic errors as wellas correlations of the data points is given. Only statistical errorsare shown for the individual LAr data points.

The addition of small concentrations of other molecules like N2, H2

and CH4 in solution to the liquid typically increases the drift velocitiesof free electrons above the saturation value [178,179], see example forCH4 admixture to LAr in Fig. 34.25. Therefore, actual drift velocitiesare critically dependent on even small additions or contaminations.

34.10. Accelerator Neutrino Detectors

Written August 2015 by M.O. Wascko (Imperial College London).

34.10.1. Introduction :

Accelerator neutrino experiments span many orders of magnitudein neutrino energy, from a few MeV to hundreds of GeV. This widerange of neutrino energy is driven by the many physics applicationsof accelerator neutrino beams. Foremost among them is neutrinooscillation, which varies as the ratio L/Eν , where L is the neutrinobaseline (distance travelled), and Eν is the neutrino energy. Butaccelerator neutrino beams have also been used to study the natureof the weak interaction, to probe nucleon form factors and structurefunctions, and to study nuclear structure.

The first accelerator neutrino experiment used neutrinos from thedecays of high energy pions in flight to show that the neutrinosemitted from pion decay are different from the neutrinos emitted bybeta decay [183]. The field of accelerator neutrino experiments didnot expand beyond this until Simon van der Meer’s invention of themagnetic focusing horn [184], which significantly increased the flux ofneutrinos aimed toward the detector. In this mini-review, we focus onexperiments employing decay-in-flight beams—pions, kaons, charmedmesons, and taus—producing fluxes of neutrinos and antineutrinosfrom ∼ 10 MeV to ∼ 100 GeV.

Neutrino interactions with matter proceed only through the weakinteraction, making the cross section extremely small and requiringhigh fluxes of neutrinos and large detector masses in order toachieve satisfactory event rates. Therefore, neutrino detector designis a balancing act taking into account sufficient numbers of nucleartargets (often achieved with inactive detector materials), adequatesampling/segmentation to ensure accurate reconstruction of the tracksand showers produced by neutrino-interaction secondary particles, andpractical readout systems to allow timely analysis of data.


34.10.2. Signals and Backgrounds :

The neutrino interaction processes available increase with increasingneutrino energy as interaction thresholds are crossed; in generalneutrino-interaction cross sections grow with energy; for a detaileddiscussion of neutrino interactions see [185]. The multiplicity ofsecondary particles from each interaction process grows in complexitywith neutrino energy, while the forward-boost due to increasing Eν

compresses the occupied phase space in the lab frame, impactingdetector designs. Because decay-in-fight beams produce neutrinos atwell-defined times, leading to very small duty factors, the predominantbackgrounds stem from unwanted beam-induced neutrino interactions,i.e. neutrinos interacting via other processes than the one beingstudied. This becomes increasingly true at high energies because thesecondary particles produced by neutrino interactions yield detectorsignals that resemble cosmic backgrounds less and less.

Below, we describe a few of the dominant neutrino interactionprocesses, with a focus on the final state particle content andtopologies.

34.10.2.1. Charged-Current Quasi-Elastic Scattering and Pions:

Below ∼ 2 GeV neutrino energy, the dominant neutrino-nucleusinteraction process is quasi-elastic (QE) scattering. In the chargedcurrent (CC) mode, the CCQE base neutrino reaction is νℓ n → ℓ− p,where ℓ = e, µ, τ , and similarly for antineutrinos, νℓ p → ℓ+ n. Thefinal state particles are a charged lepton, and perhaps a recoilingnucleon if it is given enough energy to escape the nucleus. Detectorsdesigned to observe this process should have good single-particle trackresolution for muon neutrino interactions, but should have good µ/eseparation for electron neutrino interactions. Because the interactioncross section falls sharply with Q2, the lepton typically carries awaymore of the neutrino’s kinetic energy than the recoiling nucleon. Thefraction of backward-scattered leptons is large, however, so detectorswith 4π coverage are desirable. The dominant backgrounds in thischannel tend to come from single pion production events in which thepion is not detected.

Near 1 GeV, the quasi-elastic cross section is eclipsed by pionproduction processes. A typical single pion production (CC1π)reaction is νℓ n → ℓ− π+ n, but many more final state particlecombinations are possible. Single pion production proceeds throughthe coherent channel and many incoherent processes, dominated byresonance production. With increasing neutrino energy, higher-orderresonances can be excited, leading to multiple pions in the final state.Separating these processes from quasi-elastic scattering, and indeedfrom each other, requires tagging, and ideally reconstructing, the pions.Since these processes can produce neutral pions, electromagnetic (EM)shower reconstruction is more important here than it is for the quasi-elastic channel. The predominant backgrounds for pion productionchange with increasing neutrino energy. Detection of pion processesis also complicated because near threshold the quasi-elastic channelcreates pion backgrounds through final state interactions of therecoiling nucleon, and at higher energies backgrounds come frommigration of multiple pion events in which one or more pions is notdetected.

34.10.2.2. Deep Inelastic Scattering:

Beyond a few GeV, the neutrino has enough energy to probethe nucleon at the parton scale, leading to deep inelastic scattering(DIS). In the charged-current channel, the DIS neutrino reaction isνℓ N → ℓ− X , where N is a nucleon and X encompasses the entirerecoiling hadronic system. The final state particle reconstructionrevolves around accurate reconstruction of the lepton momentumand containment and reconstruction of the hadronic shower energy.Because of the high neutrino energies involved, DIS events are veryforward boosted, and can have extremely long particle tracks. For thisreason, detectors measuring DIS interactions must be large to containthe hadronic showers in the detector volume.

34.10.2.3. Neutral Currents:

Neutrino interactions proceeding through the neutral current (NC)channel are identified by the lack of a charged lepton in the final state.For example, the NC elastic reaction is νl N → νl N , and the NCDIS reaction is νl N → νl X . NC interactions are suppressed relativeto CC interactions by a factor involving the weak mixing angle; theprimary backgrounds for NC interactions come from CC interactionsin which the charged lepton is misidentified.

34.10.3. Instances of Neutrino Detector Technology :

Below we describe many of the actual detectors that have beenbuilt and operated for use in accelerator neutrino beams.

34.10.3.1. Spark Chambers:

In the first accelerator neutrino beam experiment, Lederman,Schwartz, and Steinberger [183] used an internally-triggered sparkchamber detector, filled with 10 tons of Al planes and surroundedby external scintillator veto planes, to distinguish muon tracks fromelectron showers, and hence muon neutrinos from electron neutrinos.The inactive Al planes served as the neutrino interaction target andas radiators for EM shower development. The detector successfullyshowed the presence of muon tracks from neutrino interactions. It wasalso sensitive to the hadronic showers induced by NC interactions,which were unknown at the time. More than a decade later, theAachen-Padova [186] experiment at CERN also employed an Al sparkchamber to detect ∼ 2 GeV neutrinos.

34.10.3.2. Bubble Chambers:

Several large bubble chamber detectors were employed as acceleratorneutrino detectors in the 1970s and 80s, performing many of the firststudies of the properties of the weak interaction. Bubble chambersprovide exquisite granularity in the reconstruction of secondaryparticles, allowing very accurate separation of interaction processes.However, the extremely slow and labor-intensive acquisition andanalysis of the data from photographic film led to them being phasedout in favor of electronically read out detectors.

The Gargamelle [187] detector at CERN used Freon and propanegas targets to make the first observation of neutrino-induced NCinteractions and more. The BEBC [188] detector at CERN was abubble chamber that was alternately filled with liquid hydrogen,deuterium, and a neon-hydrogen mixture; BEBC was also outfittedwith a track-sensitive detector to improve event tagging, andsometimes used with a small emulsion chamber. The SKAT [192]heavy freon bubble chamber was exposed to wideband neutrino andantineutrino beams at the Serpukhov laboratory in the former SovietUnion. A series of American bubble chambers in the 1970’s and 1980’smade measurements on free nucleons that are still crucial inputs forneutrino-nucleus scattering predictions. The 12-foot bubble chamberat ANL [189] in the USA used both deuterium and hydrogen targets,as did the 7-foot bubble chamber at BNL [190]. Fermilab’s 15 footbubble chamber [191] used deuterium and heavy neon targets.

34.10.3.3. Iron Tracking Calorimeters:

Because of the forward boost of high energy interactions, longdetectors made of magnetized iron interspersed with active detectorlayers have been very successfully employed. The long magnetizeddetectors allow measurements of the momentum of penetrating muons.The iron planes also act as shower-inducing layers, allowing separationof EM and hadronic showers; the large number of iron planesprovide enough mass for high statistics and/or shower containment.Magnetized iron spectrometers have been used for studies of the weakinteraction, measurements of structure functions, and searches forneutrino oscillation. Non-magnetized iron detectors have also beensuccessfully employed as neutrino monitors for oscillation experimentsand also for neutrino-nucleus interaction studies.

The CDHS [201] detector used layers of magnetized iron modulesinterspersed with wire drift chambers, with a total (fiducial) mass of1250 t (750 t), to detector neutrinos in the range 30–300 GeV. Withineach iron module, 5 cm (or 15 cm) iron plates were interspersedwith scintillation counters. The FNAL Lab-E neutrino detectorwas used by the CCFR [202] and NuTeV [203] collaborations to


perform a series of experiments in the Fermilab high energy neutrinobeam (50 GeV< Eν < 300 GeV). The detector was comprised ofsix iron target calorimeter modules, with 690 t total target mass,followed by three muon spectrometer modules, followed by two driftchambers. Each iron target calorimeter module comprised 5.2 cmthick steel plates interspersed with liquid scintillation counters anddrift chambers. The muon spectrometer was comprised of toroidal ironmagnets interleaved with drift chambers. The MINOS [204] detectors,a near detector of 980 t at FNAL and a far detector of 5400 t in theSoudan mine, are functionally identical magnetized iron calorimeters,comprised of iron plates interleaved with layers of 4 cm wide plasticscintillator strips in alternating orientations. The T2K [222] on-axisdetector, INGRID, consists of 16 non-magnetized iron scintillatorsandwich detectors, each with nine 6.5 cm iron plane (7.1 t total)interspersed between layers of 5 cm wide plastic scintillator stripsreadout out by multi-pixel photon counters (MPPCs) coupled to WLSfibers. Fourteen of the INGRID modules are arranged in a cross-hairconfiguration centered on the neutrino beam axis.

34.10.3.4. Cherenkov Detectors:

Open volume water Cherenkov detectors were originally built tosearch for proton decay. Large volumes of ultra-pure water werelined with photomultipliers to collect Cherenkov light emitted by thepassage of relativistic charged particles. See Sec. 35.3.1 for a detaileddiscussion of deep liquid detectors for rare processes.

When used to detect ∼ GeV neutrinos, the detector medium acts asa natural filter for final state particles below the Cherenkov threshold;this feature has been exploited successfully by the K2K, MiniBooNE(using mineral oil instead of water), and T2K neutrino oscillationexperiments. However, at higher energies Cherenkov detectors becomeless accurate because the overlapping rings from many final stateparticles become increasingly difficult to resolve.

The second-generation Cherenkov detector in Japan, Super-Kamiokande [193]( Super-K), comprises 50 kt (22.5 kt fiducial) ofwater viewed by 11,146 50 cm photomultiplier tubes, giving 40%photocathode coverage; it is surrounded by an outer detector regionviewed by 1,885 20 cm photomultipliers. Super-K is the far detectorfor K2K and T2K, and is described in greater detail elsewherein this review. The K2K experiment also employed a 1 kt waterCherenkov detector in the suite of near detectors [194], with 690photomultipliers (40% photocathode coverage) viewing the detectorvolume. The MiniBooNE detector at FNAL was a 0.8 kt [195] mineraloil Cherenkov detector, with 1,520 20 cm photomultipliers (10%photocathode coverage) surrounded by a veto detector with 240 20 cmphotomultipliers.

34.10.3.5. Scintillation Detectors:

Liquid and solid scintillator detectors also employ fully (or nearlyfully) active detector media. Typically organic scintillators, which emitinto the ultraviolet range, are dissolved in mineral oil or plastic andread out by photomultipliers coupled to wavelength shifters (WLS).Open volume scintillation detectors lined with photomultipliersare conceptually similar to Cherenkov detectors, although energyreconstruction is calorimetric in nature as opposed to kinematic (seealso Sec. 35.3.1). For higher energies and higher particle multiplicities,it becomes beneficial to use segmented detectors to help distinguishparticle tracks and showers from each other.

The LSND [197] detector at LANL was an open volume liquidscintillator detector (of mass 167 t) employed to detect relativelylow energy (<300 MeV) neutrinos. The NOνA [200] detectors usesegmented volumes of liquid scintillator in which the scintillationlight is collected by WLS fibers in the segments that are coupled toavalanche photodiodes (APDs) at the ends of the volumes. The NOνAfar detector, located in Ash River, MN, is comprised of 896 layers of15.6 m long extruded PVC scintillator cells for a total mass of 14 kt;the NOνA near detector is comprised of 214 layers of 4.1 m scintillatorvolumes for a total mass of of 300 t. Both are placed in the NuMIbeamline at 0.8 off-axis. The SciBar (Scintillation Bar) detectorwas originally built for K2K at KEK in Japan and then re-used forSciBooNE [198] at FNAL. SciBar used plastic scintillator strips with1.5 cm×2.5 cm rectangular cross section, read out by multianode

photomultipliers (MAPMTs) coupled to WLS fibers, arranged inalternating horizontal and vertical layers, with a total mass of 15 t.Both SciBooNE and K2K employed an EM calorimeter downstreamof SciBar and a muon range detector (MRD) downstream of that.The MINERvA [199] detector, in the NuMI beam at FNAL, utilizesa central tracker comprising 8.3 t of plastic scintillator strips withtriangular cross section, and is also read out by MAPMTs coupledto WLS fibers. MINERvA employs several more subsystems and isdescribed more fully below.

34.10.3.6. Liquid Argon Time Projection Chambers:

Liquid argon time projection chambers (LAr-TPCs) were conceivedin the 1970s as a way to achieve a fully active detector with sub-centimeter track reconstruction [205]. A massive volume of purifiedliquid argon is put under a strong electric field (hundreds of V/cm),so that the liberated electrons from the paths of ionizing particlescan be drifted to the edge of the volume and read out, directly bycollecting charge from wire planes or non-destructively through chargeinduction in the wire planes. A dual-phase readout method is alsobeing developed, in which the charge is drifted vertically and thenpassed through an amplification region inside a gas volume above theliquid volume; the bottom of the liquid volume is equipped with aPMT array for detecting scintillation photons form the liquid argon.The first large scale LAr-TPC was the ICARUS T-600 module [206],comprising 760 t of liquid argon with a charge drift length of 1.5 mread out by wires with 3 mm pitch, which operated in LNGS, bothstandalone and also exposed to the CNGS high energy neutrino beam.The ArgoNeuT [207] detector at FNAL, with fiducial mass 25 kg ofargon read out with 4 mm pitch wires, was exposed to the NuMIneutrino and antineutrino beams. The MicroBooNE [208] detectorat FNAL comprises 170 t of liquid Ar, read out with 3 mm wirepitch, which began collecting data in the Booster Neutrino Beam Oct2015. A LAr-TPC has also been chosen as the detector design for thefuture DUNE neutrino oscillation experiment, from FNAL to SanfordUnderground Research Facility; both single and dual phase modulesare planned.

34.10.3.7. Emulsion Detectors:

Photographic film emulsions have been employed in particle physicsexperiments since the 1940s [209]. Thanks to advances in scanningtechnology and automation [213], they have been successfullyemployed as neutrino detectors. Emulsions are used for experimentsobserving CC tau neutrino interactions, where the short lifetime ofthe tau, ττ = 2.90 × 10−13s, leading to the short mean path length,c × τ = 87µm, requires extremely precise track resolution. Theyare employed in hybrid detectors in which the emulsion bricks areembedded inside fine-grained tracker detectors. In the data analysis,the tracker data are used to select events with characteristics typical ofa tau decay in the final state, such as missing energy and unbalancedtransverse momentum. The reconstructed tracks are projected backinto an emulsion brick and used as the search seed for a neutrinointeraction vertex.

E531 [210] at Fermilab tested many of the emulsion-tracker hybridtechniques employed by later neutrino experiments, in a detector withapproximately 9 kg of emulsion target. The CHORUS [211] experimentat CERN used 1,600 kg of emulsion, in a hybrid detector with afiber tracker, high resolution calorimeter, and muon spectrometer,to search for νµ → ντ oscillation. The DONuT [212] experimentat FNAL used a hybrid detector, with 260 kg of emulsion bricksinterspersed with fiber trackers, followed by a magnetic spectrometer,and calorimeter, to make the first direct observation of tau neutrinoCC interactions. More recently, the OPERA [214,215,216] experimentused an automated hybrid emulsion detector, with 1,300 t of emulsion,to make the first direct observation of the appearance of ντ in a νµ

beam.


34.10.3.8. Hybrid Detectors:

The CHARM detector [217] at CERN was built to study neutral-current interactions and search for muon neutrino oscillation. Itwas a fine-grained ionization calorimeter tracker with approximately150 t of marble as neutrino target, surrounded by a magnetized ironmuon system for tagging high angle muons, and followed downstreamby a muon spectrometer. The CHARM II detector [218] at CERNcomprised a target calorimeter followed by a downstream muonspectrometer. Each target calorimeter module consists of a 4.8 cmthick glass plate followed by a layer of plastic streamer tubes, withspacing 1 cm, instrumented with 2 cm wide pickup strips. Every fifthmodule is followed by a 3 cm thick scintillator layer. The total massof the target calorimeter was 692 t.

The Brookhaven E-734 [219] detector was a tracking calorimetermade up of 172 t liquid scintillator modules interspersed withproportional drift tubes, followed by a dense EM calorimeter and amuon spectrometer downstream of that. The detector was exposed toa wideband horn-focused beam with peak neutrino energy near 1 GeV.The Brookhaven E-776 [220] experiment comprised a finely segmentedEM calorimeter, with 2.54 cm concrete absorbers interspersed withplanes of drift tubes and acrylic scintillation counters, with total mass240 t, followed by a muon spectrometer.

The NOMAD [221] detector at CERN consisted of central trackerdetector inside a 0.4 T dipole magnet (the magnet was originally usedby the UA1 experiment at CERN) followed by a hadronic calorimeterand muon detectors downstream of the magnet. The main neutrinotarget is 3 t of drift chambers followed downstream by transitionradiation detectors which are followed by an EM calorimeter. NOMADwas exposed to the same wideband neutrino beam as was CHORUS.

MINERvA, introduced above, is, in its entirety, a hybrid detector,based around a central plastic scintillator tracker. The scintillatortracker is surrounded by electromagnetic and hadronic calorimetry,which is achieved by interleaving thin lead (steel) layers betweenthe scintillator layers for the ECAL (HCAL). MINERvA is situatedupstream of the MINOS near detector which acts as a muonspectrometer. Upstream of the scintillator tracker is a nuclear targetregion containing inactive layers of C (graphite), Pb, Fe (steel),and O (water). MINERvA’s physics goals span a wide range ofneutrino-nucleus interaction studies, from form factors to nucleareffects.

T2K [222] in Japan employs two near detectors at 280 m from theneutrino beam target, one centered on the axis of the horn-focusedJ-PARC neutrino beam and one placed 2.5 off-axis. The on-axisdetector, INGRID, is described above. The 2.5 off-axis detector,ND280, employs the UA1 magnet (at 0.2 T) previously used byNOMAD. Inside the magnet volume are three separate detectorsystems: the trackers, the Pi0 Detector (P0D), and several ECalmodules. The tracker detectors comprise two fine-grained scintillatordetectors (FGDs), read out by MPPCs coupled to WLS fibers,interleaved between three gas TPCs read out by micromegas planes.The downstream FGD contains inactive water layers in addition tothe scintillators. Upstream of the tracker is the P0D, a samplingtracker calorimeter with active detector materials comprising plasticscintillator read out by MPPCs and WLS fibers, and inactive sheets ofbrass radiators and refillable water modules. Surrounding the trackerand P0D, but still inside the magnet, are lead-scintillator EM samplingcalorimeters.

34.11. Superconducting magnets for collider

detectors

Revised September 2015 by Y. Makida (KEK)

34.11.1. Solenoid Magnets : In all cases SI unit are assumed, sothat the magnetic field, B, is in Tesla, the stored energy, E, is injoules, the dimensions are in meters, and µ0 = 4π × 10−7.

The magnetic field (B) in an ideal solenoid with a flux return ironyoke, in which the magnetic field is < 2 T, is given by

B =µ0 n I

L(34.39)

where n is the number of turns, I is the current and L is the coillength. In an air-core solenoid, the central field is given by

B(0, 0) = µ0 n IL√

L2 + 4R2, (34.40)

where R is the coil radius.

In most cases, momentum analysis is made by measuring thecircular trajectory of the passing particles according to p = mv = qrB,where p is the momentum, m the mass, q the charge, r the bendingradius. The sagitta, s, of the trajectory is given by

s = q B ℓ2/8p , (34.41)

where ℓ is the path length in the magnetic field. In a practicalmomentum measurement in colliding beam detectors, it is moreeffective to increase the magnetic volume than the field strength, since

dp/p ∝ p/B ℓ2 , (34.42)

where ℓ corresponds to the solenoid coil radius R. The energy storedin the magnetic field of any magnet is calculated by integrating B2

over all space:

E =1

2µ0

∫

B2dV (34.43)

If the coil thin and inside an iron return yoke , (which is the case if itis to superconducting coil), then

E ≈ (B2/2µ0)πR2L . (34.44)

For a detector in which the calorimetry is outside the aperture of thesolenoid, the coil must be thin in terms of radiation and absorptionlengths. This usually means that the coil is superconducting andthat the vacuum vessel encasing it is of minimum real thickness andfabricated of a material with long radiation length. There are twomajor contributors to the thickness of a thin solenoid:

1) The conductor consisting of the current-carrying superconductingmaterial (usually Nb-Ti/Cu) and the quench protecting stabilizer(usually aluminum) are wound on the inside of a structural supportcylinder (usually aluminum also). The coil thickness scales as B2R,so the thickness in radiation lengths (X0) is

tcoil/X0 = (R/σhX0)(B2/2µ0) , (34.45)

where tcoil is the physical thickness of the coil, X0 the averageradiation length of the coil/stabilizer material, and σh is thehoop stress in the coil [225]. B2/2µ0 is the magnetic pressure.In large detector solenoids, the aluminum stabilizer and supportcylinders dominate the thickness; the superconductor (Nb-TI/Cu)contributes a smaller fraction. The main coil and support cylindercomponents typically contribute about 2/3 of the total thickness inradiation lengths.

2) Another contribution to the material comes from the outercylindrical shell of the vacuum vessel. Since this shell is susceptibleto buckling collapse, its thickness is determined by the diameter,length and the modulus of the material of which it is fabricated.The outer vacuum shell represents about 1/3 of the total thicknessin radiation length.


Table 34.9: Progress of superconducting magnets for particle physicsdetectors.

Experiment Laboratory B Radius Length Energy X/X0 E/M[T] [m] [m] [MJ] [kJ/kg]

TOPAZ* KEK 1.2 1.45 5.4 20 0.70 4.3CDF* Tsukuba/Fermi 1.5 1.5 5.07 30 0.84 5.4VENUS* KEK 0.75 1.75 5.64 12 0.52 2.8AMY* KEK 3 1.29 3 40 †CLEO-II* Cornell 1.5 1.55 3.8 25 2.5 3.7ALEPH* Saclay/CERN 1.5 2.75 7.0 130 2.0 5.5DELPHI* RAL/CERN 1.2 2.8 7.4 109 1.7 4.2ZEUS* INFN/DESY 1.8 1.5 2.85 11 0.9 5.5H1* RAL/DESY 1.2 2.8 5.75 120 1.8 4.8BaBar* INFN/SLAC 1.5 1.5 3.46 27 † 3.6D0* Fermi 2.0 0.6 2.73 5.6 0.9 3.7BELLE* KEK 1.5 1.8 4 42 † 5.3BES-III IHEP 1.0 1.475 3.5 9.5 † 2.6ATLAS-CS ATLAS/CERN 2.0 1.25 5.3 38 0.66 7.0ATLAS-BT ATLAS/CERN 1 4.7–9.75 26 1080 (Toroid)†

ATLAS-ET ATLAS/CERN 1 0.825–5.35 5 2 × 250 (Toroid)†

CMS CMS/CERN 4 6 12.5 2600 † 12SiD** ILC 5 2.9 5.6 1560 † 12ILD** ILC 4 3.8 7.5 2300 † 13SiD** CLIC 5 2.8 6.2 2300 † 14ILD** CLIC 4 3.8 7.9 2300 †FCC** 6 6 23 54000 † 12

∗ No longer in service

∗∗Conceptual design in future† EM calorimeter is inside solenoid, so small X/X0 is not a goal

34.11.2. Properties of collider detector magnets :

The physical dimensions, central field stored energy and thicknessin radiation lengths normal to the beam line of the supercon-ducting solenoids associated with the major collider are given inTable 34.9 [224]. Fig. 34.26 shows thickness in radiation lengths as afunction of B2R in various collider detector solenoids.

0

0.5

1

1.5

2

2.5

3

0 1 2 3 4 5 6 7 8

Thi

ckne

ss in

rad

iatio

n le

ngth

s

B2R [T2m]

ZEUS

VENUS

BESS,WASA

ALEPH

H1

DELPHI

TOPAZ CDF

D0

CLEO-II

SSC-SDCprototype

ATLAS-CSCELLO

PEP4-TPC

Figure 34.26: Magnet wall thickness in radiation length as afunction of B2R for various detector solenoids. Gray entries arefor magnets no longer in use, and entries underlined are notlisted in Table 34.9. Open circles are for magnets not designedto be “thin.” The SSC-SDC prototype provided important R&Dfor LHC magnets.

The ratio of stored energy to cold mass (E/M) is a usefulperformance measure. It can also be expressed as the ratio of thestress, σh, to twice the equivalent density, ρ, in the coil [225]:

E

M=

E

ρ 2πtcoilRL≈ σh

2ρ(34.46)

0

5

10

15

1 10 100 1000 104

E/M

[k

J/k

g]

Stored Energy [MJ]

D0

ZEUS

VENUS

BABAR

CDF

BELLE DELPHI

ALEPH

H1

CMS

BES-III

(CLIC-SiD)

(ILC-ILD)

(ILC-SiD)

TOPAZ

CLEO-II

ATLAS-CS

SSC-SDCPrototype

Figure 34.27: Ratio of stored energy to cold mass formajor detector solenoids. Gray indicates magnets no longer inoperation.

The E/M ratio in the coil is approximately equivalent to H*, theenthalpy of the coil, and it determines the average coil temperaturerise after energy absorption in a quench:

E/M = H(T2) − H(T1) ≈ H(T2) (34.47)

where T2 is the average coil temperature after the full energyabsorption in a quench, and T1 is the initial temperature. E/Mratios of 5, 10, and 20 kJ/kg correspond to ∼65, ∼80, and ∼100 K,respectively. The E/M ratios of various detector magnets are shownin Fig. 34.27 as a function of total stored energy. One would likethe cold mass to be as small as possible to minimize the thickness,

* The enthalpy, or heat content, is called H in the thermodynam-ics literature. It is not to be confused with the magnetic field inten-sity B/µ.


but temperature rise during a quench must also be minimized. AnE/M ratio as large as 12 kJ/kg is designed into the CMS solenoid,with the possibility that about half of the stored energy can go to anexternal dump resistor. Thus the coil temperature can be kept below80 K if the energy extraction system works well. The limit is set bythe maximum temperature that the coil design can tolerate during aquench. This maximum local temperature should be <130 K (50 K +80 K), so that thermal expansion effects, which are remarkable beyond80 K, in the coil are manageable less than 50 K.

34.11.3. Toroidal magnets :

Toroidal coils uniquely provide a closed magnetic field without thenecessity of an iron flux-return yoke. Because no field exists at thecollision point and along the beam line, there is, in principle, noeffect on the beam. On the other hand, the field profile generallyhas 1/r dependence. The particle momentum may be determined bymeasurements of the deflection angle combined with the sagitta. Thedeflection (bending) power BL is

BL ≈∫ R0

Ri

BiRi dR

R sin θ=

Bi Ri

sin θln(R0/Ri) , (34.48)

where Ri is the inner coil radius, R0 is the outer coil radius, and θ isthe angle between the particle trajectory and the beam line axis . Themomentum resolution given by the deflection may be expressed as

∆p

p∝ p

BL≈ p sin θ

BiRi ln(R0/Ri). (34.49)

The momentum resolution is better in the forward/backward (smallerθ) direction. The geometry has been found to be optimal whenR0/Ri ≈ 3–4. In practical designs, the coil is divided into 6–12lumped coils in order to have reasonable acceptance and accessibility.This causes the coil design to be much more complex. The mechanicalstructure needs to sustain the decentering force between adjacentcoils, and the peak field in the coil is 3–5 times higher than the usefulmagnetic field for the momentum analysis [223].

34.12. Measurement of particle momenta in a

uniform magnetic field [226,227]

The trajectory of a particle with momentum p (in GeV/c) andcharge ze in a constant magnetic field

−→B is a helix, with radius

of curvature R and pitch angle λ. The radius of curvature andmomentum component perpendicular to

−→B are related by

p cosλ = 0.3 z B R , (34.50)

where B is in tesla and R is in meters.

The distribution of measurements of the curvature k ≡ 1/R isapproximately Gaussian. The curvature error for a large number ofuniformly spaced measurements on the trajectory of a charged particlein a uniform magnetic field can be approximated by

(δk)2 = (δkres)2 + (δkms)

2 , (34.51)

where δk = curvature error

δkres = curvature error due to finite measurement resolution

δkms = curvature error due to multiple scattering.

If many (≥ 10) uniformly spaced position measurements are madealong a trajectory in a uniform medium,

δkres =ǫ

L′ 2

√

720

N + 4, (34.52)

where N = number of points measured along track

L′ = the projected length of the track onto the bending plane

ǫ = measurement error for each point, perpendicular to thetrajectory.

If a vertex constraint is applied at the origin of the track, thecoefficient under the radical becomes 320.

For arbitrary spacing of coordinates si measured along the projectedtrajectory and with variable measurement errors ǫi the curvature errorδkres is calculated from:

(δkres)2 =

4

w

Vss

VssVs2s2 − (Vss2)2, (34.53)

where V are covariances defined as Vsmsn = 〈smsn〉 − 〈sm〉〈sn〉 with〈sm〉 = w−1 ∑

(sim/ǫi

2) and w =∑

ǫi−2.

The contribution due to multiple Coulomb scattering is approxi-mately

δkms ≈(0.016)(GeV/c)z

Lpβ cos2 λ

√

L

X0, (34.54)

where p = momentum (GeV/c)

z = charge of incident particle in units of e

L = the total track length

X0 = radiation length of the scattering medium (in units oflength; the X0 defined elsewhere must be multiplied bydensity)

β = the kinematic variable v/c.

More accurate approximations for multiple scattering may be foundin the section on Passage of Particles Through Matter (Sec. 33of this Review). The contribution to the curvature error is givenapproximately by δkms ≈ 8srms

plane/L2, where srmsplane is defined there.

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35. Detectors for non-accelerator physics 491

35. PARTICLE DETECTORS FOR NON-ACCELERATOR PHYSICS

35. PARTICLE DETECTORS FOR NON-ACCELERATORPHYSICS . . . . . . . . . . . . . . . . . . . . . . 491

35.1. Introduction . . . . . . . . . . . . . . . . . . 491

35.2. High-energy cosmic-ray hadron and gamma-ray detec-tors . . . . . . . . . . . . . . . . . . . . . . . . 491

35.2.1. Atmospheric fluorescence detectors . . . . . . 491

35.2.2. Atmospheric Cherenkov telescopes for high-energyγ-ray astronomy . . . . . . . . . . . . . . . . . 492

35.3. Large neutrino detectors . . . . . . . . . . . . . 493

35.3.1. Deep liquid detectors for rare processes . . . . . 493

35.3.1.1. Liquid scintillator detectors . . . . . . . . 493

35.3.1.2. Water Cherenkov detectors . . . . . . . . 494

35.3.2. Neutrino telescopes . . . . . . . . . . . . . 495

35.3.2.1. Properties of media . . . . . . . . . . . 497

35.3.2.2. Technical realisation . . . . . . . . . . . 497

35.3.2.3. Results . . . . . . . . . . . . . . . . . 498

35.3.2.4. Plans beyond 2020 . . . . . . . . . . . . 499

35.3.3. Coherent radio Cherenkov radiation detectors . . 499

35.3.4. The Moon as a target . . . . . . . . . . . . 500

35.3.5. Ice-based detectors . . . . . . . . . . . . . 500

35.4. Large time-projection chambers for rare event detection 501

35.4.1. Dark matter and other low energy signals . . . . 501

35.4.2. 0νββ Decay . . . . . . . . . . . . . . . . 502

35.5. Sub-Kelvin detectors . . . . . . . . . . . . . . . 503

35.5.1. Equilibrium thermal detectors . . . . . . . . . 503

35.5.2. Nonequilibrium Detectors . . . . . . . . . . 504

35.6. Low-radioactivity background techniques . . . . . . 505

35.6.1. Defining the problem . . . . . . . . . . . . . 506

35.6.2. Environmental radioactivity . . . . . . . . . 506

35.6.3. Radioactive impurities in detector and shieldingcomponents . . . . . . . . . . . . . . . . . . . 506

35.6.4. Radon and its progeny . . . . . . . . . . . . 507

35.6.5. Cosmic rays . . . . . . . . . . . . . . . . 507

35.6.6. Neutrons . . . . . . . . . . . . . . . . . . 507

References . . . . . . . . . . . . . . . . . . . . . . 508

35.1. Introduction

Non-accelerator experiments have become increasingly importantin particle physics. These include classical cosmic ray experiments,neutrino oscillation measurements, and searches for double-beta decay,dark matter candidates, and magnetic monopoles. The experimentalmethods are sometimes those familiar at accelerators (plastic scintil-lators, drift chambers, TRD’s, etc.) but there is also instrumentationeither not found at accelerators or applied in a radically different way.Examples are atmospheric scintillation detectors (Fly’s Eye), massiveCherenkov detectors (Super-Kamiokande, IceCube), ultracold solidstate detectors (CDMS). And, except for the cosmic ray detectors,radiologically ultra-pure materials are required.

In this section, some more important detectors special to terrestrialnon-accelerator experiments are discussed. Techniques used in bothaccelerator and non-accelerator experiments are described in Sec. 28,Particle Detectors at Accelerators, some of which have been modifiedto accommodate the non-accelerator nuances.

Space-based detectors also use some unique instrumentation, butthese are beyond the present scope of RPP.

35.2. High-energy cosmic-ray hadron and gamma-

ray detectors

35.2.1. Atmospheric fluorescence detectors :

Revised August 2015 by L.R. Wiencke (Colorado School of Mines).

Cosmic-ray fluorescence detectors (FDs) use the atmosphere as agiant calorimeter to measure isotropic scintillation light that tracesthe development profiles of extensive air showers. An extensive airshower (EAS) is produced by the interactions of ultra high-energy(E > 1017 eV) subatomic particles in the stratosphere and uppertroposphere. These are the highest energy particles known to exist.The amount of scintillation light generated is proportional to energydeposited in the atmosphere and nearly independent of the primaryspecies. Experiments with FDs include the pioneering Fly’s Eye [1],HiRes [2], the Telescope Array [3], and the Pierre Auger Observatory(Auger) [4]. The Auger FD also measures the time developmentof a class of atmospheric transient luminous events called ”Elves”that are created in the ionosphere above some thunderstorms [5].The proposed space based FD instrument [6] by the JEM-EUSOcollaboration would look down on the earth’s atmosphere from spaceto view a much larger area than ground based instruments.

The fluorescence light is emitted primarily between 290 and 430 nm(Fig. 35.1), when relativistic charged particles, primarily electrons andpositrons, excite nitrogen molecules in air, resulting in transitions ofthe 1P and 2P systems. Reviews and references for the pioneering andrecent laboratory measurements of fluorescence yield, Y (λ, P, T, u),including dependence on wavelength (λ), temperature (T ), pressure(p), and humidity (u) may be found in Refs. 7–9. The results ofvarious experiments have been combined (Fig. 35.2) to obtain anabsolute average and uncertainty for Y(337 nm, 800 hPa, 293 K, dryair) of 7.04 ± 0.24 ph/MeV after corrections for different electronbeam energies and other factors. The units of ph/MeV correspondto the number of fluorescence photons produced per MeV of energydeposited in the atmosphere by the electromagnetic component of anEAS.

Wavelength (nm)290 300 310 320 330 340 350 360 370 380 390 400 410 420

15

10

5

0

Rel

ativ

e in

tens

ity

Figure 35.1: Measured fluorescence spectrum excited by 3 MeVelectrons in dry air at 800 hPa and 293 K [11].

An FD element (telescope) consists of a non-tracking sphericalmirror (3.5–13 m2 and less than astronomical quality), a close-packed “camera” of photomultiplier tubes (PMTs) (for example,Hamamatsu R9508 or Photonis XP3062) near the focal plane, anda flash ADC readout system with a pulse and track-finding triggerscheme [10]. Simple reflector optics (12 × 16 degree field of view(FOV) on 256 PMTs) and Schmidt optics (30 × 30 FOV on 440PMTs), including a correcting element, have been used. Segmentedmirrors have been fabricated from slumped or slumped/polishedglass with an anodized aluminium coating and from chemicallyanodized AlMgSiO5 affixed to shaped aluminum. A broadband UVfilter (custom fabricated or Schott MUG-6) reduces background lightsuch as starlight, airglow, man-made light pollution, and airplanestrobelights.

492 35. Detectors for non-accelerator physics

3 4 5 6 7 8 9 10

Y 337 (ph/MeV)

Kakimoto

Nagano

Lefeuvre

MACFLY

FLASH

AirLight

Dandl

Airfly

Theoretical

<Y 337> = 7.04 ± 0.24 ph/MeV

Figure 35.2: Fluoresence yield values and associated uncer-tainties at 337 nm (Y337) in dry air at 800 hPa and 293 K(Figure from [12]) . The methodology and corrections that wereapplied to obtain the average and the uncertainty are discussedextensively in this reference. The vertical axis denotes differentlaboratory experiments that measured FY. The gray bars showthree of the original measurements to illustrate the scale of thecorrections applied.

At 1020 eV, where the flux drops below 1 EAS/km2century, theaperture for an eye of adjacent FD telescopes that span the horizoncan reach 104 km2 sr. FD operation requires (nearly) moonless nightsand clear atmospheric conditions, which imposes a duty cycle of about10%. Arrangements of LEDs, calibrated diffuse sources [13], pulsedUV lasers [14], LIDARs* and cloud monitors are used for photometriccalibration, atmospheric calibration [15], and determination ofexposure [16].

The EAS generates a track consistent with a light source moving atv = c across the FOV. The number of photons (Nγ) as a function ofatmospheric depth (X) can be expressed as [8]

dNγ

dX=

dEtotdep

dX

∫

Y (λ, P, T, u) · τatm(λ, X) · εFD(λ)dλ , (35.1)

where τatm(λ, X) is the atmospheric transmission, including wave-length (λ) dependence, and εFD(λ) is the FD efficiency. εFD(λ)includes geometric factors and collection efficiency of the optics,quantum efficiency of the PMTs, and other throughput factors. Thetypical systematic uncertainties, τatm (10%) and εFD (photometriccalibration 10%), currently dominate the total reconstructed EASenergy uncertainty. ∆E/E of 20% is possible, provided the geometricfit of the EAS axis is constrained typically by multi-eye stereoprojection, or by timing from a colocated sparse array of surfacedetectors.

Analysis methods to reconstruct the EAS profile and deconvolutethe contributions of re-scattered scintillation light, and direct andscattered Cherenkov light are described in [1] and more recentlyin [17]. The EAS energy is typically obtained by integrating over theGaisser-Hillas function [18]

Ecal =

∫

∞

0wmax

(

X − X0

Xmax − X0

)(Xmax−X0)/λ

e(Xmax−X)/λdX ,

(35.2)where Xmax is the depth at which the shower reaches its maximumenergy deposit wmax. X0 and λ are two shape parameters.

* ”LIDAR stands for ”Light Detection and Ranging” and refers hereto systems that measure atmospheric properties from the light scatteredbackwards from laser pulses directed into the sky.

35.2.2. Atmospheric Cherenkov telescopes for high-energy

γ-ray astronomy :

Revised November 2015 by J. Holder (Dept. of Physics and Astronomy& Bartol Research Inst., Univ. of Delaware).

A wide variety of astrophysical objects are now known to producehigh-energy γ-ray photons. Leptonic or hadronic particles, acceleratedto relativistic energies in the source, produce γ-rays typically throughinverse Compton boosting of ambient photons or through the decayof neutral pions produced in hadronic interactions. At energies below∼30 GeV, γ-ray emission can be efficiently detected using satellite orballoon-borne instrumentation, with an effective area approximatelyequal to the size of the detector (typically < 1 m2). At higher energies,a technique with much larger effective collection area is required tomeasure astrophysical γ-ray fluxes, which decrease rapidly withincreasing energy. Atmospheric Cherenkov detectors achieve effectivecollection areas of >105 m2 by employing the Earth’s atmosphere asan intrinsic part of the detection technique.

As described in Chapter 29, a hadronic cosmic ray or high energyγ-ray incident on the Earth’s atmosphere triggers a particle cascade,or air shower. Relativistic charged particles in the cascade generateCherenkov radiation, which is emitted along the shower direction,resulting in a light pool on the ground with a radius of ∼130 m.Cherenkov light is produced throughout the cascade development,with the maximum emission occurring when the number of particlesin the cascade is largest, at an altitude of ∼10 km for primaryenergies of 100GeV–1TeV. Following absorption and scattering inthe atmosphere, the Cherenkov light at ground level peaks at awavelength, λ ≈ 300–350 nm. The photon density is typically ∼100photons/m2 for a 1 TeV primary, arriving in a brief flash of a fewnanoseconds duration. This Cherenkov pulse can be detected fromany point within the light pool radius by using large reflecting surfacesto focus the Cherenkov light on to fast photon detectors (Fig. 35.3).

10 km

130 m

Camera plane

Figure 35.3: A schematic illustration of an imaging atmosphericCherenkov telescope array. The primary particle initiates an airshower, resulting in a cone of Cherenkov radiation. Telescopeswithin the Cherenkov light pool record elliptical images; theintersection of the long axes of these images indicates the arrivaldirection of the primary, and hence the location of a γ-ray sourcein the sky.

Modern atmospheric Cherenkov telescopes, such as those builtand operated by the VERITAS [19], H.E.S.S. [20] and MAGIC [21]collaborations, consist of large (> 100m2) segmented mirrors onsteerable altitude-azimuth mounts. A camera made from an array ofphotosensors is placed at the focus of each mirror and used to recorda Cherenkov image of each air shower. In these imaging atmosphericCherenkov telescopes, single-anode photomultipliers tubes (PMTs)have traditionally been used (2048, in the case of H.E.S.S. II), butmulti-anode PMTs and silicon devices now feature in more moderndesigns. The telescope cameras typically cover a field-of-view of 3− 5


in diameter. Images are recorded at kHz rates, the vast majorityof which are due to showers with hadronic cosmic-ray primaries.The shape and orientation of the Cherenkov images are used todiscriminate γ-ray photon events from this cosmic-ray background,and to reconstruct the photon energy and arrival direction. γ-rayimages result from purely electromagnetic cascades and appear asnarrow, elongated ellipses in the camera plane. The long axis of theellipse corresponds to the vertical extension of the air shower, and itpoints back towards the source position in the field-of-view. If multipletelescopes are used to view the same shower (“stereoscopy”), thesource position is simply the intersection point of the various imageaxes. Cosmic-ray primaries produce secondaries with large transversemomenta, which initiate sub-showers. Their images are consequentlywider and less regular than those with γ-ray primaries and, since theoriginal charged particle has been deflected by Galactic magnetic fieldsbefore reaching the Earth, the images have no preferred orientation.

The measurable differences in Cherenkov image orientation andmorphology provide the background discrimination which makesground-based γ-ray astronomy possible. For point-like sources, suchas distant active galactic nuclei, modern instruments can reject over99.999% of the triggered cosmic-ray events, while retaining up to 50%of the γ-ray population. In the case of spatially extended sources,such as Galactic supernova remnants, the background rejection is lessefficient, but the technique can be used to produce γ-ray maps ofthe emission from the source. The angular resolution depends uponthe number of telescopes which view the image and the energy ofthe primary γ-ray, but is typically less than 0.1 per event (68%containment radius) at energies above a few hundred GeV.

The total Cherenkov yield from the air shower is proportional tothe energy of the primary particle. The image intensity, combinedwith the reconstructed distance of the shower core from each telescope,can therefore be used to estimate the primary energy. The energyresolution of this technique, also energy-dependent, is typically15–20% at energies above a few hundred GeV. Energy spectra ofγ-ray sources can be measured over a wide range, depending uponthe instrument characteristics, source properties (flux, spectral slope,elevation angle, etc.), and exposure time: the H.E.S.S. measurementof the hard spectrum supernova remnant RX J1713.7-3946 extendsto 100 TeV [22], for example, while pulsed emission from the CrabPulsar has been detected at 25 GeV [23]. In general, peak sensitivitylies in the range from 100 GeV to a few TeV.

The first astrophysical source to be convincingly detected using theimaging atmospheric Cherenkov technique was the Crab Nebula [24],with an integral flux of 2.1×10−11 photons cm−2 s−1 above 1 TeV [25].Modern imaging atmospheric Cherenkov telescopes have sensitivitysufficient to detect sources with less than 1% of the Crab Nebulaflux in a few tens of hours. The TeV source catalog now consists ofmore than 160 sources (see e.g. Ref. 26). The majority of these weredetected by scanning the Galactic plane from the southern hemispherewith the H.E.S.S. telescope array [27].

Major upgrades of the existing telescope arrays have recently beencompleted, including the addition of a 28 m diameter central telescopeto H.E.S.S. (H.E.S.S. II). Development is also underway for the nextgeneration instrument, the Cherenkov Telescope Array (CTA), whichwill consist of a northern and a southern hemisphere observatory, witha combined total of more than 100 telescopes [28]. Telescopes of threedifferent sizes are planned, spread over an area of > 1 km2, providingwider energy coverage, improved angular and energy resolutions, andan order of magnitude improvement in sensitivity relative to existingimaging atmospheric Cherenkov telescopes. Baseline telescope designsare similar to existing devices, but exploit technological developmentssuch as dual mirror optics and silicon photo-detectors.

35.3. Large neutrino detectors

35.3.1. Deep liquid detectors for rare processes :

Revised August 2015 by K. Scholberg & C.W. Walter (DukeUniversity)

Deep, large detectors for rare processes tend to be multi-purposewith physics reach that includes not only solar, reactor, supernovaand atmospheric neutrinos, but also searches for baryon numberviolation, searches for exotic particles such as magnetic monopoles,and neutrino and cosmic-ray astrophysics in different energy regimes.The detectors may also serve as targets for long-baseline neutrinobeams for neutrino oscillation physics studies. In general, detectordesign considerations can be divided into high-and low-energy regimes,for which background and event reconstruction issues differ. Thehigh-energy regime, from about 100 MeV to a few hundred GeV,is relevant for proton decay searches, atmospheric neutrinos andhigh-energy astrophysical neutrinos. The low-energy regime (a fewtens of MeV or less) is relevant for supernova, solar, reactor andgeological neutrinos.

Large water Cherenkov and scintillator detectors (see Table 35.1)usually consist of a volume of transparent liquid viewed byphotomultiplier tubes (PMTs) (see Sec. 34.2); the liquid serves asactive target. PMT hit charges and times are recorded and digitized,and triggering is usually based on coincidence of PMT hits withina time window comparable to the detector’s light-crossing time.Because photosensors lining an inner surface represent a drivingcost that scales as surface area, very large volumes can be used forcomparatively reasonable cost. Some detectors are segmented intosubvolumes individually viewed by PMTs, and may include otherdetector elements (e.g., tracking detectors). Devices to increase lightcollection, e.g., reflectors or waveshifter plates, may be employed. Acommon configuration is to have at least one concentric outer layerof liquid material separated from the inner part of the detector toserve as shielding against ambient background. If optically separatedand instrumented with PMTs, an outer layer may also serve as anactive veto against entering cosmic rays and other background events.The PMTs for large detectors typically range in size from 20 cm to50 cm diameter, and typical quantum efficiencies are in the 20–25%range for scintillation and water-Cherenkov photons. PMTs withhigher quantum efficiencies, 35% or higher, have recently becomeavailable. The active liquid volume requires purification and theremay be continuous recirculation of liquid. For large homogeneousdetectors, the event interaction vertex is determined using relativetiming of PMT hits, and energy deposition is determined from thenumber of recorded photoelectrons. A “fiducial volume” is usuallydefined within the full detector volume, some distance away from thePMT array. Inside the fiducial volume, enough PMTs are illuminatedper event that reconstruction is considered reliable, and furthermore,entering background from the enclosing walls is suppressed by abuffer of self-shielding. PMT and detector optical parameters arecalibrated using laser, LED, or other light sources. Quality of eventreconstruction typically depends on photoelectron yield, pixelizationand timing.

Because in most cases one is searching for rare events, largedetectors are usually sited underground to reduce cosmic-ray-relatedbackground (see Chapter 29). The minimum depth required variesaccording to the physics goals [29].

35.3.1.1. Liquid scintillator detectors:

Past and current large underground detectors based on hydrocarbonscintillators include LVD, MACRO, Baksan, Borexino, KamLANDand SNO+. Experiments at nuclear reactors include CHOOZ, DoubleCHOOZ, Daya Bay, and RENO. Organic liquid scintillators (seeSec. 34.3.0) for large detectors are chosen for high light yieldand attenuation length, good stability, compatibility with otherdetector materials, high flash point, low toxicity, appropriatedensity for mechanical stability, and low cost. They may bedoped with waveshifters and stabilizing agents. Popular choices arepseudocumene (1,2,4-trimethylbenzene) with a few g/L of the PPO(2,5-diphenyloxazole) fluor, and linear alkylbenzene (LAB). In atypical detector configuration there will be active or passive regions of


undoped scintillator, non-scintillating mineral oil or water surroundingthe inner neutrino target volume. A thin vessel or balloon made ofnylon, acrylic or other material transparent to scintillation light maycontain the inner target; if the scintillator is buoyant with respectto its buffer, ropes may hold the balloon in place. For phototubesurface coverages in the 20–40% range, yields in the few hundredsof photoelectrons per MeV of energy deposition can be obtained.Typical energy resolution is about 7%/

√

E(MeV), and typical positionreconstruction resolution is a few tens of cm at ∼ 1 MeV, scaling as∼ N−1/2, where N is the number of photoelectrons detected.

Table 35.1: Properties of large detectors for rare processes. If total target mass is dividedinto large submodules, the number of subdetectors is indicated in parentheses.

Detector Mass, kton PMTs ξ p.e./MeV Dates

(modules) (diameter, cm)

Baksan 0.33, scint (3150) 1/module (15) segmented 40 1980–

MACRO 0.56, scint (476) 2-4/module (20) segmented 18 1989–2000

LVD 1, scint. (840) 3/module (15) segmented 15 1992–

KamLAND 0.41f , scint 1325(43)+554(51)* 34% 460 2002–

Borexino 0.1f , scint 2212 (20) 30% 500 2007–

SNO+ 0.78, scint 9438 (20) 54% 400–900 2016 (exp.)

CHOOZ 0.005, scint (Gd) 192 (20) 15% 130 1997–1998

Double Chooz 0.017, scint (Gd)(2) 534/module (20) 13% 180 2011–

Daya Bay 0.160, scint (Gd)(8) 192/module (20) 5.6%† 100 2011–

RENO 0.032, scint (Gd)(2) 342/module (25) 12.6% 100 2011–

IMB-1 3.3f , H2O 2048 (12.5) 1% 0.25 1982–1985

IMB-2 3.3f , H2O 2048 (20) 4.5% 1.1 1987–1990

Kam I 0.88/0.78f , H2O 1000/948 (50) 20% 3.4 1983–1985

Kam II 1.04f , H2O 948 (50) 20% 3.4 1986–1990

Kam III 1.04f , H2O 948 (50) 20%‡ 4.3 1990–1995

SK I 22.5f , H2O 11146 (50) 39% 6 1996–2001

SK II 22.5f , H2O 5182 (50) 19% 3 2002–2005

SK III+ 22.5f , H2O 11129 (50) 39% 6 2006–

SNO 1, D2O/1.7, H2O 9438 (20) 31% § 9 1999–2006

f indicates typical fiducial mass used for data analysis; this may vary by physics topic.

* Measurements made before 2003 only considered data from the 43 cm PMTs.

† The effective Daya Bay coverage is 12% with top and bottom reflectors.

‡ The effective Kamiokande III coverage was 25% with light collectors.

§ The effective SNO coverage was 54% with light collectors.

Shallow detectors for reactor neutrino oscillation experimentsrequire excellent muon veto capabilities. For νe detection via inversebeta decay on free protons, νe + p → n + e+, the neutron is capturedby a proton on a ∼180 µs timescale, resulting in a 2.2 MeV γ ray,observable by Compton scattering and which can be used as a tag incoincidence with the positron signal. The positron annihilation γ raysmay also contribute. Inverse beta decay tagging may be improvedby addition of Gd at ∼0.1% by mass, which for natural isotopeabundance has a ∼49,000 barn cross-section for neutron capture (incontrast to the 0.3 barn cross-section for capture on free protons). Gdcapture takes ∼30 µs, and is followed by a cascade of γ rays adding upto about 8 MeV. Gadolinium doping of scintillator requires specializedformulation to ensure adequate attenuation length and stability.

Scintillation detectors have an advantage over water Cherenkovdetectors in the lack of Cherenkov threshold and the high lightyield. However, scintillation light emission is nearly isotropic,and therefore directional capabilities are relatively weak. Liquidscintillator is especially suitable for detection of low-energy events.Radioactive backgrounds are a serious issue, and include long-livedcosmogenics. To go below a few MeV, very careful selection ofmaterials and purification of the scintillator is required (see Sec. 35.6).

Fiducialization and tagging can reduce background. One can alsodissolve neutrinoless double beta decay (0νββ) isotopes in scintillator.This has been realized by KamLAND-Zen, which deployed a 1.5 m-radius balloon containing enriched Xe dissolved in scintillator insideKamLAND, and 130Te is planned for SNO+. Although for thisapproach, energy resolution is poor compared to other 0νββ searchexperiments, the quantity of isotope can be so large that the kinematicsignature of 0νββ would be visible as a clear feature in the spectrum.

35.3.1.2. Water Cherenkov detectors:

Very large imaging water detectors reconstruct ten-meter-scaleCherenkov rings produced by charged particles (see Sec. 34.5.0).The first such large detectors were IMB and Kamiokande. The onlycurrently existing instance of this class of detector, with fiducialvolume of 22.5 kton and total mass of 50 kton, is Super-Kamiokande(Super-K). For volumes of this scale, absorption and scattering ofCherenkov light are non-negligible, and a wavelength-dependent factorexp(−d/L(λ)) (where d is the distance from emission to the sensorand L(λ) is the attenuation length of the medium) must be includedin the integral of Eq. (34.5) for the photoelectron yield. Attenuationlengths on the order of 100 meters have been achieved.

Cherenkov detectors are excellent electromagnetic calorimeters,and the number of Cherenkov photons produced by an e/γ is nearlyproportional to its kinetic energy. For massive particles, the numberof photons produced is also related to the energy, but not linearly.For any type of particle, the visible energy Evis is defined as theenergy of an electron which would produce the same number ofCherenkov photons. The number of collected photoelectrons dependson the scattering and attenuation in the water along with the photo-cathode coverage, quantum efficiency and the optical parameters


of any external light collection systems or protective materialsurrounding them. Event-by-event corrections are made for geometryand attenuation. For a typical case, in water Np.e. ∼ 15 ξ Evis(MeV),where ξ is the effective fractional photosensor coverage. Cherenkovphotoelectron yield per MeV of energy is relatively small comparedto that for scintillator, e.g., ∼ 6 pe/MeV for Super-K with a PMTsurface coverage of ∼ 40%. In spite of light yield and Cherenkovthreshold issues, the intrinsic directionality of Cherenkov light allowsindividual particle tracks to be reconstructed. Vertex and directionfits are performed using PMT hit charges and times, requiring thatthe hit pattern be consistent with a Cherenkov ring.

High-energy (∼100 MeV or more) neutrinos from the atmosphereor beams interact with nucleons; for the nucleons bound inside the16O nucleus, nuclear effects must be considered both at the interactionand as the particles leave the nucleus. Various event topologies canbe distinguished by their timing and fit patterns, and by presenceor absence of light in a veto. “Fully-contained” events are those forwhich the neutrino interaction final state particles do not leave theinner part of the detector; these have their energies relatively wellmeasured. Neutrino interactions for which the lepton is not containedin the inner detector sample have higher-energy parent neutrinoenergy distributions. For example, in “partially-contained” events, theneutrino interacts inside the inner part of the detector but the lepton(almost always a muon, since only muons are penetrating) exits.“Upward-going muons” can arise from neutrinos which interact in therock below the detector and create muons which enter the detectorand either stop, or go all the way through (entering downward-goingmuons cannot be distinguished from cosmic rays). At high energies,multi-photoelectron hits are likely and the charge collected by eachPMT (rather than the number of PMTs firing) must be used; thisdegrades the energy resolution to approximately 2%/

√

ξ Evis(GeV).The absolute energy scale in this regime can be known to ∼2–3%using cosmic-ray muon energy deposition, Michel electrons and π0

from atmospheric neutrino interactions. Typical vertex resolutionsfor GeV energies are a few tens of cm [30]. Angular resolution fordetermination of the direction of a charged particle track is a fewdegrees. For a neutrino interaction, because some final-state particlesare usually below Cherenkov threshold, knowledge of direction of theincoming neutrino direction itself is generally worse than that of thelepton direction, and dependent on neutrino energy.

Multiple particles in an interaction (so long as they are aboveCherenkov threshold) may be reconstructed, allowing for the exclusivereconstruction of final states. In searches for proton decay, multipleparticles can be kinematically reconstructed to form a decayingnucleon. High-quality particle identification is also possible: γ raysand electrons shower, and electrons scatter, which results in fuzzyrings, whereas muons, pions and protons make sharp rings. Thesepatterns can be quantitatively separated with high reliabilityusing maximum likelihood methods [31]. A e/µ misidentificationprobability of ∼ 0.4%/ξ in the sub-GeV range is consistent with theperformance of several experiments for 4% < ξ < 40%. Sources ofbackground for high energy interactions include misidentified cosmicmuons and anomalous light patterns when the PMTs sometimes“flash” and emit photons themselves. The latter class of events canbe removed using its distinctive PMT signal patterns, which may berepeated. More information about high energy event selection andreconstruction may be found in reference [32].

In spite of the fairly low light yield, large water Cherenkovdetectors may be employed for reconstructing low-energy events,down to e.g. ∼ 4-5 MeV for Super-K [33]. Low-energy neutrinointeractions of solar neutrinos in water are predominantly elasticscattering off atomic electrons; single electron events are thenreconstructed. At solar neutrino energies, the visible energy resolution(∼ 30%/

√

ξ Evis(MeV)) is about 20% worse than photoelectroncounting statistics would imply. Using an electron LINAC and/ornuclear sources, approximately 0.5% determination of the absoluteenergy scale has been achieved at solar neutrino energies. Angularresolution is limited by multiple scattering in this energy regime(25–30). At these energies, radioactive backgrounds become adominant issue. These backgrounds include radon in the water itselfor emanated from detector materials, and γ rays from the rock and

detector materials. In the few to few tens of MeV range, radioactiveproducts of cosmic-ray-muon-induced spallation are troublesome, andare removed by proximity in time and space to preceding muons, atsome cost in dead time. Gadolinium doping using 0.2% Gd2(SO4)3 isplanned for Super-K to improve selection of low-energy νe and otherevents with accompanying neutrons [34].

The Sudbury Neutrino Observatory (SNO) detector [35] is theonly instance of a large heavy water detector and deserves mentionhere. In addition to an outer 1.7 kton of light water, SNO contained1 kton of D2O, giving it unique sensitivity to neutrino neutral current(νx + d → νx + p + n), and charged current (νe + d → p + p + e−)deuteron breakup reactions. The neutrons were detected in threeways: In the first phase, via the reaction n + d → t + γ + 6.25 MeV;Cherenkov radiation from electrons Compton-scattered by the γ rayswas observed. In the second phase, NaCl was dissolved in the water.35Cl captures neutrons, n + 35Cl → 36Cl + γ + 8.6 MeV. The γ rayswere observed via Compton scattering. In a final phase, specializedlow-background 3He counters (“neutral current detectors” or NCDs)were deployed in the detector. These counters detected neutrons vian + 3He → p + t + 0.76 MeV; ionization charge from energy loss of theproducts was recorded in proportional counters.

35.3.2. Neutrino telescopes :

Revised Nov. 2015 by Ch. Spiering (DESY/Zeuthen) and U.F. Katz(Univ. Erlangen)

The primary goal of neutrino telescopes (NTs) is the detection ofastrophysical neutrinos, in particularly those which are expected toaccompany the production of high-energy cosmic rays in astrophysicalaccelerators. NTs in addition address a variety of other fundamentalphysics issues like indirect search for dark matter, study of neutrinooscillations, search for exotic particles like magnetic monopoles orstudy of cosmic rays and their interactions [36,37,38].

NTs are large-volume arrays of “optical modules” (OMs) installedin open transparent media like water or ice, at depths that completelyblock the daylight. The OMs record the Cherenkov light inducedby charged secondary particles produced in reactions of high-energyneutrinos in or around the instrumented volume. The neutrinoenergy, Eν , and direction can be reconstructed from the hit patternrecorded. NTs typically target an energy range Eν & 100 GeV;sensitivity to lower energies is achieved in dedicated setups with denserinstrumentation.

In detecting cosmic neutrinos, three sources of backgrounds have tobe considered: (i) atmospheric neutrinos from cosmic-ray interactionsin the atmosphere, which can be separated from cosmic neutrinosonly on a statistical basis; (ii) down-going punch-through atmosphericmuons from cosmic-ray interactions, which are suppressed by severalorders of magnitude with respect to the ground level due to thelarge detector depths. They can be further reduced by selectingupward-going or high-energy muons or by self-veto methods sensitiveto the muon entering the detector; (iii) random backgrounds due tophotomultiplier (PMT) dark counts, 40K decays (mainly in sea water)or bioluminescence (only water), which impact adversely on eventrecognition and reconstruction. Note that atmospheric neutrinos andmuons allow for investigating neutrino oscillations and cosmic rayanisotropies, respectively.

Recently, it has become obvious that a precise measurement ofthe energy-zenith-distribution of atmospheric neutrinos may allow fordetermining the neutrino mass hierarchy by exploiting matter-inducedoscillation effects in the Earth.

Neutrinos can interact with target nucleons N through chargedcurrent ( νℓN → ℓ∓X , CC) or neutral current ( νℓN → νℓX , NC)processes. A CC reaction of a νµ produces a muon track and ahadronic particle cascade, whereas all NC reactions and CC reactionsof νe produce particle cascades only. CC interactions of ντ can haveeither signature, depending on the τ decay mode. In most astrophysicalmodels, neutrinos are produced through the π/K → µ → e decaychain, i.e., with a flavour ratio νe : νµ : ντ ≈ 1 : 2 : 0. For sourcesoutside the solar system, neutrino oscillations turn this ratio toνe : νµ : ντ ≈ 1 : 1 : 1 upon arrival on Earth.

The total neutrino-nucleon cross section is about 10−35 cm2 at


Eν = 1 TeV and rises roughly linearly with Eν below this energy andas E0.3–0.5

ν above, flattening out towards high energies. The CC:NCcross-section ratio is about 2:1. At energies above some TeV, neutrinoabsorption in the Earth becomes noticeable; for vertically upward-moving neutrinos (zenith angle θ = 180), the survival probability is74 (27, < 2)% for 10 (100, 1000)TeV. On average, between 50% (65%)and 75% of Eν is transfered to the final-state lepton in neutrino(antineutrino) reactions between 100 GeV and 10 PeV.

Table 35.2: Past, present and planned neutrino telescope projectsand their main parameters. The milestone years give the times ofproject start, of first data taking with partial configurations, ofdetector completion, and of project termination. Projects with firstdata expected past 2020 are indicated in italics. The size refers to thelargest instrumented volume reached during the project development.See [38] for references to the different projects where unspecified.

Experiment, Medium, Size Remarks

Milestones Location [km3]

DUMAND, Pacific/Hawaii Terminated due to

1978/–/–/1995 technical/funding problems

NT-200 Lake Baikal 10−4 First proof of principle

1980/1993/1998/–

GVD [39] Lake Baikal 0.5–1.5 High-energy ν astronomy,

2012/2015/–/– first cluster installed

NESTOR Med. Sea 2004 data taking with prototype

1991/–/–/–

NEMO Med. Sea R&D project, prototype tests

1998/–/–/–

AMANDA Ice/South Pole 0.015 First deep-ice neutrino telescope

1990/1996/2000/2009

ANTARES Med. Sea 0.010 First deep-sea neutrino telescope

1997/2006/2008/2016

IceCube Ice/South Pole 1.0 First km3-sized detector

2001/2005/2010/–

PINGU [40] Ice/South Pole 0.003 Planned low-energy extension

2014/–/–/– of IceCube

IceCube-Gen2 [41] Ice/South Pole 5–10 Planned high-energy extension

2014/–/–/–

KM3NeT/ARCA Med. Sea 1–2 First construction phase started

2013/(2017)/–/–

KM3NeT/ORCA Med. Sea 0.003 Low-energy configuration for

2014/(2017)/–/– neutrino mass hierarchy

KM3NeT Phase 3 Med. Sea 3–6 6 building blocks + ORCA

2013/–/–/–

The final-state lepton follows the initial neutrino direction with aRMS mismatch angle 〈φνℓ〉 ≈ 1.5/

√

Eν [TeV], indicating the intrinsickinematic limit to the angular resolution of NTs. For CC νµ reactionsat energies above about 10TeV, the angular resolution is dominatedby the muon reconstruction accuracy of a few times 0.1 at most.For muon energies Eµ & 1 TeV, the increasing light emission due toradiative processes allows for reconstructing Eµ from the measureddEµ/dx with an accuracy of σ(log Eµ) ≈ 0.3; at lower energies, Eµ canbe estimated from the length of the muon track if it is contained in thedetector. These properties make CC νµ reactions the prime channelfor the identification of individual astrophysical neutrino sources.

Hadronic and electromagnetic particle cascades at the relevantenergies are 5–20m long, i.e., short compared to typical distancesbetween OMs. The total amount of Cherenkov light provides adirect measurement of the cascade energy with an accuracy of about20% at energies above 10TeV and 10% beyond 100TeV for eventscontained in the instrumented volume. Neutrino flavour and reactionmechanism can, however, hardly be determined and neutrinos from

NC reactions or τ decays may carry away significant “invisible”energy. Above 100TeV, the directional reconstruction accuracy ofcascades is 10–15degrees in polar ice and about 2 degrees in water,the difference being due to the inhomogeneity of the ice and thestronger light scattering in ice. These features, together with the smallbackground of atmospheric νe and ντ events, makes the cascadechannel particularly interesting for searches for a diffuse, high-energyexcess of extraterrestrial over atmospheric neutrinos. In water,

cascade events can also be used for the search for point sources ofcosmic neutrinos. The inferior angular accuracy compared to muontracks, however, leads to a higher number of background events persource from atmospheric neutrinos.

The detection efficiency of a NT is quantified by its effective area,e.g., the fictitious area for which the full incoming neutrino fluxwould be recorded (see Fig. 35.4). The increase with Eν is due tothe rise of neutrino cross section and muon range, while neutrinoabsorption in the Earth causes the decrease at large θ. Identificationof downward-going neutrinos requires strong cuts against atmosphericmuons, hence the cut-off towards low Eν . Due to the small crosssection, the effective area is many orders of magnitude smaller thanthe geometrical dimension of the detector; a νµ with 1TeV can, e.g.,be detected with a probability of the order 10−6 if the telescope is onits path.

Detection of upward going muons makes the effective volume ofthe detector much larger than its geometrical volume. The method,however, is only sensitive to CC νµ interactions and cannot be


log10 E (GeV)

log

10 e

ffec

tive

area

(m

2)

2 3 4 5 6 7 8 9

1) 150 < θ < 180

2) 90 < θ < 120

3) 0 < θ < 30

2

1

3

4

3

2

1

0

−1

−2

−3

Figure 35.4: Effective νµ area for IceCube as an example of acubic-kilometre NT, as a function of neutrino energy for threeintervals of the zenith angle θ. The effective areas shown herecorrespond to a specific event selection for point source searches.

extended much more than 5–10degrees above the geometric horizon,where the background of atmospheric muons becomes prohibitive.Alternatively, one can select events that start inside the instrumentedvolume. In contrast to neutrinos, incoming muons generate early hitsin the outer layers of the detector. Such a veto-based event selectionis sensitive to neutrinos of all flavours from all directions, albeit witha reduced effective volume since a part of the instrumented volumeis sacrificed for the veto. The muon veto also rejects down-goingatmospheric neutrinos that typically are accompanied by muonsin the same air shower and thus reduces the atmospheric-neutrinobackground. Actually, the breakthrough in detecting high-energycosmic neutrinos has been achieved with this technique.

Note that the fields of view of NTs at the South Pole and in theNorthern hemisphere are complementary for each reaction channeland neutrino energy.

35.3.2.1. Properties of media:

The efficiency and quality of event reconstruction depend stronglyon the optical properties (absorption and scattering length, intrinsicoptical activity) of the medium in the spectral range of bialkaliphotocathodes (300–550nm). Large absorption lengths result in abetter light collection, large scattering lengths in superior angularresolution. Deep-sea sites typically have effective scattering lengths of> 100 m and, at their peak transparency around 450 nm, absorptionlengths of 50–65m. The absorption length for Lake Baikal is 22–24m.The properties of South Polar ice vary strongly with depth; at thepeak transparency wave length (400 nm), the scattering length isbetween 5 and 75m and the absorption length between 15 and 250m,with the best values in the depth region 2200–2450m and the worstones in the layer 1950–2100m.

Noise rates measured by 25 cm PMTs in deep polar ice are about0.5 kHz per PMT and almost entirely due to radioactivity in theOM components. The corresponding rates in sea water are typically60 kHz, mostly due to 40K decays. Bioluminescence activity can locallycause rates on the MHz scale for seconds; the frequence and intensityof such “bursts” depends strongly on the sea current, the season,the geographic location, and the detector geometry. Experience fromANTARES shows that these backgrounds are manageable without amajor loss of efficiency or experimental resolution.

35.3.2.2. Technical realisation:

Optical modules (OMs) and PMTs: An OM is a pressure-tight glasssphere housing one or several PMTs with a time resolution in thenanosecond range, and in most cases also electronics for control, HVgeneration, operation of calibration LEDs, time synchronisation andsignal digitisation.

Hybrid PMTs with 37 cm diameter have been used for NT-200,conventional hemispheric PMTs for AMANDA (20 cm) and forANTARES, IceCube and Baikal-GVD (25 cm). A novel concept hasbeen chosen for KM3NeT. The OMs (43 cm) are equipped with 31

PMTs (7.5 cm), plus control, calibration and digitisation electronics.The main advantages are that (i) the overall photocathode areaexceeds that of a 25 cm PMT by more than a factor of 3; (ii) theindividual readout of the PMTs results in a very good separationbetween one- and two-photoelectron signals which is essential foronline data filtering and random background suppression; (iii) the hitpattern on an OM provides directional information; (iv) no mu-metalshielding against the Earth magnetic field is required. Figure 35.5shows the OM designs of IceCube and KM3NeT.

Figure 35.5: Schematic views of the digital OMs of IceCube(left) and KM3NeT (right).

Readout and data filtering: In current NTs the PMT data aredigitised in situ, for ANTARES and Baikal-GVD in special electronicscontainers close to the OMs, for IceCube and KM3NeT inside theOMs. For IceCube, data are transmitted via electrical cables of up to3.3 km length, depending on the location of the strings and the depthof the OMs; for ANTARES, KM3NeT and Baikal-GVD optical fibreconnections have been chosen (several 10 km for the first two and 4 kmfor GVD).

The full digitised waveforms of the IceCube OMs are transmittedto the surface for pulses appearing in local coincidences on a string;for other pulses, only time and charge information is provided. ForANTARES (time and charge) and KM3NeT (time over threshold), allPMT signals above an adjustable noise threshold are sent to shore.

The raw data are subsequently processed on online computerfarms, where multiplicity and topology-driven filter algorithms areapplied to select event candidates. The filter output data rate isabout 10GByte/day for ANTARES and of the order 1 TByte/day forIceCube (100GByte/day transfered via satellite) and KM3NeT.

Calibration: For efficient event recognition and reconstruction, theOM timing must be synchronised at the few-nanosecond level andthe OM positions and orientations must be known to a few 10 cmand a few degrees, respectively. Time calibration is achieved bysending synchronisation signals to the OM electronics and also bylight calibration signals emitted by LED or laser flashers emittedin situ at known times (ANTARES, KM3NeT). Precise positioncalibration is achieved by measuring the travel time of light calibrationsignals sent from OM to OM (IceCube) or acoustic signals sentfrom transducers at the sea floor to receivers on the detector strings(ANTARES, KM3NeT, Baikal-GVD). Absolute pointing and angularresolution can be determined by measuring the “shadow of the moon”(i.e., the directional depletion of muons generated in cosmic-rayinteractions). IceCube has shown that both are below 1, confirmingMC calculations which indicate a precision of ≈ 0.5 for energiesabove 10TeV. For KM3NeT, simulations indicate that sub-degreeprecision in the absolute pointing can be reached within a few weeksof operation.

Detector configurations: IceCube (see Fig. 35.6) consists of 5160Digital OMs (DOMs) installed on 86 strings at depths of 1450to 2450m in the Antarctic ice; except for the DeepCore region,string distances are 125m and vertical distances between OMs 17m.324 further DOMs are installed in IceTop, an array of detector stationson the ice surface above the strings. DeepCore is a high-densitysub-array at large depths (i.e., in the best ice layer) at the centre ofIceCube.


Eiffel Tower

324 m

IceCube

Lab

50 m

1450 m

2450 m

Figure 35.6: Schematic view of the IceCube neutrino obser-vatory comprising the deep-ice detector including its nesteddense part DeepCore, and the surface air shower array IceTop.The IceCube Lab houses data acquisition electronics and thecomputer farm for online processing. Operation of AMANDAwas terminated in 2009.

The NT200 detector in Lake Baikal at a depth of 1100m consistsof 8 strings attached to an umbrella-like frame, with 12 pairs of OMsper string. The diameter of the instrumented volume is 42m, itsheight 70m. The Baikal collaboration has installed the first clusterof a future cubic-kilometre array. A first phase, covering a volume ofabout 0.4 km3, will consist of 12 clusters, each with 192–288 OMs at8 strings; its completion is scheduled for 2020. A next stage couldcomprise 27 clusters and cover up to 1.5 km3.

ANTARES comprises 12 strings with lateral separations of 60–70m,each carrying 25 triplets of OMs at vertical distances of 14.5m.The OMs are located at depths 2.1–2.4 km, starting 100m abovethe sea floor. A further string carries devices for calibration andenvironmental monitoring. A system to investigate the feasibility ofacoustic neutrino detection is also implemented.

KM3NeT will consist of building blocks of 115 strings each, with18 OMs per string. Prototype operations have successfully verifiedthe KM3NeT technology [42]. Phase 2.0 of KM3NeT aims todemonstrate two separate detector arrangements, ARCA and ORCA.ARCA (Astroparticle Research with Cosmics in the Abyss) will searchfor high-energy astrophysical neutrinos using a sparce arrangementof OMs, with vertical separations of 36m and a lateral separationbetween strings of 90m. ORCA (Oscillation Research with Cosmicsin the Abyss) intends to measure the neutrino mass hierarchy usinga densely-packed arrangement, with 6–12m vertical and 20m lateralseparations.

A first installation phase of ARCA near Capo Passero, East ofSicily and of ORCA near Toulon has started in 2014 and comprises24 (7) ARCA(ORCA) strings to be deployed by the end of 2016.Completion of the full three blocks is expected for 2020.

35.3.2.3. Results:

Atmospheric neutrino fluxes have been precisely measured withAMANDA and ANTARES ( νµ) and with IceCube ( νµ, νe); theresults are in agreement with predicted spectra. No astrophysicalpoint sources have been identified yet, and no indications of neutrinofluxes from dark matter annihilations or of exotic phenomena havebeen found (see [38] and references therein). IceCube has furthermorereported an energy-dependent anisotropy of cosmic-ray inducedmuons.

In 2013, an excess of track and cascade events between 30TeVand 1PeV above background expectations was reported by IceCube;this analysis used the data taken in 2010 and 2011 and for thefirst time employed containment conditions and an atmosphericmuon veto for suppression of down-going atmospheric neutrinos(High-Energy Starting Event analysis, HESE). A display of oneof the selected events is shown in Fig. 35.7. The observed excessreached a significance of 5.7σ in a subsequent analysis of 3 years

of data [43] and cannot be explained by atmospheric neutrinos andmisidentified atmospheric muons alone. Some clustering of the HESEevents close to the Galactic Centre was observed (see Fig. 35.8). Thehypothesis that this low-significance excess could be due to a pointsource with a spectral index of ≥ 2 was constrained by an analysis ofANTARES data looking at lower energies and with superior pointingto the same sky region [44]. Meanwhile the energy range of theIceCube HESE analysis has been extended down to 1TeV and thehigh-energy excess confirmed; also, events with through-going muonsshowed a corresponding excess of cosmic origin. In [45], the variousanalyses have been combined. Assuming the cosmic neutrino flux tobe isotropic, flavour-symmetric and ν-ν-symmetric at Earth, the all-flavour spectrum is well described by a power law with normalization6.7+1.1

−1.2 × 10−18 GeV−1s−1sr−1cm−2 at 100TeV and a spectral index−2.50 ± 0.09 for energies between 25TeV and 2.8PeV. A spectralindex of −2, an often quoted benchmark value, is disfavoured with asignificance of 3.8σ.

Figure 35.7: Event display of one of the starting-track events(event no. 5 in Fig. 35.8) from [43]. The deposited energy is70TeV, the colour code indicates the signal timing (red: early;green: late).

Figure 35.8: Arrival directions of 37 candidate events forcosmic neutrinos in equatorial coordinates (from [43]) . Shower-like events (median angular resolution 15 degrees) are markedwith + and those containing muon tracks degree) with ×.Approximately 40% of the events are expected to originate fromatmospheric backgrounds. The grey curve denotes the galacticplane and the grey dot the galactic centre. Colours show the teststatistic for a point source clustering test at each location, withno significant clustering observed.

At lower energies, down to 10GeV, IceCube/DeepCore andANTARES have identified clear signals of oscillations of atmosphericneutrinos. The closely spaced OMs of DeepCore allow selecting avery pure sample of low-energy νµ (6–56GeV) that produce upward


moving muons inside the detector. The neutrino energy is determinedfrom the energy of the hadronic shower at the vertex and the muonrange. Fits to the energy/zenith-dependent deficit of muon neutrinosprovide constraints on the oscillation parameters sin2 θ23 and ∆m2

23(see the update of fig. 14.6 in the 2014 PDG).

See [46] and [47] for summaries of recent results of IceCube andANTARES, respectively.

35.3.2.4. Plans beyond 2020:

It is planned to extend the sensitivity of IceCube towards bothlower and higher energies. A substantially denser instrumentationof a sub-volume of DeepCore would lead to an Eν threshold forneutrino detection of a few GeV. This project (Phased IceCube NextGeneration Upgrade, PINGU) [40] primarily aims at measuring theneutrino mass hierarchy. For higher energies, a large-volume extensioncalled IceCube-Gen2, combined with a powerful surface veto, isdiscussed [41]. More information on the future extensions of GVDand KM3NeT are given above and in Table 35.2.

35.3.3. Coherent radio Cherenkov radiation detectors :

Revised August 2015 by S.R. Klein (LBNL/UC Berkeley)

Radio-frequency detectors are an attractive way to search forcoherent Cherenkov radiation from showers produced from interationsof ultra-high energy cosmic neutrinos. These neutrinos are producedwhen protons with energy E > 4 × 1019 eV interact with cosmicmicrowave background radation (CMB) photons and are excited toa ∆+ resonance. The subsequent ∆+ → nπ+ decay leads to theproduction of neutrinos with energies above 1018 eV [48]. Neutrinosare the only long-range probe of the ultra-high energy cosmos, becauseprotons, heavier nuclei and photons with energies above 5 × 1019 eVare limited to ranges of less than 100 Mpc by interactions with CMBphotons and early starlight.

To detect this cosmic neutrino signal (of at least a few eventsper year, assuming that ultra-high energy cosmic-rays are protons)requires a detector of about 100 km3 in volume, made out of anon-conducting solid (or potentially liquid) medium, with a longabsorption length for radio waves. The huge target volumes requirethat this be a commonly available natural material. A dense mediumwould be ideal to reduce the detector volume, but, unfortunately,the available natural media are of only moderate density. OpticalCherenkov and acoustical detectors are limited by a short (∼300 m)attenutuation length [49] so would require a prohibitive number ofsensors. Radio-detection is the only current approach that can scaleto this volume. The two commonly used media are Antarctic (orGreenland) ice and the lunar regolith [50]. Table 35.3 compares thecharacteristics of these different media, including several possible icelocations.

Table 35.3: Characteristics of different detection mediafor radio-Cherenkov signals. The attenuation length is at afrequency of 300 MHz; the Greenland figure is extrapolatedupward from the 75 MHz measurements. The Moon and icehave similar Cherenkov angles because they have similar indicesof refraction.

Medium Density Cherenkov Ang. Cutoff Freq. Atten. Length

Lunar Regolith 2.5 g/cm3 560 3.0 GHz 9m/f(GHz) [50]Antarctic Ice (South Pole) 0.92 g/cm3 560 1.15 GHz 900 m [54]Ross Ice Shelf 0.92 g/cm3 560 1.15 GHz 406 m [55]Greenland 0.92 g/cm3 560 1.15 GHz 1022 m [56]

Electromagnetic and hadronic showers produce radio pulses via theAskaryan effect [51], as discussed in Sec. 33. The shower containsmore electrons than positrons, leading to coherent emission.

High-frequency radiation is concentrated around the Cherenkovangle. On the cone, the electric field strength at a frequency f froman electromagnetic shower from a νe may be roughly parameterized

as [52]

ECh(V/MHz) = 2.53 × 10−7 Eν

1TeV

f

fc

[

1

1 + (f/fc)1.44

]

. (35.3)

The electric field strength increases linearly with frequency, up toa cut-off fc, which is set by the transverse size of the shower [53];the maximum wavelength is roughly the Moliere radius divided bycos(θC ) where θC is the Cherenkov angle. Some examples are given inTable 35.3.

Near fc, radiation is narrowly concentrated around the Cherenovangle [53]. At lower frequencies, the limited length of the emittingregion leads to a diffractive broadening in emission angle with respectto the Cherenkov cone. The electric field from Eq. (35.3) is reducedby [52],

E

ECh= exp

(

−1

2

(θ − θC)2

(2.20 × [1GHz/f ])2

)

, (35.4)

At very low frequencies, the distribution is nearly isotropic.

Along the Cherenkov cone, the initial pulse width is ≈ 1 nsec, butit may be broadened by dispersion as it propagates, particularly forsignals traversing the ionosphere. As long as the dispersion can becompensated for, a large bandwidth detector is the most sensitive.Spectral information can be used to reject background, and to helpreconstruct the neutrino direction, because the cutoff frequencydepends on the observation angle (with respect to the Cherenkovcone).

The detection threshold is determined by the distance to theantenna and the noise characteristics of the detector. Since the signalis a radio wave, its amplitude decreases as 1/R, plus absorption inthe intervening medium. Once anthropogenic noise is eliminated (notalways easy), the main noise source is thermal noise. This can bereduced with careful design; locating a detector in cold ice also helps.Other potential backgrounds include cosmic-ray air showers, chargegenerated by blowing snow, and lightning.

The field is linearly proportional to the neutrino energy, so thepower (field strength squared) is proportional to the square of theneutrino energy. For an antenna located in the detection medium, thetypical threshold is around 1017 eV; for stand-off (remote sensing)detectors, the threshold rises roughly linearly with the distance.These thresholds can be reduced significantly by using directionalantennas and/or combining the signals from multiple antennas usingbeam-forming techniques. Experiments have used both approachesto reduce trigger-level noise, or to reject background at the analysislevel. Optimally, the threshold will drop linearly with the squareroot of number of antennas, since the signal adds linearly while thebackground is added with random phases.

The signal is linearly polarized in the plane perpendicular to theneutrino direction. This polarization is an important check that anyobserved signal is indeed coherent Cherenkov radiation. Polarizationmeasurements can be used to help reconstruct the neutrino direction.

At energies above 1020 eV, the Landau-Pomeranchuk-Migdal effectsignificant spreads out electromagnetic showers, producing what are


effectively subshowers with significant separation. In this regime, theradio emission becomes even more concentrated around the Cherenkovcone, and then, at higher energies the emission begins to varyevent-by-event. Because of this, many of the experiments that studyhigher energy neutrinos focus on the hadronic shower from the strucknucleus. This contains on average only about 20% of the energy, butwith large fluctuations. It is of interest for very high energy searches(far above 1020 eV) because it is much less subject to the LPM effects.

Radio detectors have observed cosmic-ray air showers in theatmosphere. The physics of radio-wave generation in air showers ismore complex because there is a large contribution due to chargeseparation as electrons and positrons are bent in different directionsas they propagate, leading to a growing charge dipole (transversecurrent) [57]. This time-varying transverse current emits radiation,spread over the transverse size of the shower. Since the radiatingparticles are moving relativistically downward, a ground-basedobserver sees a Lorentz contracted pulse which can have frequencycomponents reaching the GHz range, limited by the thickness of theparticle shower. There is also a contribution from geosynchrotronradiation, as e± are bent in the same field [57]. The Askaryan effectis relatively small compared to these other sources. Experimentsoptimized for ν detection can also detect air showers [58], whichpresents a potential background. Magnetic monopoles would also emitradio waves, and neutrino experiments have also set monpole fluxlimits [59].

35.3.4. The Moon as a target :

Because of its large size and non-conducting regolith, and theavailability of large radio-telescopes, the Moon is an attractivetarget [60]; some of the lunar experiments are listed in Table 35.4.Conventional radio-telescopes are reasonably well suited to lunarneutrino searches, with natural beam widths not too dissimilarfrom the size of the Moon. Still, there are experimental challenges.The composition of the lunar regolith is not well known, and theattenuation length for radio waves must be estimated. The biglimitation of lunar experiments is that the 240,000 km target-antennaseparation leads to neutrino energy thresholds above 1020 eV.

Table 35.4: Experiments that have set limits on neutrinointeractions in the Moon; current limits are shown in Fig. 1 of[50], with Lunaska (2015) from [68].

Experiment Year Dish Size Frequency Bandwidth Obs. Time

Parkes 1995 64 m 1425 MHz 500 MHz 10 hrsGlue 1999+ 70 m, 34 m 2200 MHz 40-150 MHz 120 hrsNuMoon 2008 11×25 m 115–180 MHz — 50 hrsLunaska 2008 3× 22 m 1200–1800 MHz — 6 nightsLunaska 2015 64 1200-1500 MHz 300 MHz 127 hoursResun 2008 4× 25 m 1450 MHz 50 MHz 45 hours

The effective volume probed by experiments depends on thegeometry, which itself depends on the frequency range used. At lowfrequencies, radiation is relatively isotropic, so signals can be detectedfrom most of the Moon’s surface, for most angles of incidence. Also,radio signals penetrate more deeply at low frequencies, so the volumeis larger than at shorter wavelengths. At higher frequencies, theelectric field strength is higher, but radiation is concentrated near theCherenkov angle. So, high-frequency experiments are only sensitivefor a narrow range of geometries where the neutrino interacts nearthe Moon’s limb with the Cherenkov cone pointed toward the Earth.Because of the stronger electric fields at high frequencies, theseexperiments are sensitive to lower energy neutrinos, albeit with asmaller effective volume, which gives them a lower flux sensitivity.

With modern technology, it is increasingly viable to search oververy broad frequency ranges [61]. One technical challenge is dueto dispersion (frequency dependent time delays) in the atmosphere.Dispersion can be largely removed with a de-dispersion filter, usingeither analog circuitry or post-collection digital processing.

Anthropogenic backgrounds are a major concern for ultra-high energy neutrino experiments. Lunar experiments use differenttechniques to reduce this background. Some experiments use multipleantennas, separated by at least hundreds of meters; by requiring acoincidence within a small time window, anthropogenic noise can berejected. If the timing is good enough, beam-forming techniques canbe used to further reduce the background. An alternative approachis to use beam forming with multiple feed antennas viewing a singlereflector, to ensure that the signal points back to the moon.

These efforts have considerable scope for expansion. In the nearfuture, several large radio detector arrays should reach significantlylower limits. The LOFAR array is beginning to take data with 36detector clusters spread over Northwest Europe. In the longer term,the Square Kilometer Array (SKA) with 1 km2 effective area will pushthresholds down to near 1020 eV.

35.3.5. Ice-based detectors :

Lower energy thresholds require a smaller antenna-target separation.Natural ice is an attractive medium for this, with attenuation lengthsover 300 m. The attenuation length varies with the frequency and icetemperature, with higher attenuation in warmer ice. Table 35.3 listssome measurements of radio attenuation.

Although the ice is mostly uniform, the top ≈ 100 m of Antarcticice, the ’firn,’ contains a gradual transition from packed snow at thesurface (typical surface density 0.35 g/cm3) to solid ice (density 0.92g/cm3) below [62]. The index of refraction depends linearly on thedensity, so radio waves curve downward in the firn. This bendingreduces the effectiveness of surface or aerial antennas. The thicknessof the firn varies with location; it is thicker in central Antarcticathan in the coastal ice sheets. For above-ice observations, it is alsonecessary to consider the surface roughness of the ice, which can affectsignals as they transition from the ice to the atmosphere.

There are two types of Antarctic neutrino experiments. In oneclass, antennas mounted on scientific balloons observe the ice fromabove. The ANITA experiment is one example. It made two flightsaround Antarctica, floating at an altitude around 35 km [63]. Its40 (32 in the first flight) dual-polarization horn antennas scannedthe surrounding ice, out to the horizon (650 km away). Because ofthe small angle of incidence, ANITA could make use of polarizationinformation; ν signals should be vertically polarized, while mostbackground from cosmic-ray air showers is expected to be horizontallypolarized.

Because of the significant source-detector separation, ANITA ismost sensitive at energies above 1019 eV, above the peak of the GZKneutrino spectrum. As with the lunar experiments, ANITA had tocontend with anthropogenic backgrounds. The ANITA collaborationuses their multiple antennas as a phased array to achieve good pointingaccuracy, and used that to remove all apparent signals that pointedtoward known or suspected areas of human habitation. By using theseveral-meter separation between antennas, they achieved a pointingaccuracy of 0.2-0.40 in elevation, and 0.5-1.10 in azimuth. ANITA hasset the most stringent limits on GZK neutrinos to date.

The proposed EVA experiment will use a portion of a fixed-shapeballoon as a large parabolic radio antenna. Because of the largeantenna surface, they hope to achieve threshold around 1017 eV.

Other ice based experiments use antennas located within the activevolume, allowing them to reach thresholds around 1017 eV. Thisapproach was pioneered by the RICE experiment, which buried 18half-wave dipole antennas in holes drilled for AMANDA [64] at theSouth Pole, at depths from 100 to 300 m. The hardware was sensitivefrom 200 MHz to 1 GHz. Each antenna fed an in-situ preamplifierwhich transmitted the signals to surface digitizing electronics.

Three groups are prototyping detectors, with the goal of a detectorwith a ∼100 km3 active volume. For all three concepts, the hardwareis modular, so the detector volume scales roughly linearly with theavailable funding. The Askaryan Radio Array (ARA) is located at theSouth Pole [65], while the Antarctic Ross Iceshelf Antenna NeutrinoArray (ARIANNA) is on the Ross Ice Shelf [66]. The GreenlandNeutrino Observatory (GNO) collaboration is proposing a detectornear the U.S. Summit Station in Greenland [67].


All of the in-ice experiments use multiple antennas, with varyingdegrees of connection. ARIANNA and ARA use the timing betweenmultiple antennas in a single station to determine the arrival direction.At larger distance scales, such as between ARA and ARIANNAstations, the relative timing uncertainty is larger, and the antennasare treated as effectively independent, with independent triggers, andthe data is only combined in offline analyses.

One big difference between the experiments is the depth oftheir antennas. ARA buries their antennas up to 200 m deep inthe ice, to avoid the firn. Because of the refraction, a surfaceantenna cannot ‘see’ a signal from a near-surface interaction somedistance away. However, drilling holes has costs, and the limited holediameter (15 cm in ARA) requires compromises between antennadesign (particularly for horizontally polarized waves), mechanicalsupport, power and communications. In contrast, ARIANNA placestheir antennas in shallow, near-surface holes. This greatly simplifiesdeployment and avoids limitations on antenna design, but at a cost ofreduced sensitivity to neutrino interactions near the surface. BecauseARIANNA is at a green-field site, anthropogenic noise is much less ofa problem.

The current ARA proposal, ARA-37 [65], calls for an array of37 stations, each consisting of 16 embedded antennas. ARA willdetect signals from 150 to 850 MHz for vertical polarization, and250 MHz to 850 MHz for horizontal polarization. ARA plans to usebicone antennas for vertical polarization, and quad-slotted cylindersfor horizontal polarization. The collaboration uses notch filters andsurface veto antennas to eliminate most anthropogenic noise, andvetos events when aircraft are in the area, or weather balloons arebeing launched.

ARIANNA is in Moore’s Bay, on the Ross Ice Shelf, where ≈ 575m of ice sits atop the Ross Sea [69]. The site was chosen becausethe ice-seawater interface is smooth there, so the interface acts asa mirror for radio waves. The major advantage of this approachis that ARIANNA is sensitive to downward going neutrinos, andshould be able to see more of the Cherenkov cone for horizontalneutrinos. One disadvantage of the site is that the ice is warmer, sothe radio attenuation length will be shorter. Each ARIANNA stationwill use six or eight log-periodic dipole antennas, pointing downward;two upward-pointing antennas will be used to veto cosmic-ray airshowers and other backgrounds [66]. The multiple antennas allowfor single-station directional and polarization measurements. TheARIANNA site is about 110 km from McMurdo station, and isshielded by Minna Bluff.

All three experiments share some significant challenges. Solarcells provide power during the 6-month summer, but the winter isa challenge. To date, wind power has not worked well, due to acombination of the low temperatures, harsh environment, and limitedwind speed. ARA and GNO can run through the winter, at a cost ofstringing long cables between stations and the base, but ARIANNAwill likely only take data for 7 months/year. Also, because of it’slatitude, GNO could run for a large fraction of the year using solarpower.

35.4. Large time-projection chambers for rare event

detection

Written Nov. 2015 by T. Shutt (SLAC).

Rare event searches require detectors that combine large targetmasses and low levels of radioactivity, and that are located deepunderground to eliminate cosmic-ray related backgrounds. Past andpresent efforts include searches for the scattering of particle darkmatter, neutrinoless double beta decay, and the measurement of solarneutrinos, while next generation experiments will also probe coherentscattering of solar, atmospheric and diffuse supernova backgroundneutrinos. Large time project chambers (TPCs), adapted from particlecollider experiments, have emerged as a leading technology for theseefforts. Events are measured in a central region confined by a fieldcage and usually filled with a liquid noble element target. Ionizedelectrons are drifted (in the z direction) to an anode region by useof electrode grids and field shaping rings, where their magnitude and

x − y location is measured. In low background TPCs, scintillationgenerated at the initial event site is also measured, and the timedifference between this prompt signal and the later-arriving chargesignal gives the event location in z for a known electron drift speed.Thus, 3D imaging is a achieved in a monolithic central volume. Nobleelements have relatively high light yields (comparable to or exceedingthe best inorganic scintillators), and the charge signal can be amplifiedby multiplication or electroluminescence. Radioactive backgrounds aredistinguished by event imaging, the separate measurements of chargeand light, and scintillation pulse shape. For recent reviews of nobleelement detectors, see [70,71].

Methods for achieving very low radioactive backgrounds arediscussed in general in section 34.6. The basic architecture of largeTPCs is very favorable for this application because gas or liquid targetscan be relatively easily purified, while the generally more radioactivereadout and support materials are confined to the periphery. The 3Dimaging of the TPC then allows self shielding in the target material,which is quite powerful when the target is large compared to meanscattering lengths of ∼ MeV neutrons and gammas from radioactivity(∼ 10 cm in LXe, for example). The use of higher density targets(i.e., liquid instead of gas and/or higher mass elements) maximizesthe ratio of target to surrounding material mass. The TPC geometryallows highly hermetic external shielding, with recent experimentsusing large water shields, in some cases enhanced with an active liquidscintillator layer.

In noble element targets, all non-noble impurities are readilyremoved (e.g., by chemical reaction in a commercial getter) so thatonly radioactive noble isotopes are a significant background concern.Xe, Ne and He have have no long lived radioactive isotopes (apartfrom the 136Xe, discussed below). Kr has ∼ 1 MBq/kg of the betaemitter 85Kr created by nuclear fuel reprocessing, making it unusableas a target, while the 1 Bq/kg level of the beta emitter 39Ar is anuisance for Ar-based experiments. Both of these can be backgroundsin other target materials, as can Rn emanating from detectorcomponents. Relatively low background materials are available formost of the structures surrounding the central target, with theexception of radioactive glasses and ceramics usually present in PMTs,feedthroughs and electrical components. Very low background PMTswith synthetic quartz windows, developed over the last decade, havebeen a key enabling technology for dark matter searches. Theseare not yet low enough in background for some double beta decaysearches, which use radio-clean Si-based photon detectors.

An important technical challenge in liquid detectors is achievingthe high voltages needed for electron drift and measurement. Quenchgases which stabilize charge gain and speed electron transport in wirechambers cannot be used, since these absorb scintillation light (andalso suppress charge extraction in dual-phase detectors, discussedbelow). At low energies (e.g., in a dark matter search) it is alsoimportant to suppress low-level emission of electrons and associatedphotons. Drift of electrons over meter scales with minimal loss fromattachment on trace levels of dissolved impurities (e.g., O2) has sofar required continuous circulating purification. The relatively slowreadout due to ∼ msec/m drift speeds is not a major pile-up concernin low background experiments.

35.4.1. Dark matter and other low energy signals :

A major goal of low background experiments is detection of WIMP(Weakly Interacting Massive Particle) dark matter through scatteringon nuclei in a terrestrial detector (for a recent review, see [72]) .Energy transfers are generally small, a few tens of keV at most. Liquidnoble TPCs distinguish nuclear recoils (NR) from dark matter fromthe usually dominant background of electron recoils (ER) from gammarays and beta decays by requiring single scatters and based on theircharge to light ratio or scintillation pulse shape, as described below.Neutrons are a NR background, but can be recognized in a largeimaging TPC if they multiply scatter. To detect small charge signals,a dual phase technique is used wherein electrons from interactions inthe liquid target are drifted to the liquid surface and extracted withhigh field (∼ 5 kV/cm) into the gas phase leading to an amplifiedelectroluminescence signal measured by an array of PMTs locatedjust above. (Both charge multiplication and electroluminescence are


possible in liquid, but have seen little use because the signals have verybroad dispersion). This technique readily measures single electronswith ∼ cm x − y resolution. The sides of the chamber are linedwith highly (diffusively) reflective PTFE, and a second PMT arrayis located below the active volume to maximize the sensitivity to theinitial scintillation signal.

The microscopic processes leading to signals in liquid nobles arecomplex. Energy deposited by an event generates pairs of free electronand ions, and also atoms in their lowest excited state. These rapidlyform excimers which de-excite by emitting light. Excimers arise inboth triplet and singlet states which have the same energy but differentdecay times. In an event track, some fraction of electrons recombinewith ions, while the rest escape and are measured. Recombinationleads to further excimer formation and hence more scintillationphotons. Finally, some part of the energy is lost as heat - a smallfraction for ER but a dominant and energy dependent fraction for NR.This complexity distinguishes ER and NR: for the same visible energy,the slower nuclear recoils form a denser track with less charge andmore light than recoiling electrons, and they generate fewer long-livedtriplet state scintillation photons than singlet-state photons. Chargeand light yields depend on drift field, energy, and the initial particle(ER or NR), requiring extensive calibrations. The existing data hasbeen incorporated into the NEST Monte Carlo framework. Typicalyields are several tens of electrons and photons per keV of depositedenergy (with up to 10-15% efficiency for these photons being detected).

The scattering rates of WIMPs are model dependent, but areusually highest for spin-independent scattering which has an A2

dependence, so that experiments to date have used LXe and LArtargets. LXe experiments have had the best WIMP sensitivity for mostWIMP masses for the last decade, including the current world-leadingsensitivity from the 300 kg LUX experiment. Other Xe experimentsinclude XENON10 and XENON100, ZEPLIN III, and PandaX. Nextgeneration experiments under construction include XENON1T with 1ton fiducial mass, and LZ with 5.6 tons fiducial mass. If a dark mattersignal is seen, its spin dependence could be probed with Xe targetsisotopically separated into spin-rich and spin-poor targets.

The reach of LXe TPCs depends critically on the level of ERbackground rejection provided by the ratio of charge to light. Reportedvalues (at 50% NR acceptance) range from 99.6% in LUX to 99.99% inZEPLIN III, which had a very high (4 kV/cm) drift field. While thereis a basic framework [73] for how this improves with light collectionand varies with electric field, a fully predictive understanding is notyet in hand. Pulse shape discrimination is present, but weak at lowenergy. The ∼ 178 nm scintillation light of Xe is just long enough tobe transmitted through high purity synthetic quartz PMTs windows.Kr suppression to the ∼ ppt or better level is needed, and has beenaccomplished via distillation or chromatography.

Two experiments to date have produced dark matter limits usingdual phase Ar TPCs: WARP and DarkSide-50, while ArDM is underdevelopment. A primary attraction of Ar compared to Xe is muchlower raw material costs. However beta decays from 39Ar, producedby cosmic-ray interactions in the atmosphere, give a low energyER background roughly 108 times higher than the fundamental ERbackground from p-p solar neutrinos. Remarkably, however, pulseshape discrimination (PSD) of ER backgrounds is very powerful inLAr for sufficiently high energy, based on the favorably different ratioof populations of the singlet (6 ns lifetime) and triplet (∼ 1.5 µslifetime) states. DarkSide has shown roughly 108 discrimination with≥ 50% WIMP acceptance above 47 keV. They have also extracted“aged” Ar with the 32.9 yr half-life 39 Ar reduced by a factor of 1400,via processing of underground (cosmic ray shielded) gas deposits. Thislowers the energy threshold and allows ton-scale experiments withoutsignificant pile-up. Charge and light discrimination has also beendemonstrated at high energy, but it is less well characterized than inLXe. While the strong PSD in LAr allows relaxed requirements forER backgrounds, U and Th contamination must still be kept verylow because their decay chains create neutrons via (α, n) reactions,particularly in low Z elements such as PMT glass and PTFE.Waveshifter is used (typically TPB) because PMTs are blind to the128 nm scintillation light.

With sufficient control of dissolved Kr and Rn, the ER background

in the next LXe experiments will be the as-yet unmeasured low energyspectrum of solar neutrinos from the main p-p burning reaction. LZ’ssensitivity is about a decade above the“floor” of coherent electronscattering of astrophysical neutrinos, which, absent a directionalmeasurement (see below), are essentially indistinguishable fromWIMPs. A 30-50 ton LXe TPC would approach the practical limit setby this floor for WIMP masses above ∼ 5 GeV if a ∼ 99.98% rejection(at 30% NR acceptance) of p-p solar ν ER backgrounds [74] is achieved,while a ∼ 200 ton LAr detector would achieve similar sensitivity forWIMPs above ∼ 50 GeV. Sensitivity to lower WIMP mass could beobtained by adding Ne to a LXe TPC, or, more speculatively,with asuperfluid He TPC [75] read out with superconducting sensors (similarto the proposed HERON solar neutrino experiment).

Measurement of NR recoil track direction would provide proof ofthe galactic origin of a dark matter signal since the prevailing WIMPdirection varies on a daily basis as the earth spins. This cannot beachieved for the sub-micron tracks in any existing solid or liquidtechnology, but the mm-scale tracks in a low pressure gas (typically,P ∼ 50 Torr) could be imaged with sufficiently dense instrumentation.Directionality can be established with O(102) events by measuringjust the track direction, while, with finer resolution that distinguishesthe diffuse (dense) tail and dense (diffuse) head of NR (ER) tracks,only O(10) events are required. Such imaging requires a high energythreshold, decreasing WIMP sensitivity, but also powerfully rejectingless dense ER background tracks.

A variety of TPC configurations are being pursued to accomplishthis, most with a CF4 target. The longest established effort, DRIFT,avoids diffusion washing out tracks for electron drift distancesgreater than ∼ 20 cm by attaching electrons to CS2, which driftswith vastly reduced diffusion. Other efforts drift electrons directlyand use a variety of techniques for their measurement: DMTPC(electroluminescence + CCDs), MIMAC (MicroMegas), NEWAGE(GEMs), and D3 (Si pixels). WIMP limits have been obtainedby DRIFT, NEWAGE, and DMTPC. A related suggestion is thatthe amount of recombination in a high pressure Xe gas with anelectron-cooling additive could be sensitive to the angle between thetrack and electric field [76], eliminating the need for track imaging.Directional measurements appear to be the only possibility to pushbeyond the floor of coherent neutrino scatters [77], though this wouldrequire very large target mass.

35.4.2. 0νββ Decay :

Another major class of rare event search is neutrinoless doublebeta decay (0νββ). A limited set of nuclei are unstable againstsimultaneous beta decay of two neutrons. Observation of the lepton-number violating neutrinoless version of this decay would establishthat neutrinos are Majorana particles and provide a direct measureof neutrino mass. For a recent review, see [78]. The signal in 0νββdecay is distinctive: the full Q-value energy of the nuclear decayappears as equal energy back-to-back recoil electrons. A large TPCis advantageous for observing this low rate decay for all the reasonsdescribed above. The first detector to observe the standard modelprocess 2 neutrino double beta decay was a gaseous TPC whichimaged the two electrons tracks from 82Se embedded in a foil. Moderndetectors use Xe as the detector medium because it includes the ββisotope 136Xe (Q-value 2458 keV), which, as an inert gas, can also bemore readily enriched from its natural 8.9% abundance than any otherββ isotope. EXO-200, which currently has one of the best searchlimits [79], is a large single-phase LXe TPC with roughly 110 activekg of Xe enriched to 80.7% 136Xe, and a multi-ton successor nEXOhas been proposed which would fully cover the inverted neutrino masshierarchy. These detectors are similar to dark matter TPCs, but, notneeding charge gain, use single phase with charge measured directlyon crossed wire grids. Light readout is done with LAAPDs (EXO-200)and SiPMs (nEXO).

The dominant background is gamma rays originating outside theactive volume. Most of these undergo multiple Compton-scatterswhich are efficiently recognized and rejected through sub-cm positionresolution, though the few percent of gammas at this energy thatphotoabsorb are not. Self shielding of gamma rays is less powerfulthan in dark matter, since in the former case there is some small


probability of penetrating to some depth followed by the modestlysmall probability of photo-absorption. The latter case consists ofthree small probability processes: penetration to some depth, avery low-energy scatter, and the gamma exiting without a secondinteraction. Because of this and the fact that background and thesignal are both electron recoils, the requirements on radioactivity in allthe materials of a ββ TPC are much more stringent than an otherwisesimilar dark matter detector, unless other background rejectiontools are available. Percent-level energy resolution is crucial to avoidbackground from 2νββ decays and gammas including the prominent2615 MeV line from 208Tl in the Th chain. Here the combined chargeand light measurement eliminates the otherwise dominant fluctuationsin recombination which lead to anti-correlated fluctuations in chargeand light. EXO-200 has achieved σ ≈ 1.5% (at 2458 keV), and valuesbelow 1% appear possible.

The NEXT collaboration uses a high pressure gas phase XeTPC with electroluminescent readout of the charge to achieve mmspatial resolution so that the two-electron topology of 0νββ eventscan be distinguished from single electrons from photoabsorption ofbackground gammas. In addition, the low recombination fractionin the gas phase suppresses recombination fluctuations, in principleallowing σ below 0.2% via the charge channel alone. Finally, adefinitive identification of a 0νββ signal would be provided byextraction and tagging of the ionized Ba daughter via atomic physicstechniques [80], either in gas or liquid phases.

35.5. Sub-Kelvin detectors

Written September 2015 by K. Irwin (Stanford and SLAC).

Many particle physics experiments utilize detectors operated attemperatures below 1 K. These include WIMP searches, beta-decayexperiments to measure the absolute mass of the electron neutrino,and searches for neutrinoless-double-beta decay (0νββ) to probe theproperties of Majorana neutrinos. Sub-Kelvin detectors also provideimportant cosmological constraints on particle physics throughsensitive measurement of the cosmic microwave background (CMB).CMB measurements probe the physics of inflation at ∼ 1016 GeV, andthe absolute mass, hierarchy, and number of neutrino species.

Detectors that operate below 1 K benefit from reduced thermalnoise and lower material specific heat and thermal conductivity.At these temperatures, superconducting materials, sensors withhigh responsivity, and cryogenic preamplifiers and multiplexers areavailable. We provide a simple overview of the techniques and theexperiments using sub-K detectors. A useful review of the broadapplication of low-temperature detectors is provided in [81], andthe proceedings of the International Workshop on Low TemperatureDetectors [82] provide an overview of the field.

Sub-Kelvin detectors can be categorized as equilibrium thermaldetectors or non-equilibrium detectors. Equilibrium detectors measurea temperature rise in a material when energy is deposited. Non-equilibrium detectors are based on the measurement of prompt,non-equilibrated signals and on the excitation of materials with anenergy gap.

35.5.1. Equilibrium thermal detectors :

An equilibrium thermal detector consists of a thermometerand absorber with combined heat capacity C coupled to a heatbath through a weak thermal conductance G. The rise time of athermal detector is limited by the internal equilibration time of thethermometer-absorber system and the electrical time constant of thethermometer. The thermal relaxation time over which heat escapes tothe heat bath is τ = C/G. Thermal detectors are often designed sothat an energy input to the absorber is thermalized and equilibratedthrough the absorber and thermometer on timescales shorter thanτ , making the operation particularly simple. An equilibrium thermaldetector can be operated as either a calorimeter, which measures anincident energy deposition E, or as a bolometer, which measures anincident power P .

In a calorimeter, an energy E deposited by a particle interactioncauses a transient change in the temperature ∆T = E/C, where theheat capacity C can be dominated by the phonons in a lattice, the

quasiparticle excitations in a superconductor, or the electronic heatcapacity of a metal. The thermodynamic energy fluctuations in theabsorber and thermometer have variance

∆E2rms = kBT 2C (35.5)

when operated near equilibrium, where ∆Erms is the root-mean-square energy fluctuation, kB is the Boltzmann constant and T is theequilibrium temperature. When a sufficiently sensitive thermometer isused, and the energy is thermalized at frequencies large compared tothe thermal response frequency (fth = 1/2πτ), the signal-to-noise ratiois nonzero at frequencies higher than fth. In this case, detector energyresolution can be somewhat better than ∆Erms [83]. Deviationsfrom the ideal calorimeter model can cause excess noise and positionand energy dependence in the signal shape, leading to degradation inachieved energy resolution.

In a bolometer, a power P deposited by a stream of particlescauses a change in the equilibrium temperature ∆T = P/G. The weakthermal conductance G to the heat bath is usually limited by the flowof heat through a phonon or electron system. The thermodynamicpower fluctuations in the absorber and thermometer have powerspectral density

SP = NEP 2 = 4kBT 2G (35.6)

when operated near equilibrium, where the units of NEP (noiseequivalent power) are W/

√Hz.

The minimization of thermodynamic energy and power fluctuationsis a primary motivation for the use of sub-Kelvin thermal detectors.These low temperatures also enable the use of materials and structureswith extremely low C and G, and the use of superconducting materialsand amplifiers.

When very large absorbers are required (e.g. WIMP dark mattersearches), dielectric crystals with extremely low specific heat areoften used. These materials are operated well below the Debyetemperature TD of a crystal, where the specific heat scales as T 3. Inthis low-temperature limit, the dimensionless phononic heat capacityat fixed volume reduces to

CV

N kB=

12 π4

5

(

T

TD

)3

, (35.7)

where N is the number of atoms in the crystal. Normal metals havehigher low-temperature specific heat than dielectric crystals, but theyalso have superior thermalization properties, making them attractivefor some applications in which extreme precision and high energyresolution are required (e.g. beta endpoint experiments to measureneutrino mass using 163Ho). At low temperature, the heat capacity ofnormal metals is dominated by electrons, and is linear in temperature,with convenient form

C =ρ

AγV T, (35.8)

where V is the sample volume, γ is the molar specific heat ofthe material, ρ is the mass density, and A is the atomic weight.Superconducting absorbers are also used. Superconductors combinesome of the thermalization advantages of normal metals with the lowerspecific heats associated with insulators when operated well belowTc, where the electronic heat capacity freezes out, and the materialis dominated by phononic heat capacity. At higher temperatures,superconducting materials have more complicated heat capacities,but at their transition temperature Tc, BCS theory predicts that theelectronic heat capacity of a superconductor is ∼2.43 times the normalmetal value.

When very low thermal conductances are required for powermeasurement (e.g. the measurement of the cosmic microwavebackground), the weak thermal link is sometimes provided bythin membranes of non-stoichiometric silicon nitride. The thermalconductance of these membranes is:

G = 4σAT 3ξ, (35.9)

where σ has a value of 15.7 mW/cm2K4, A is the cross-sectional areaperpendicular to the heat flow, and ξ is a numerical factor with a


Table 35.5: Some selected experiments using sub-Kelvin equilibrium bolometers tomeasure the CMB. These experiments constrain the physics of inflation and the absolutemass, hierarchy, and number of neutrino species. The experiment location determines thepart of the sky that is observed. The size of the aperture determines the angular resolution.The table also indicates the type of sensor used, the number of sensors, the frequencyrange, and the number of frequency bands. The number of sensors and frequency rangeand bands for ongoing upgrades are provided for some experiments in parentheses.

Sub-K CMB Location Aperture Sensor # Sensors Frequency Bands

Experiment type (planned) (planned) (planned)

Ground-based

Atacama Cosmology Chile 6 m TES 1,800 90–150 GHz 2Telescope (2007–) (5,334) (28–220 GHz) (5)

BICEP/Keck (2006–) South Pole 26/68 cm TES 3,200 95–220 GHz 3

CLASS Chile 60 cm TES 36 40 GHz 1(2015–) (5,108) (40–220 GHz) (4)

POLARBEAR / Chile 3.5 m TES 1,274 150 GHz 1Simons (2012–) (22,764) (90–220 GHz) (3)

South Pole South 10 m TES 1,536 95–150 GHz 2Telescope (2007–) Pole (16,260) (95–220 GHz) (3)

Balloon

EBEX (2013–) McMurdo 1.5 m TES ∼1,000 150–410 GHz 3

PIPER (2016–) New Mexico 2 m TES 5,120 200–600 GHz 4

SPIDER (2014–) McMurdo 30 cm TES 1,959 90–280 GHz 3

Satellite

Planck HFI (2003–) L2 1.5 m NTD 52 100-857 GHz 9

value of one in the case of specular surface scattering but less thanone for diffuse surface scattering. The thermal impedance between theelectron and phonon systems can also limit the thermal conductance.

The most commonly used sub-Kelvin thermometer is the super-conducting transition-edge sensor (TES) [84]. The TES consists of asuperconductor biased at the transition temperature Tc, in the regionbetween the superconducting and normal state, where its resistanceis a strong function of temperature. The TES is voltage biased.The Joule power provides strong negative electrothermal feedback,which improves linearity, speeds up response to faster than τ = C/G,and provides tolerance for Tc variation between multiple TESs ina large array. The current flowing through a TES is read out bya superconducting quantum interference device (SQUID) amplifier.These amplifiers can be cryogenically multiplexed, allowing a largenumber of TES devices to be read out with a small number of wiresto room temperature.

Neutron-transmutation-doped (NTD) germanium and implantedsilicon semiconductors read out by cryogenic FET amplifiersare also used as thermometers [83]. Their electrical resistance isexponentially dependent on 1/T , and is determined by phonon-assistedhopping conduction between impurity sites. Finally, the temperaturedependence of the permeability of a paramagnetic material is used asa thermometer. Detectors using these thermometers are referred to asmetallic magnetic calorimeters (MMC) [85]. These detectors operatewithout dissipation and are inductively readout by SQUIDs.

Equilibrium thermal detectors are simple, and they have importantadvantages in precision measurements because of their insensitivityto statistical variations in energy down-conversion pathways, aslong as the incident energy equilibrates into an equilibrium thermaldistribution that can be measured by a thermometer.

35.5.2. Nonequilibrium Detectors :

Nonequilibrium detectors use many of the same principles andtechniques as equilibrium detectors, but are also sensitive to detailsof the energy down-conversion before thermalization. Sub-Kelvinnonequilibrium detectors measure athermal phonon signals in adielectric crystal, electron-hole pairs in a semiconductor crystal,athermal quasiparticle excitations in a superconductor, photonemission from a scintillator, or a combination of two of the aboveto better discriminate recoils from nuclei or electrons. Because thephonons are athermal, sub-Kelvin nonequilibrium detectors can useabsorbers with larger heat capacity, and they use information aboutthe details of energy down-conversion pathways in order to betterdiscriminate signal from background.

In WIMP and neutrino experiments using sub-Kelvin dielectricsemiconductors, the recoil energy is typically & 0.1 keV. The majorityof the energy is deposited in phonons and a minority in ionization and,in some cases, scintillation. The semiconductor bandgap is typically∼ eV, and kBT < 10 µeV at T < 1 K. Thus, high-energy chargepairs and athermal phonons are initially produced. The charge pairscascade quickly to the gap edge. The high-energy phonons experienceisotopic scattering and anharmonic decay, which downshifts thephonon spectrum until the phonon mean free path approaches thecharacteristic dimension of the absorber. If the crystal is sufficientlypure, these phonons propagate ballistically, preserving informationabout the interaction location. They are not thermalized, and thusnot affected by an increase in the crystal heat capacity, allowingthe use of larger absorbers. Sensors similar to those used in sub-Kequilibrium thermal detectors measure the athermal phonons at thecrystal surface.

Superconductors can also be used as absorbers in sub-Kelvindetectors when T ≪ Tc. The superconducting gap is typically∼ meV. Energy absorption breaks Cooper pairs and producesquasiparticles. These particles cascade to the superconducting gapedge, and then recombine after a material-dependent lifetime. Duringthe quasiparticle lifetime, they diffuse through the material. Insuperconductors with large mean free path, the diffusion length canbe more than 1 mm, allowing diffusion to a detector.

In some experiments (e.g. SuperCDMS and CRESST), athermal


Table 35.6: Selected experiments using sub-Kelvin calorimeters. The table shows onlycurrently operated experiments, and is not exhaustive. WIMP experiments searchfor dark matter, and beta-decay and neutrinoless double beta decay (0νββ) exper-iments constrain neutrino mass, hierarchy, and Majorana nature. The experimentlocation determines the characteristics of the radioactive background. The dates ofcurrent program phase, detection mode (equilibrium or nonequilibrium phonon mea-surements, and measurement of ionization or scintillation signals), the absorber andtotal mass, the sensor type, and the number of sensors and crystals (if different)are given. Many sub-K calorimeter experiments are also in planning and constructionphases, including EURECA (dark matter), HOLMES and NuMECs (beta decay),and CUPID-0 (0νββ decay). Many of the existing experiments are being upgradedto larger mass absorbers, different absorber materials, or lower energy threshhold.

Sub-K Location Detection Absorber Sensor # Sensor

Calorimeter mode Total mass type # Crystal

WIMP

CRESST II Gran Sasso Noneq. phon. CaWO4 TES 18(2003–) Italy and scint. 5.4 kg

EDELWEISS III LSM Modane Eq. thermal Ge NTD Ge 36(2015–) France and ion. 22 kg +HEMT

SuperCDMS Soudan, USA Noneq. phon. Ge TES 120(2012–) SNOLAB, Canada and ion. 9 kg +JFET 15

Beta decay

ECHo Heidelberg Eq. thermal Au:163Ho MMC 16(2012–) Germany 0.2µg

0νββ decay

CUORE Gran Sasso Eq. thermal TeO2 NTD Ge 988(2015–) Italy 741 kg

AMoRe Pilot Yang Yang Noneq. phon. CaMoO4 MMC 5(2015–) S. Korea and scint. 1.5 kg

LUCIFER Gran Sasso Eq. thermal ZnSe NTD Ge 1(2010–) Italy and scint. 431 g

phonons and quasiparticle diffusion are combined to increase achievableabsorber mass. Athermal phonons in a three-dimensional dielectriccrystal break Cooper pairs in a two-dimensional superconducting filmon the detector surface. The resulting quasiparticles diffuse to thermalsensors (typically a TES) where they are absorbed and detected.While thin superconducting films have diffusion lengths shorter thanthe diffusion lengths in single crystal superconductors, segmenting thefilms into small sections and coupling them to multiple TES sensorsallows the instrumentation of large absorber volume. The TES sensorscan be wired in parallel to combine their output signal.

The combined measurement of the phonon signal and a secondarysignal (ionization or scintillation) can provide a powerful discriminationof signal from background events. Nuclear-recoil events in WIMPsearches produce proportionally smaller ionization or scintillationsignal than electron-scattering events. Since many of the backgroundevents are electron recoils, this discrimination provides a powerfulveto. Similarly, beta-decay events produce proportionally smallerscintillation signal than alpha-particle events, allowing rejection ofalpha backgrounds in neutrino experiments.

Combined phonon and ionization measurement has been imple-mented in experiments including CDMS I/II, SuperCDMS, andEDELWEISS I/II/III. These experiments use semiconductor crystalabsorbers, in which dark-matter scattering events would producerecoiling particles and generate electron-hole pairs and phonons. Theelectron-hole pairs are separated and drifted to the surface of thecrystal by applying an electric field, where they are measured by aJFET or HEMT using similar techniques to those used in 77 K Gex-ray spectrometers. However, the field strength must be much lowerin sub-K detectors to limit the generation of phonon signals by theNeganov-Luke effect, which can confuse the background discrimina-tion. For detectors with very low threshhold, the Neganov-Luke effectcan also be used to detect generated charge through the inducedphonon signal.

Combined phonon and scintillation measurement has beenimplemented in CRESST II, ROSEBUD, AMoRE and LUCIFER. Forexample, the CRESST-II experiment uses CaWO4 crystal absorbers,and measures both the phonon signal and the scintillation signal withTES calorimeters. A wide variety of scintillating crystals are underconsideration, including different tungstates and molybdates, BaF2,ZnSe, and bismuth germanate (BGO).

35.6. Low-radioactivity background techniques

Revised August 2015 by A. Piepke (University of Alabama).

The physics reach of low-energy rare-event searches e.g. for darkmatter, neutrino oscillations, or double beta decay is often limitedby background caused by radioactivity. Depending on the chosendetector design, the separation of the physics signal from thisunwanted interference can be achieved on an event-by-event basisby active event tagging, utilizing some unique event features, orby reducing the flux of the background radiation by appropriateshielding and material selection. In both cases, the background rate isproportional to the flux of the interfering radiation. Its reduction isthus essential for realizing the full physics potential of the experiment.In this context, “low energy” may be defined as the regime of natural,anthropogenic, or cosmogenic radioactivity, all at energies up to about10 MeV. See [86,87] for in-depth reviews of this subject. Following theclassification of [86], sources of background may be categorized intothe following classes:

1. environmental radioactivity,

2. radio-impurities in detector or shielding components,

3. radon and its progeny,

4. cosmic rays,

5. neutrons from natural fission, (α, n) reactions and from cosmic-raymuon spallation and capture.


35.6.1. Defining the problem : The application defines therequirements. Background goals can be as demanding as a fewlow-energy events per year in a ton-size detector. The strength ofthe physics signal of interest can often be estimated theoretically orfrom limits derived by earlier experiments. The experiments are thendesigned for the desired signal-to-background ratio. This requiresfinding the right balance between “clarity of measurement”, ease ofconstruction, and budget. In a practical sense, it is important toformulate background goals that are sufficient for the task at handbut achievable, in a finite time. It is standard practice to use detectorsimulations to translate the background requirements into limits forthe radioactivity content of various detector components, requirementsfor radiation shielding, and allowable cosmic-ray fluxes. This strategyallows the identification of the most critical components early andfacilitates the allocation of analysis and development resources ina rational way. The CERN code GEANT4 [88] is a widely usedtool for this purpose. It has incorporated sufficient nuclear physicsto allow accurate background estimations. Custom-written eventgenerators, modeling e.g., particle correlations in complex decayschemes, deviations from allowed beta spectra or γ − γ-angularcorrelations, are used as well.

35.6.2. Environmental radioactivity : The long-lived naturalradio-nuclides 40K, 232Th, and 238U have average abundances of1.6, 11.1 and 2.7 ppm (corresponding to 412, 45 and 33 Bq/kg,respectively) in the earth’s crust, with large local variations. Inmost applications, γ radiation emitted due to the decay of naturalradioactivity and its unstable daughters constitutes the dominantcontribution to the local radiation field. Typical low-backgroundapplications require levels of natural radioactivity on the order of ppbor ppt in the detector components. Passive or active shielding is usedto suppress external γ radiation down to an equivalent level. Fig. 35.9shows the energy-dependent attenuation length λ(Eγ) as a function ofγ-ray energy Eγ for three common shielding materials (water, copper,lead). The thickness ℓ required to reduce the external flux by a factorf > 1 is estimated, assuming exponential damping:

ℓ = λ(Eγ) · ln f . (35.10)

At 100 keV, a typical energy scale for dark matter searches (or2.615 MeV, for a typical double-beta decay experiment), attenuationby a factor f = 105 requires 67(269) cm of H2O, 2.8(34) cm of Cu,or 0.18(23) cm of Pb. Such estimates allow for an order-of-magnitudedetermination of the experiment dimensions.

Water

Copper

Lead

Att

enua

tion

len

gth

(cm

)

0.1

0.01

10−3

10−4

10−5

100.0

10.0

1.0

10−110−3 0.01 1.0 10.0 100.0Gamma energy (MeV)

Figure 35.9: γ-ray attenuation lengths in some commonshielding materials. The mass attenuation data has beentaken from the NIST data base XCOM; see “Atomic NuclearProperties” at pdg.lbl.gov.

A precise estimation of the the magnitude of the external gamma-ray background, including scattering and the effect of analysis-energycuts, requires Monte Carlo simulations based on the the knowledge

of the radioactivity present in the laboratory. Detailed modeling ofthe γ-ray flux in a large laboratory, or inside the hermetic shielding,needs to cope with a very small probability of generating any signalin the detector. It is often advantageous to calculate solid angle ofthe detector to the background sources and mass attenuation of theradiation shield separately, or to employ importance sampling. Theformer method can lead to loss of energy-direction correlations whilein the latter has to balance CPU-time consumption against the lossof statistical independence. These approaches reduce the computationtime required for a statistically meaningful number of detector hits tomanageable levels.

Water is commonly used as shielding medium for large detectors,as it can be obtained cheaply and purified effectively in large quantity.Water purification technology is commercially available. Ultra-purewater, instrumented with photomultiplier tubes, can serve as activecosmic-ray veto counter. Water is also an effective neutron moderatorand shield. In more recent underground experiments that involvedetectors operating at cryogenic temperature, liquefied gases (e.g.argon) are being used for shielding as well.

35.6.3. Radioactive impurities in detector and shielding com-

ponents : After suppressing the effect of external radioactivity,radioactive impurities, contained in the detector components orattached to their surfaces, become important. Every material containsradioactivity at some level. The activity can be natural, cosmogenic,man-made, or a combination of them. The determination of theactivity content of a specific material or component requires case-by-case analyses, and is rarely obtainable from the manufacturer.However, there are some general rules that can be used to guidethe pre-selection. For detectors designed to look for electrons (forexample in double-beta decay searches or neutrino detection viainverse beta decay or elastic scattering), intrinsic radioactivity is oftenthe principal source of background. For devices detecting nuclearrecoils (for example in dark matter searches), this is often of secondaryimportance as ionization signals can be actively discriminated onan event-by-event basis. Decay induced nuclear reactions become aconcern.

For natural radioactivity, a rule of thumb is that syntheticsubstances are cleaner than natural materials. Typically, more highlyprocessed materials have lower activity content than raw substances.Substances with high electro-negativity tend to be cleaner as therefining process preferentially removes K, Th, and U. For example, Alis often found to contain considerable amounts of Th and U, whileelectrolytic Cu is very low in primordial activities. Plastics or liquidhydrocarbons, having been refined by distillation, are often quiteradiopure. Tabulated radioassay results for a wide range of materialscan be found in Refs. [89] and [90]. Radioassay results from previousunderground physics experiments are being archived at an onlinedatabase [91].

The long-lived 238U daughter 210Pb (T1/2=22.3 y) is found in allshielding lead, and is a background concern at low energies. This isdue to the relatively high endpoint energy (Qβ=1.162 MeV) of its

beta-unstable daughter 210Bi. Lead refined from selected low-U oreshave specific activities of about 5–30 Bq/kg. For applications thatrequire lower specific activity, ancient lead (for example from Romanships) is sometimes used. Because the ore processing and lead refiningremoved most of the 238U, the 210Pb decayed during the long waitingtime to the level supported by the U-content of the refined lead.Lining the lead with copper to range out the low-energy radiation isanother remedy. However, intermediate-Z materials carry additionalcosmogenic-activation risks when handled above ground, as will bediscussed below. 210Pb is also found in solders.

Man-made radioactivity, released during above-ground nucleartesting and nuclear power production, is a source of background.The fission product 137Cs can often be found attached to the surfaceof materials. The radioactive noble gas 85Kr, released into theatmosphere by nuclear reactors and nuclear fuel re-processing, issometimes a background concern, especially due to its high solubilityin organic materials. Post-World War II steel typically contains a fewtens of mBq/kg of 60Co.

Surface activity is not a material property per se but is added


during manufacturing and handling. Surface contamination can oftenbe effectively removed by clean machining, etching, or a combinationof both. The assembly of low-background detectors is often performedin controlled enclosures (e.g. clean rooms or glove boxes) to avoidcontaminating surfaces with environmental substances, such as dust,containing radioactivity at much higher concentrations than thedetector components. Surfaces are cleaned with high purity chemicalsand de-ionized water. When not being processed components arebest stored in sealed bags to limit dust deposition on the surface,even inside clean rooms. Surface contamination can be quantifiedby means of wipe-testing with acid or alcohol wetted Whatman 41filters. Pre-soaking of the filters in clean acid reduces the amount ofTh and U contained in the paper and boosts analysis sensitivity. Thepaper filters are ashed after wiping and the residue is digested inacid. Subsequent analysis by means of mass spectroscopy or neutronactivation analysis is capable of detecting less than 1 pg/cm2 of Thand U.

The most demanding low-rate experiments require screening of allcomponents, which can be a time consuming task. The requirementsfor activity characterization depend on the experiment and the locationand amount of a particular component. Monte Carlo simulations areused to quantify these requirements. Sensitivities of the orderµBq/kg or less are sometimes required for the most critical detectorcomponents. At such a level of sensitivity, the characterizationbecomes a challenging problem in itself. Low-background α, β, andγ-ray counting, mass spectroscopy, and neutron activation analysis arethe commonly used diagnostic techniques.

35.6.4. Radon and its progeny : The noble gas 222Rn, a pureα-emitter, is a 238U decay product. Due to its relatively long half-lifeof 3.8 d it is released by surface soil and is found in the atmosphereeverywhere. 220Rn (232Th decay product) is mostly unimportant formost low-background experiments because of its short half-life. The222Rn activity in air ranges from 10 to 100 mBq/L outdoors and 100to thousands of mBq/L indoors. The natural radon concentrationdepends on the weather and shows daily and seasonal variations.Radon levels are lowest above the oceans. For electron detectors, itis not the Rn itself that creates background, but its progeny 214Pb,214Bi, 210Bi, which emit energetic beta and γ radiation. Thus, notonly the detector itself has to be separated from contact with air, butalso internal voids in the shield which contain air can be a backgroundconcern. Radon is quite soluble in water and even more so in organicsolvents. For large liquid scintillation detectors, radon mobility dueto convection and diffusion is a concern. To define a scale: typicaldouble-beta-decay searches are are restricted to < µBq/kgdetector(or 1 decay per kgdetector and per 11.6 days) activities of 222Rn inthe active medium. This corresponds to a steady-state population of0.5 atoms/kgdetector or 50 µL/kgdetector of air (assuming 20 mBq/Lof radon in the air). The demand on leak tightness can thus be quitedemanding. The decay of Rn itself is a concern for some recoil typedetectors, as nuclear recoil energies in α decays are substantial (76keV in the case of 222Rn).

Low-background detectors are often kept sealed from the air andcontinuously flushed with boil-off nitrogen, which contains only smallamounts of Rn. For the most demanding applications, the nitrogen ispurified by multiple distillations, or by using pressure swing adsorptionchromatography. Then only the Rn outgassing of the piping (due toits intrinsic U content) determines the radon concentration. Radondiffuses readily through thin plastic barriers. If the detector is to beisolated from its environment by means of a membrane, the choice ofmaterial is important [92].

Prolonged exposure of detector components or raw materials toair leads to the accumulation of the long-lived radon daughter 210Pbon surfaces. Due to its low Q-value of 63.5 keV, 210Pb itself isonly a problem when extreme low energy response is important.However, because of its higher Q-value, the lead daughter 210Bi, is aconcern up to the MeV scale. The alpha unstable Bi-daughter 210Po(Eα = 5304 keV) contributes not only to the alpha background butcan also induce the emission of energetic neutrons via (α,n) reactionson low-Z materials (such as F, C, Si...etc). The neutrons, in turn, maycapture on other detector components, creating energetic background.

The (α,n) reaction yield induced by the α decay of 210Po is typicallysmall (6 · 10−6 n/α in Teflon, for example). Some data is available onthe deposition of radon daughters from air onto materials, see e.g. [94].This data indicates effective radon daughter collection distances of aa few cm in air. These considerations limit the allowable air exposuretime. In case raw materials (e.g. in the form of granules) wereexposed to air at the production site, the bulk of the finished detectorcomponents may be loaded with 210Pb and its daughters. These aredifficult to detect as no energetic gamma radiation is emitted in theirdecays. Careful air-exposure management is the only way to reducethis source of background. This can be achieved by storing the partsunder a protective low-radon cover gas or keeping them sealed fromradon.

State-of-the-art detectors can detect radon even at the level offew atoms. Solid state, scintillation, or gas detectors utilize alphaspectroscopy or are exploiting the fast β − α decay sequences of 214Biand 214Po. The efficiency of these devices is sometimes boosted byelectrostatic collection of charged radon from a large gas volume intoa small detector.

35.6.5. Cosmic rays : Cosmic radiation, discussed in detail inChapter 29, is a source of background for just about any non-accelerator experiment. Primary cosmic rays are about 90% protons,9% alpha particles, and the rest heavier nuclei (Fig. 29.1). They aretotally attenuated within the first the first few hg/cm2 of atmosphericthickness. At sea level secondary particles (π± : p : e± : n : µ±) areobserved with relative intensities 1 : 13 : 340 : 480 : 1420 (Ref. 95; alsosee Fig. 29.4).

All but the muon and the neutron components are readily absorbedby overburden such as building ceilings and passive shielding. Only ifthere is very little overburden (<∼10 g/cm2 or so [86]) do pions andprotons need to be considered when estimating the production rate ofcosmogenic radioactivity.

Sensitive experiments are thus operated deep underground whereessentially only muons can penetrate. As shown in Fig. 29.7, themuon intensity falls off rapidly with depth. Active detection systems,capable of tagging events correlated in time with cosmic-ray activity,are needed, depending on the overburden.

The muonic background is related to low-radioactivity techniquesinsofar as photo-nuclear interactions with atomic nuclei can producelong-lived radioactivity directly or indirectly via the creation ofneutrons. This happens at any overburden, however, at strongly depthdependent rates. Muon bremsstrahlung, created in high-Z shieldingmaterials, contributes to the low energy background too. Active muondetection systems are effective in reducing this background, but onlyfor activities with sufficiently short half-lives, allowing vetoing withreasonable detector dead time.

Cosmogenic activation of detector components at the surface canbe an issue for low-background experiments. Proper managementof parts and materials above ground during manufacturing anddetector assembly minimizes the accumulation of long-lived activity.Cosmogenic activation is most important for intermediate-Z materialssuch as Cu and Fe. For the most demanding applications, metals arestored and transported under sufficient shielding to stop the hadroniccomponent of the cosmic rays. Parts can be stored undergroundfor long periods before being used. Underground machine shops aresometimes used to limit the duration of exposure at the surface. Someexperiments are even electro-forming copper underground.

35.6.6. Neutrons : Neutrons contribute to the background of low-energy experiments in different ways: directly through nuclear recoilin the detector medium, and indirectly, through the production ofradio-nuclides, capture γs and inelastic scattering inside the detectorand its components. The indirect mechanisms allow even remotematerials to contribute to the background by means of penetratingγ radiation. Neutrons are thus an important source of low-energybackground. They are produced in different ways:

1. At the earth’s surface the flux of cosmic-ray secondary neutronsis exceeded only by that of muons;

2. Energetic tertiary neutrons are produced by cosmic-ray muons bynuclear spallation in the detector and laboratory walls;


3. In high-Z materials, often used in radiation shields, nuclearcapture of negative muons results in the emission of neutrons;

4. Natural radioactivity has a neutron component through sponta-neous fission and (α, n)-reactions.

A calculation with the hadronic simulation code FLUKA [93], usingthe known energy distribution of secondary neutrons at the earth’ssurface [96], yields a mass attenuation of 1.5 hg/cm2 in concretefor secondary neutrons. In case energy-dependent neutron-capturecross sections are known, such calculations can be used to obtain theproduction rate of particular radio-nuclides.

At an overburden of only few meters water equivalent, neutronproduction by muons becomes the dominant mechanism. Neutronproduction rates are high in high-Z shielding materials. A high-Zradiation shield, discussed earlier as being effective in reducingbackground due to external radioactivity, thus acts as a sourcefor cosmogenic tertiary high-energy neutrons. Depending on theoverburden and the radioactivity content of the laboratory, there isan optimal shielding thickness. Water shields, although bulky, are anattractive alternative due to their low neutron production yield andself-shielding.

Shields made from plastic or water are commonly used to reducethe neutron flux. The shield is sometimes doped with a substancehaving a high thermal neutron capture cross section (such as boron)to absorb thermal neutrons more quickly. The hydrogen, contained inthese shields, serves as a target for elastic scattering, and is effectivein reducing the neutron energy. Neutrons from natural radioactivityhave relatively low energies and can be effectively suppressed by aneutron shield. Ideally, such a neutron shield should be inside the leadto be effective for tertiary neutrons. However, this is rarely done as itincreases the neutron production target (in form of the passive shield),and the costs increase as the cube of the linear dimensions. An activecosmic-ray veto is an effective solution, correlating a neutron with itsparent muon. This solution works best if the veto system is as far awayfrom the detector as feasible (outside the radiation shield) in orderto correlate as many background-producing muons with neutrons aspossible. The vetoed time after a muon hit needs to be sufficiently longto assure muon bremsstrahlung and neutron-induced backgrounds aresufficiently suppressed. An upper limit to the allowable veto periodis given by the veto-induced deadtime, which is related to the muonhit rate on the veto detector. This consideration also constitutes thelimiting factor for the physical size of the veto system (besides thecost). The background caused by neutron-induced radioactivity withlive-times exceeding the veto time cannot be addressed in this way.Moving the detector deep underground, and thus reducing the muonflux, is the only technique that addresses all sources of cosmogenic theneutron background.

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(2004).63. P. Gorham et al. [ANITA Collab.], Phys. Rev. Lett. 103, 051103

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510 36. Radioactivity and radiation protection

36. RADIOACTIVITY AND RADIATION PROTECTION

Revised August 2013 by S. Roesler and M. Silari (CERN).

36.1. Definitions [1,2]

It would be desirable if legal protection limits could be expressed indirectly measurable physical quantities. However, this does not allowto quantify biological effects of the exposure of the human body toionizing radiation.

For this reason, protection limits are expressed in terms of so-calledprotection quantities which, although calculable, are not measurable.Protection quantities quantify the extent of exposure of the humanbody to ionizing radiation from both whole and partial body externalirradiation and from intakes of radionuclides.

In order to demonstrate compliance with dose limits, so-calledoperational quantities are typically used which aim at providingconservative estimates of protection quantities. Often radiationprotection detectors used for individual and area monitoring arecalibrated in terms of operational quantities and, thus, thesequantities become “measurable”.

36.1.1. Physical quantities :

• Fluence, Φ (unit: 1/m2): The fluence is the quotient of dN byda, where dN is the number of particles incident upon a small sphereof cross-sectional area da

Φ = dN/da . (36.1)

In dosimetric calculations, fluence is frequently expressed in termsof the lengths of the particle trajectories. It can be shown that thefluence, Φ, is given by

Φ = dl/dV,

where dl is the sum of the particle trajectory lengths in the volumedV .

• Absorbed dose, D (unit: gray, 1 Gy=1 J/kg=100 rad): Theabsorbed dose is the energy imparted by ionizing radiation in a volumeelement of a specified material divided by the mass of this volumeelement.

• Kerma, K (unit: gray): Kerma is the sum of the initial kineticenergies of all charged particles liberated by indirectly ionizingradiation in a volume element of the specified material divided by themass of this volume element.

• Linear energy transfer, L or LET (unit: J/m, often given inkeV/µm, 1 keV/µm≈ 1.602 × 10−10 J/m): The linear energy transferis the mean energy, dE, lost by a charged particle owing to collisionswith electrons in traversing a distance dl in matter. Low-LETradiation: X rays and gamma rays (accompanied by charged particlesdue to interactions with the surrounding medium) or light chargedparticles such as electrons that produce sparse ionizing events farapart at a molecular scale (L < 10 keV/µm). High-LET radiation:

neutrons and heavy charged particles that produce ionizing eventsdensely spaced at a molecular scale (L > 10 keV/µm).

• Activity, A (unit: becquerel, 1 Bq=1/s=27 pCi): Activity is theexpectation value of the number of nuclear decays occurring in a givenquantity of material per unit time.

36.1.2. Protection quantities :

• Organ absorbed dose, DT (unit: gray): The mean absorbeddose in an organ or tissue T of mass mT is defined as

DT =1

mT

∫

mT

Ddm .

• Equivalent dose, HT (unit: sievert, 1 Sv=100 rem): Theequivalent dose HT in an organ or tissue T is equal to the sumof the absorbed doses DT,R in the organ or tissue caused bydifferent radiation types R weighted with so-called radiation weightingfactors wR:

HT =∑

R

wR × DT,R . (36.2)

Table 36.1: Radiation weighting factors, wR.

Radiation type wR

Photons, electrons and muons 1

Neutrons, En < 1 MeV 2.5 + 18.2 × exp[−(lnEn)2/6]

1 MeV ≤ En ≤ 50 MeV 5.0 + 17.0 × exp[−(ln(2En))2/6]

En > 50 MeV 2.5 + 3.25 × exp[−(ln(0.04En))2/6]

Protons and charged pions 2

Alpha particles, fission

fragments, heavy ions 20

It expresses long-term risks (primarily cancer and leukemia) fromlow-level chronic exposure. The values for wR recommended byICRP [2] are given in Table 36.1.

• Effective dose, E (unit: sievert): The sum of the equivalentdoses, weighted by the tissue weighting factors wT (

∑

T wT = 1) ofseveral organs and tissues T of the body that are considered to bemost sensitive [2], is called “effective dose”:

E =∑

T

wT × HT . (36.3)

36.1.3. Operational quantities :

• Ambient dose equivalent, H∗(10) (unit: sievert): The doseequivalent at a point in a radiation field that would be produced bythe corresponding expanded and aligned field in a 30 cm diametersphere of unit density tissue (ICRU sphere) at a depth of 10 mm onthe radius vector opposing the direction of the aligned field. Ambientdose equivalent is the operational quantity for area monitoring.

• Personal dose equivalent, Hp(d) (unit: sievert): The doseequivalent in ICRU tissue at an appropriate depth, d, below a specifiedpoint on the human body. The specified point is normally taken tobe where the individual dosimeter is worn. For the assessment ofeffective dose, Hp(10) with a depth d = 10 mm is chosen, and forthe assessment of the dose to the skin and to the hands and feet thepersonal dose equivalent, Hp(0.07), with a depth d = 0.07 mm, is used.Personal dose equivalent is the operational quantity for individual

monitoring.

36.1.4. Dose conversion coefficients :

Dose conversion coefficients allow direct calculation of protectionor operational quantities from particle fluence and are functions ofparticle type, energy and irradiation configuration. The most commoncoefficients are those for effective dose and ambient dose equivalent.The former are based on simulations in which the dose to organsof anthropomorphic phantoms is calculated for approximate actualconditions of exposure, such as irradiation of the front of the body(antero-posterior irradiation) or isotropic irradiation.

Conversion coefficients from fluence to effective dose are given foranterior-posterior irradiation and various particles in Fig. 36.1 [3].For example, the effective dose from an anterior-posterior irradiationin a field of 1-MeV neutrons with a fluence of 1 neutron per cm2

is about 290 pSv. In Monte Carlo simulations such coefficients allowmultiplication with fluence at scoring time such that effective dose toa human body at the considered location is directly obtained.

36.2. Radiation levels [4]

• Natural background radiation: On a worldwide average, theannual whole-body dose equivalent due to all sources of naturalbackground radiation ranges from 1.0 to 13 mSv (0.1–1.3 rem) withan annual average of 2.4 mSv [5]. In certain areas values up to50 mSv (5 rem) have been measured. A large fraction (typically morethan 50%) originates from inhaled natural radioactivity, mostly radonand radon daughters. The latter can vary by more than one order ofmagnitude: it is 0.1–0.2 mSv in open areas, 2 mSv on average in ahouse and more than 20 mSv in poorly ventilated mines.

36. Radioactivity and radiation protection 511

110−4 10410−610−810−10 0.01 100Energy (GeV)

104

103

100

10

1

Eff

ectiv

e D

ose

Con

vers

ion

Fact

or (

pSv

cm2 )

Protons

PhotonsNeutrons

Muons

π+

Figure 36.1: Fluence to effective dose conversion coefficientsfor anterior-posterior irradiation and various particles [3].

• Cosmic ray background radiation: At sea level, the whole-body dose equivalent due to cosmic ray background radiation isdominated by muons; at higher altitudes also nucleons contribute.Dose equivalent rates range from less than 0.1 µSv/h at sea level to afew µSv/h at aircraft altitudes. Details on cosmic ray fluence levelsare given in the Cosmic Rays section (Sec. 29 of this Review).

• Fluence to deposit one Gy: Charged particles: The flu-ence necessary to deposit a dose of one Gy (in units ofcm−2) is about 6.24 × 109/(dE/dx), where dE/dx (in units ofMeV g−1 cm2) is the mean energy loss rate that may be obtainedfrom Figs. 33.2 and 33.4 in Sec. 33 of this Review, and fromhttp://pdg.lbl.gov/AtomicNuclearProperties. For example, it isapproximately 3.5 × 109 cm−2 for minimum-ionizing singly-chargedparticles in carbon. Photons: This fluence is about 6.24× 109/(Ef/ℓ)for photons of energy E (in MeV), an attenuation length ℓ (ing cm−2), and a fraction f . 1, expressing the fraction of the photonenergy deposited in a small volume of thickness ≪ ℓ but large enoughto contain the secondary electrons. For example, it is approximately2 × 1011 cm−2 for 1 MeV photons on carbon (f ≈ 1/2).

36.3. Health effects of ionizing radiation

Radiation can cause two types of health effects, deterministic andstochastic:

• Deterministic effects are tissue reactions which cause injury to apopulation of cells if a given threshold of absorbed dose is exceeded.The severity of the reaction increases with dose. The quantity in usefor tissue reactions is the absorbed dose, D. When particles other thanphotons and electrons (low-LET radiation) are involved, a RelativeBiological Effectiveness (RBE)-weighted dose may be used. The RBEof a given radiation is the reciprocal of the ratio of the absorbed doseof that radiation to the absorbed dose of a reference radiation (usuallyX rays) required to produce the same degree of biological effect. It isa complex quantity that depends on many factors such as cell type,dose rate, fractionation, etc.

• Stochastic effects are malignant diseases and heritable effects forwhich the probability of an effect occurring, but not its severity, is afunction of dose without threshold.

• Lethal dose: The whole-body dose from penetrating ionizingradiation resulting in 50% mortality in 30 days (assuming no medicaltreatment) is 2.5–4.5 Gy (250–450 rad)†, as measured internally on thebody longitudinal center line. The surface dose varies due to variablebody attenuation and may be a strong function of energy.

• Cancer induction: The cancer induction probability is about 5%per Sv on average for the entire population [2].

• Recommended effective dose limits: The InternationalCommission on Radiological Protection (ICRP) recommends a limitfor radiation workers of 20 mSv effective dose per year averaged over

† RBE-weighted when necessary

5 years, with the provision that the dose should not exceed 50 mSv inany single year [2]. The limit in the EU-countries and Switzerland is20 mSv per year, in the U.S. it is 50 mSv per year (5 rem per year).Many physics laboratories in the U.S. and elsewhere set lower limits.The effective dose limit for general public is typically 1 mSv per year.

36.4. Prompt neutrons at accelerators

Neutrons dominate the particle environment outside thick shielding(e.g., > 1 m of concrete) for high energy (> a few hundred MeV)electron and hadron accelerators. In addition, for accelerators withenergies above about 10 GeV, muons contribute significantly atsmall angles with regard to the beam, even behind several meters ofshielding. Another special case are synchrotron light sources whereparticular care has to be taken to shield the very intense low-energyphotons extracted from the electron synchrotron into the experimentalareas. Due to its importance at high energy accelerators this sectionfocuses on prompt neutrons.

36.4.1. Electron accelerators :

At electron accelerators, neutrons are generated via photonuclearreactions from bremsstrahlung photons. Neutron production takesplace above a threshold value which varies from 10 to 19 MeV for lightnuclei (with important exceptions, such as 2.23 MeV for deuteriumand 1.67 MeV for beryllium) and from 4 to 6 MeV for heavy nuclei.It is commonly described by different mechanisms depending on thephoton energy: the giant dipole resonance interactions (from thresholdup to about 30 MeV, often the dominant process), the quasi-deuteroneffect (between 30 MeV and a few hundred MeV), the delta resonancemechanism (between 200 MeV and a few GeV) and the vector mesondominance model at higher energies.

The giant dipole resonance reaction consists in a collectiveexcitation of the nucleus, in which neutrons and protons oscillate inthe direction of the photon electric field. The oscillation is dampedby friction in a few cycles, with the photon energy being transferredto the nucleus in a process similar to evaporation. Nucleons emittedin the dipolar interaction have an anisotropic angular distribution,with a maximum at 90

, while those leaving the nucleus as a result

of evaporation are emitted isotropically with a Maxwellian energydistribution described as [6]:

dN

dEn=

En

T 2e−En/T , (36.4)

where T is a nuclear ‘temperature’ (in units of MeV) characteristicof the particular target nucleus and its excitation energy. For heavynuclei the ‘temperature’ generally lies in the range of T = 0.5–1.0MeV. Neutron yields from semi-infinite targets per kW of electronbeam power are plotted in Fig. 36.2 as a function of the electron beamenergy [6].

Typical neutron energy spectra outside of concrete (80 cm thick,2.35 g/cm3) and iron (40 cm thick) shields are shown in Fig. 36.3.In order to compare these spectra to those caused by proton beams(see below) the spectra are scaled by a factor of 100, which roughlycorresponds to the difference in the high energy hadronic cross sectionsfor photons and hadrons (e.g., the fine structure constant). The shapeof these spectra are generally characterized by a low-energy peak ataround 1 MeV (evaporation neutrons) and a high-energy shoulder ataround 70–80 MeV. In case of concrete shielding, the spectrum alsoshows a pronounced peak at thermal neutron energies.

36.4.2. Proton accelerators :

At proton accelerators, neutron yields emitted per incident protonby different target materials are roughly independent of proton energybetween 20 MeV and 1 GeV, and are given by the ratio C : Al : Cu-Fe: Sn : Ta-Pb = 0.3 : 0.6 : 1.0 : 1.5 : 1.7 [9]. Above about 1 GeV, theneutron yield is proportional to Em, where 0.80 ≤ m ≤ 0.85 [10].

Typical neutron energy spectra outside of concrete and ironshielding are shown in Fig. 36.3. Here, the radiation fields are causedby a 25 GeV proton beam interacting with a thick copper target.The comparison of these spectra with those for an electron beam ofthe same energy reflects the difference in the hadronic cross sections


Figure 36.2: Neutron yields from semi-infinite targets per kWof electron beam power, as a function of the electron beamenergy, disregarding target self-shielding [6].

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-12 10-10 10-8 10-6 10-4 10-2 100

E d

Φ/d

E (

cm-2

per

prim

ary)

Energy (GeV)

80cm concrete, electrons x 10080cm concrete, protons

40cm iron, electrons x 10040cm iron, protons

Figure 36.3: Neutron energy spectra calculated with theFLUKA code [7,8] from 25 GeV proton and electron beamson a thick copper target. Spectra are evaluated at 90 to thebeam direction behind 80 cm of concrete or 40 cm of iron. Allspectra are normalized per beam particle. In addition, spectrafor electron beam are multiplied by a factor of 100.

between photons and hadrons above a few 100 MeV. Differencesare increasing towards lower energies because of different interactionmechanisms. Furthermore, the slight shift in energy above about100 MeV follows from the fact that the energies of the interactingphotons are lower than 25 GeV. Apart from this the shapes of the twospectra are similar.

The neutron-attenuation length is shown in Fig. 36.4 for concreteand mono-energetic broad-beam conditions. As can be seen in thefigure it reaches a value of about 117 g/cm2 above 200 MeV. As thecascade through thick shielding is carried by high-energy particlesthis value is equal to the equilibrium attenuation length for particlesemitted at 90 degrees in concrete.

Att

en

uati

on

len

gth

(g c

m−2

)

Neutron Energy (MeV)

Concrete

ρ = 2.4 g cm−3

High energy limit

1 2 5 10 20 50 100 200 500 1000 0

25

50

75

100

125

150

Figure 36.4: The variation of the attenuation length formono-energetic neutrons in concrete as a function of neutronenergy [9].

36.5. Photon sources

The dose equivalent rate in tissue (in mSv/h) from a gamma pointsource emitting one photon of energy E (in MeV) per second at adistance of 1 m is 4.6× 10−9 µen/ρ E, where µen/ρ is the mass energyabsorption coefficient. The latter has a value of 0.029 ± 0.004 cm2/gfor photons in tissue over an energy range between 60 keV and 2 MeV(see Ref. 11 for tabulated values).

Similarly, the dose equivalent rate in tissue (in mSv/h) atthe surface of a semi-infinite slab of uniformly activated materialcontaining 1 Bq/g of a gamma emitter of energy E (in MeV) is2.9 × 10−4 Rµ E, where Rµ is the ratio of the mass energy absorptioncoefficients of the photons in tissue and in the material.

0.1

1

10

100

1000

0.1 1 10 100 1000 10000

dD /

dt

(nS

v / h

)

Cooling Time, tc (h)

Copper, gamma

24Na

44Sc

44mSc

46Sc

48Sc

48V

52Mn

52mMn

54Mn

56Mn

55Co

56Co58Co

57Ni

60Cu

61Cu

12.4 cmmeasurementFLUKA - total

FLUKA - gamma24Na

44Sc, 44mSc, 46Sc, 48Sc48V

52Mn, 52mMn, 54Mn, 56Mn55Co, 56Co, 58Co

57Ni60Cu, 61Cu

Figure 36.5: Contribution of individual gamma-emittingnuclides to the total dose rate at 12.4 cm distance to an activatedcopper sample [12].


0.1

1

10

100

1000

0.1 1 10 100 1000 10000

dD /

dt

(nS

v / h

)

Cooling Time, tc (h)

Copper, beta+

43Sc44Sc

48V

52Mn

55Co

58Co

57Ni

61Cu

62Cu

64Cu45Ti

12.4 cmmeasurementFLUKA - total

FLUKA - beta+43Sc, 44Sc

48V52Mn

55Co, 58Co57Ni

61Cu, 62Cu, 64Cu45Ti

Figure 36.6: Contribution of individual positron-emittingnuclides to the total dose rate at 12.4 cm distance to an activatedcopper sample [12].

36.6. Accelerator-induced radioactivity

Typical medium- and long-lived activation products in metalliccomponents of accelerators are 22Na, 46Sc, 48V, 51Cr, 54Mn, 55Fe,59Fe, 56Co, 57Co, 58Co, 60Co, 63Ni and 65Zn. Gamma-emittingnuclides dominate doses by external irradiation at longer decay times(more than one day) while at short decay times β+ emitters are alsoimportant (through photons produced by β+ annihilation). Due totheir short range, β− emitters are relevant, for example, only fordose to the skin and eyes or for doses due to inhalation or ingestion.Fig. 36.5 and Fig. 36.6 show the contributions of gamma and β+

emitters to the total dose rate at 12.4 cm distance to a coppersample [12]. The sample was activated by the stray radiation fieldcreated by a 120 GeV mixed hadron beam dumped in a coppertarget during about 8 hours at intensities between 107 − 108 hadronsper second. Typically, dose rates at a certain decay time are mainlydetermined by radionuclides having a half-life of the order of thedecay time. Extended irradiation periods might be an exception tothis general rule as in this case the activity of long-lived nuclides canbuild up sufficiently so that it dominates that one of short-lived evenat short cooling times.

Activation in concrete is dominated by 24Na (short decay times)and 22Na (long decay times). Both nuclides can be produced either bylow-energy neutron reactions on the sodium-component in the concreteor by spallation reactions on silicon, calcium and other consituentssuch as aluminum. At long decay times nuclides of radiological interestin activated concrete can also be 60Co, 152Eu, 154Eu and 134Cs, allof which produced by (n,γ)-reactions with traces of natural cobalt,europium and cesium, Thus, such trace elements might be importanteven if their content in concrete is only a few parts per million or lessby weight.

The explicit simulation of radionuclide production with general-purpose Monte Carlo codes has become the most commonly appliedmethod to calculate induced radioactivity and its radiologicalconsequences. Nevertheless, other more approximative approaches,such as “ω-factors” [9], can still be useful for fast order-of-magnitudeestimates. These ω-factors give the dose rate per unit star density(inelastic reactions above a certain energy threshold, e.g. 50 MeV)on contact to an extended, uniformly activated object after a 30-day irradiation and 1-day decay. For steel or iron, ω ≃ 3 × 10−12

(Sv cm3/star). This does not include possible contributions fromthermal-neutron activation.

36.7. Radiation protection instrumentation

The capacity to distinguish and measure the high-LET (mostlyneutrons) and the low-LET components (photons, electrons, muons)of the radiation field at workplaces is of primary importanceto evaluate the exposure of personnel. At proton machines theprompt dose equivalent outside a shield is mainly due to neutrons,with some contribution from photons and, to a minor extent,charged particles. At high-energy electron accelerators the dominantstray radiation during operation consists of high-energy neutrons,because the shielding is normally thick enough to absorb most of thebremsstrahlung photons. Most of the personnel exposure at acceleratorfacilities is often received during maintenance interventions, and isdue to gamma/beta radiation coming from residual radioactivity inaccelerator components.

Radiation detectors used both for radiation surveys and areamonitoring are normally calibrated in ambient dose equivalent H∗(10).

36.7.1. Neutron detectors :

• Rem counters: A rem counter is a portable detector consisting ofa thermal neutron counter embedded in a polyethylene moderator,with a response function that approximately follows the curve ofthe conversion coefficients from neutron fluence to H∗(10) over awide energy range. Conventional rem counters provide a responseto neutrons up to approximately 10-15 MeV, extended-range unitsare heavier as they include a high-Z converter but correctly measureH∗(10) up to several hundred MeV.

• Bonner Sphere Spectrometer (BSS): A BSS is made up ofa thermal neutron detector at the centre of moderating spheres ofdifferent diameters made of polyethylene (PE) or a combination of PEand a high-Z material. Each sphere has a different response functionversus neutron energy, and the neutron energy, at which the sensitivitypeaks, increases with sphere diameter. The energy resolution of thesystem is rather low but satisfactory for radiation protection purposes.The neutron spectrum is obtained by unfolding the experimentalcounts of the BSS with its response matrix by a computer code that isoften based on an iterative algorithm. BSS exist in active (using 3Heor BF3 proportional counters or 6LiI scintillators) and passive versions(using CR-39 track detectors or LiF), for use e.g. in strongly pulsedfields. With 3He counters the discrimination with respect to gammarays and noise is excellent.

• Bubble detectors: A bubble detector is a dosimeter based ona super-heated emulsion (super-heated droplets suspended in a gel)contained in a vial and acting as a continuously sensitive, miniaturebubble chamber. The total number of bubbles evolved from theradiation-induced nucleation of drops gives an integrated measure ofthe total neutron exposure. Various techniques exist to record andcount the bubbles, e.g., visual inspection, automated reading withvideo cameras or acoustic counting. Bubble detectors are insensitiveto low-LET radiation. Super-heated emulsions are used as personal,area and environmental dosimeters, as well as neutron spectrometers.

• Track etched detectors: Track etched detectors (TEDs) are basedon the preferential dissolution of suitable, mostly insulator, materialsalong the damage trails of charged particles of sufficiently high-energydeposition density. The detectors are effectively not sensitive toradiation which deposits the energy through the interactions ofparticles with low LET. These dosimeters are generally able todetermine neutron ambient dose equivalent down to around 100 µSv.They are used both as personal dosimeters and for area monitoring,e.g., in BSS.

36.7.2. Photon detectors :

• GM counters: Geiger Muller (GM) counters are low cost devicesand simple to operate. They work in pulse mode and since they onlycount radiation-induced events, any spectrometric information is lost.In general they are calibrated in terms of air kerma, for instance ina 60Co field. The response of GM counters to photons is constantwithin 15% for energies up to 2 MeV and shows considerable energydependence above.

• Ionization chambers: Ionization chambers are gas-filled detectorsused both as hand-held instruments (e.g., for radiation surveys)


and environmental monitors. They are normally operated in currentmode although pulse-mode operation is also possible. They possess arelatively flat response to a wide range of X- and gamma ray energies(typically from 10 keV to several MeV), can measure radiation overa wide intensity range and are capable of discriminating between thebeta and gamma components of a radiation field (by use of, e.g., abeta window). Pressurized ion chambers (filled, e.g., with Ar or Hgas to several tens of bars) are used for environmental monitoringapplications. They have good sensitivity to neutrons and chargedhadrons in addition to low LET radiation (gammas and muons), withthe response function to the former being strongly non-linear withenergy.

• Scintillators: Scintillation-based detectors are used in radiationprotection as hand-held probes and in fixed installations, e.g., portalmonitors. A scintillation detector or counter is obtained coupling ascintillator to an electronic light sensor such as a photomultiplier tube(PMT), a photodiode or a silicon photomultiplier (SiPM). There is awide range of scintillating materials, inorganic (such as CsI and BGO),organic or plastic; they find application in both photon dosimetry andspectrometry.

36.7.3. Personal dosimeters :

Personal dosimeters, calibrated in Hp(10), are worn by personsexposed to ionizing radiation for professional reasons to record the dosereceived. They are typically passive detectors, either film, track etcheddetectors, 6Li/7Li-based dosimeters (e.g. LiF), optically stimulatedluminescense (OSL) or radiophotoluminescence detectors (RPL) butsemi-active dosimeters using miniaturized ion-chambers also exist.

Electronic personal dosimeters are small active units for on-linemonitoring of individual exposure, designed to be worn on the body.They can give an alarm on both the integral dose received or dose rateonce a pre-set threshold is exceeded.

36.8. Monte Carlo codes for radiation protection

studies

The use of general-purpose particle interaction and transport MonteCarlo codes is often the most accurate and efficient choice for assessingradiation protection quantities at accelerators. Due to the vast spreadof such codes to all areas of particle physics and the associatedextensive benchmarking with experimental data, the modeling hasreached an unprecedented accuracy. Furthermore, most codes allowthe user to simulate all aspects of a high energy particle cascade inone and the same run: from the first interaction of a TeV nucleusover the transport and re-interactions (hadronic and electromagnetic)of the produced secondaries, to detailed nuclear fragmentation, thecalculation of radioactive decays and even of the electromagneticshower caused by the radiation from such decays. A brief account ofthe codes most widely used for radiation protection studies at highenergy accelerators is given in the following.

• FLUKA [7,8]: FLUKA is a general-purpose particle interactionand transport code. It comprises all features needed for radiationprotection, such as detailed hadronic and nuclear interaction modelsup to 10 PeV, full coupling between hadronic and electromagneticprocesses and numerous variance reduction options. The latter includeweight windows, region importance biasing, and leading particle,interaction, and decay length biasing (among others). The capabilitiesof FLUKA are unique for studies of induced radioactivity, especiallywith regard to nuclide production, decay, and transport of residualradiation. In particular, particle cascades by prompt and residualradiation are simulated in parallel based on the microscopic modelsfor nuclide production and a solution of the Bateman equations foractivity build-up and decay.

• GEANT4 [13,14]: GEANT4 is an object-oriented toolkit con-sisting of a kernel that provides the framework for particle transport,including tracking, geometry description, material specifications,management of events and interfaces to external graphics systems.The kernel also provides interfaces to physics processes. It allows theuser to freely select the physics models that best serve the particularapplication needs. Implementations of interaction models exist overan extended range of energies, from optical photons and thermal

neutrons to high-energy interactions required for the simulation ofaccelerator and cosmic ray experiments. To facilitate the use of vari-ance reduction techniques, general-purpose biasing methods such asimportance biasing, weight windows, and a weight cut-off method havebeen introduced directly into the toolkit. Other variance reductionmethods, such as leading particle biasing for hadronic processes, comewith the respective physics packages.

• MARS15 [15,16]: The MARS15 code system is a set of MonteCarlo programs for the simulation of hadronic and electromagneticcascades. It covers a wide energy range: 1 keV to 100 TeV for muons,charged hadrons, heavy ions and electromagnetic showers; and 0.00215eV to 100 TeV for neutrons. Hadronic interactions above 5 GeV canbe simulated with either an inclusive or an exclusive event generator.MARS15 is coupled to the MCNP4C code that handles all interactionsof neutrons with energies below 14 MeV. Different variance reductiontechniques, such as inclusive particle production, weight windows,particle splitting, and Russian roulette, are available in MARS15.A tagging module allows one to tag the origin of a given signalfor source term or sensitivity analyses. Further features of MARS15include a MAD-MARS Beam-Line Builder for a convenient creation ofaccelerator models.

• MCNPX [17,18]: MCNPX originates from the Monte CarloN-Particle transport (MCNP) family of neutron interaction andtransport codes and, therefore, features one of the most comprehensiveand detailed descriptions of the related physical processes. Later it wasextended to other particle types, including ions and electromagneticparticles. The neutron interaction and transport modules use standardevaluated data libraries mixed with physics models where such librariesare not available. The transport is continuous in energy. MCNPXcontains one of the most powerful implementations of variancereduction techniques. Spherical mesh weight windows can be createdby a generator in order to focus the simulation time on certainspatial regions of interest. In addition, a more generalized phase spacebiasing is also possible through energy- and time-dependent weightwindows. Other biasing options include pulse-height tallies withvariance reduction and criticality source convergence acceleration.

• PHITS [19,20]: The Particle and Heavy-Ion Transport code SystemPHITS was among the first general-purpose codes to simulate thetransport and interactions of heavy ions in a wide energy range, from10 MeV/nucleon to 100 GeV/nucleon. It is based on the high-energyhadron transport code NMTC/JAM that was extended to heavy ions.The transport of low-energy neutrons employs cross sections fromevaluated nuclear data libraries such as ENDF and JENDL below 20MeV and LA150 up to 150 MeV. Electromagnetic interactions aresimulated based on the ITS code in the energy range between 1 keVand 1 GeV. Several variance reduction techniques, including weightwindows and region importance biasing, are available in PHITS.

References:

1. International Commission on Radiation Units and Measurements,Fundamental Quantities and Units for Ionizing Radiation, ICRUReport 60 (1998).

2. ICRP Publication 103, The 2007 Recommendations of the

International Commission on Radiological Protection, Annals ofthe ICRP, Elsevier (2007).

3. M. Pelliccioni, Radiation Protection Dosimetry 88, 279 (2000).

4. E. Pochin, Nuclear Radiation: Risks and Benefits, ClarendonPress, Oxford, 1983.

5. United Nations, Report of the United Nations Scientific

Committee on the Effect of Atomic Radiation, General Assembly,Official Records A/63/46 (2008).

6. W.P. Swanson, Radiological Safety Aspects of the Operation of

Electron Linear Accelerators, IAEA Technical Reports SeriesNo. 188 (1979).

7. A. Ferrari, et al., FLUKA, A Multi-particle Transport Code(Program Version 2005), CERN-2005-010 (2005).

8. G. Battistoni, et al., The FLUKA code: Description andbenchmarking, Proceedings of the Hadronic Shower Simulation

Workshop 2006, Fermilab 6–8 September 2006, M. Albrow,R. Raja, eds., AIP Conference Proceeding 896, 31–49, (2007).


9. R.H. Thomas and G.R. Stevenson, Radiological Safety Aspects

of the Operation of Proton Accelerators, IAEA Technical ReportSeries No. 283 (1988).

10. T.A. Gabriel, et al., Nucl. Instrum. Methods A338, 336 (1994).11. http://physics.nist.gov/PhysRefData/XrayMassCoef/

cover.html.12. S. Roesler, et al., “Simulation of Remanent Dose Rates

and Benchmark Measurements at the CERN-EU High EnergyReference Field Facility,” in Proceedings of the Sixth International

Meeting on Nuclear Applications of Accelerator Technology, SanDiego, CA, 1-5 June 2003, 655–662 (2003).

13. S. Agostinelli, et al., Nucl. Instrum. Methods A506, 250 (2003).14. J. Allison, et al., IEEE Transactions on Nuclear Science 53, 270

(2006).

15. N.V. Mokhov, S.I. Striganov, MARS15 Overview Proceedings

of the Hadronic Shower Simulation Workshop 2006, Fermilab6–8 September 2006, M. Albrow, R. Raja, eds., AIP Conference

Proceeding 896, 50–60, (2007).16. N.V. Mokhov, MARS Code System, Version 15 (2009), www-

ap.fnal.gov/MARS.17. D.B. Pelowitz, ed., Los Alamos National Laboratory report,

LA-CP-05-0369 (2005).18. G. McKinney, et al., Proceedings of the International Workshop

on Fast Neutron Detectors University of Cape Town, SouthAfrica (2006).

19. H. Iwase, K. Niita, and T. Nakamura, Journal of Nuclear Scienceand Technology 39, 1142 (2002).

20. K. Niita, et al., Radiation Measurements 41, 1080 (2006).

516 37. Commonly used radioactive sources

37. COMMONLY USED RADIOACTIVE SOURCES

Table 37.1. Revised November 1993 by E. Browne (LBNL).

Particle Photon

Type of Energy Emission Energy EmissionNuclide Half-life decay (MeV) prob. (MeV) prob.2211

Na 2.603 y β+, EC 0.545 90% 0.511 Annih.1.275 100%

5425Mn 0.855 y EC 0.835 100%

Cr K x rays 26%5526

Fe 2.73 y EC Mn K x rays:0.00590 24.4%0.00649 2.86%

5727

Co 0.744 y EC 0.014 9%0.122 86%0.136 11%Fe K x rays 58%

6027

Co 5.271 y β− 0.316 100% 1.173 100%1.333 100%

6832

Ge 0.742 y EC Ga K x rays 44%- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

→ 6831

Ga β+, EC 1.899 90% 0.511 Annih.1.077 3%

9038

Sr 28.5 y β− 0.546 100%- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

→ 9039

Y β− 2.283 100%

10644

Ru 1.020 y β− 0.039 100%- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

→ 10645

Rh β− 3.541 79% 0.512 21%0.622 10%

10948

Cd 1.267 y EC 0.063 e− 41% 0.088 3.6%0.084 e− 45% Ag K x rays 100%0.087 e− 9%

11350

Sn 0.315 y EC 0.364 e− 29% 0.392 65%0.388 e− 6% In K x rays 97%

13755

Cs 30.2 y β− 0.514 94% 0.662 85%1.176 6%

13356

Ba 10.54 y EC 0.045 e− 50% 0.081 34%0.075 e− 6% 0.356 62%

Cs K x rays 121%20783

Bi 31.8 y EC 0.481 e− 2% 0.569 98%0.975 e− 7% 1.063 75%1.047 e− 2% 1.770 7%

Pb K x rays 78%22890

Th 1.912 y 6α: 5.341 to 8.785 0.239 44%3β−: 0.334 to 2.246 0.583 31%

2.614 36%(→224

88Ra → 220

86Rn → 216

84Po → 212

82Pb → 212

83Bi → 212

84Po)

24195

Am 432.7 y α 5.443 13% 0.060 36%5.486 85% Np L x rays 38%

24195

Am/Be 432.2 y 6 × 10−5 neutrons (4–8 MeV) and4 × 10−5γ’s (4.43 MeV) per Am decay

24496

Cm 18.11 y α 5.763 24% Pu L x rays ∼ 9%5.805 76%

25298

Cf 2.645 y α (97%) 6.076 15%6.118 82%

Fission (3.1%)≈ 20 γ’s/fission; 80% < 1 MeV≈ 4 neutrons/fission; 〈En〉 = 2.14 MeV

“Emission probability” is the probability per decay of a given emission;because of cascades these may total more than 100%. Only principalemissions are listed. EC means electron capture, and e− meansmonoenergetic internal conversion (Auger) electron. The intensity of0.511 MeV e+e− annihilation photons depends upon the number ofstopped positrons. Endpoint β± energies are listed. In some caseswhen energies are closely spaced, the γ-ray values are approximateweighted averages. Radiation from short-lived daughter isotopes isincluded where relevant.

Half-lives, energies, and intensities are from E. Browne andR.B. Firestone, Table of Radioactive Isotopes (John Wiley & Sons,New York, 1986), recent Nuclear Data Sheets, and X-ray and

Gamma-ray Standards for Detector Calibration, IAEA-TECDOC-619(1991).

Neutron data are from Neutron Sources for Basic Physics and

Applications (Pergamon Press, 1983).

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