Post on 18-Jan-2016
Ionization Cooling for a ν-Factory or Collider
David Neuffer
Fermilab
7/15/06
2
Outline Cooling Requirements
ν-Factory Collider
Ionization Cooling Cooling description Heating – Longitudinal Cooling Emittance Exchange- Partition Number Helical wiggler-PIC-REMEX
Low-Energy “Cooling” Emittance exchange Li lens Solenoid
Cooling Scenarios
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References A. N. Skrinsky and V.V. Parkhomchuk, Sov. J. Nucl. Physics 12, 3(1981). D. Neuffer, Particle Accelerators 14, 75 (1983) D. Neuffer, “+- Colliders”, CERN report 99-12 (1999). D. Neuffer, “Introduction to Muon Cooling, NIM A532,p. 26 (2004). C. X. Wang and K. J. Kim, “Linear Theory of 6-D Ionization Cooling”, (PRL)
MuCOOL Note 240, April 2002. (also COOL03), NIM A532, p. 260 (2004)
Y. Derbenev and R. Johnson, Phys. Rev. ST Accel. Beams 8, E041002 (2005); COOL05 proc.
Simulation tools R. Fernow, ICOOL http://pubweb.bnl.gov/users/fernow/www/icool/readme.html T. Roberts, G4BeamLine (Muons, Inc.) http://www.muonsinc.com/
ColliderOverview
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Collider ParametersParameter 4TeV(2000) 4TeV low emittance Collision Energy(2E) 4000 4000 GeV Energy per beam(E) 2000 2000 GeV Luminosity(L=f0nsnbN2/42) 1035 1035 cm-2s-1 Source Parameters 3.8 MW 1.0 MW p-beam Proton energy(Ep) 16 8 GeV Protons/pulse(Np) 42.51013 221013 Pulse rate(f0) 15 20 Hz acceptance(/p) 0.2 0.05 -survival (N/Nsource) 0.25 0.2 Collider Parameters Mean radius(R) 1200 1000 m /bunch(N±) 1.251012 21011 Number of bunches(nB) 4 2 Storage turns(2ns) 1500 2000 Norm. emittance(N) 0.610-2 2.510-4 cm-rad Geom.. emittance(t =N/) 310-7 1.310-8 cm-rad Interaction focus o 0.3 0.1 cm IR Beam size =(o)½ 3.1 0.36 m E/E at collisions 0.12 0.2%
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Overview of -Factory Proton Driver (1-4 MW) – proton
bunches on target produce s Front-end: decay +
collect and cool s: (phase rotation + ionization cooling)
Accelerator - to full energy ( linac + RLAs to 20—50 GeV)
- Storage ring Store ’s until decay (~300 B turns)
e + e* decays
produce neutrino beams directed toward:
Long base line neutrino detector (2000—8000 km away …)
1020 to 1021(e, *) /SS/year
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Producing and Capturing Collaboration baseline:
10GeV p-beam on Target (Hg-jet) immersed in 201.75 T solenoid, taking ~300 MeV/c
μ-Collider:Rf: ~200 MHz,Capture string of ~20 bunches-Recombine aftercooling
ν-Factory:Rf: ~200 MHz,12 MV/mCapture in stringOf ~50 bunches
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Cooling Requirements Beam from target has
,rms 2×10-2 m-rad; ║,rms 1m
-Storage Ring -Factory Goal is to collect maximum number of + and/or -
that fit within accelerator / storage ring acceptances
Transverse cooling by ~10 is sufficient ,rms 0.2 to 0.8×10-2m-rad; ║,rms 0.06 m-rad/bunch
Collider Goal is maximal cooling of maximum number of both
+ AND -; high luminosity needed. Cooling by > ~100 in each of x, y, z is required ,rms 0.5 to 0.025×10-4m-rad; ║,rms 0.04 m-rad
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Cooling Summary
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Transverse cooling: Particle loses momentum
P( and ) in material
Particle regains P (only) in RF
Multiple Scattering in material increases rms emittance:
Muon Cooling-general principle
P
s
ds
dP1
P
s
ds
dP1PP xx
zL)cp(
E
22
x
R2
2s2
x
2
N,
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Ionization Cooling Principle
p
s
ds
dp1pp xx
Loss of transverse momentum in absorber:
p
s
ds
dp1N,N,
2
2
2 3 2
2
1
1
2
N
N
ms
s
N r
R
d
ds
dP
P d
d
d s
dE
E ds
E
m c L E
s
Heating bymultiple scattering
Absorber Accelerator
Momentum loss is opposite to motion, p, p x , p y , E decrease
Momentum gain is purely longitudinal
Large emittance
Small emittance
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Combining Cooling and Heating:
Low-Z absorbers (H2, Li, Be, …) to reduce multiple scattering High Gradient RF
To cool before -decay (2.2 s) To keep beam bunched
Strong-Focusing at absorbers To keep multiple scattering less than beam divergence …
Quad focusing ? Li lens focusing ? Solenoid focusing?
ds
d
2ds
dE
E
1
ds
d2
rms
N2N
2 2 2
2 2 2
rms s
R
d z E
ds c p L
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Transverse cooling limits Transverse Cooling –
equilibrium emittance
2
, 22 s
N eq dE
R ds
E
m c L
equilibrium scattering angle
2
2 22 s
dE
R ds
E
m c L
Material Properties for Ionization Cooling
Material Symbol Z, A Density dE/ds (min.) LR LR dE/ds σθ∙βγ½ gxN/ gm/cm3 MeV/cm Cm MeV mm-mrad/cm Hydrogen H2 1, 1 0.071 0.292 865 252.6 0.061 37 Lithium Li 3, 7 0.534 0.848 155 130.8 0.084 71 Lith. H LiH 3+, 7+ 0.9 1.34 102 137 0.0824 68 Beryllium Be 4, 9 1.848 2.98 35.3 105.2 0.094 88 Carbon C 6, 12 2.265 4.032 18.8 75.8 0.110 122 Aluminum Al 13, 27 2.70 4.37 8.9 38.9 0.154 238 Copper Cu 29,63.5 8.96 12.90 1.43 18.45 0.224 503 Tungsten W 74, 184 19.3 22.1 0.35 7.73 0.346 1200
Want materials with small multiple scattering (large LR),but relatively large dE/ds, density ()
Want small at absorbers => strong focusing - equilibrium emittances (/) smallest for low-Z materials
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Ionization Cooling problems Must focus to very small β
β : 1m → ~1mm
Intrinsic scattering of beam is large θrms > ~0.1 radians
Intrinsic momentum spread is large σP/P > ~0.03
Cooling must occur within muon lifetime = 2.2γ s or L = 660 βγ m pathlength
Does not (directly) cool longitudinally
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Longitudinal “Cooling”
Energy cooling occurs if the derivative :
(dE/ds)/E= gL(dp/ds)/p > 0
gL(E) is negative for E < ~ 0.2 GeV
and only weakly positive for
E > ~ 0.2 GeV
Ionization cooling does not
effectively cool longitudinally
2
2
2 2 2e
β
γL 2 2m c β γ 2
I(Z)
(1- )2g = - + 2
γ ln -β
Energy straggling increases energy spread
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2rms 2 2e e e 2
d ΔE= 4π r m c n γ 1-
ds
2 2 22 2 e
A e e 2 2
2m c γ βdE Z 1 δ= 4πN ρr m c ln -1-
ds A β I(Z) 2β
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“Emittance exchange” enables longitudinal cooling:
Cooling derivative is changed by use of dispersion + wedge(Dependence of energy loss on energy can be increased)
00
1 /dE dEds ds
L
dp dsdE gdsE E cp p
-12
L 2 2T
1 (ka) a dpΔg = =
γ 1+ (ka) p da
(if due to path length)
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Partition Numbers, δE-δt cooling
00,LL gg
g
P (MeV/c)
gL
0
-1
With emittance exchange the longitudinal partition number gL changes:
0x 1g
But the transverse cooling partition number decreases:
The sum of the cooling partition numbers(at P = P ) remains constant:
0,LLyxg g2ggg)P(
Σg > 0
2
2
2 2 2e
β
γ2g
2m c β γ 2I(Z)
(1- )Σ = 2β + 2
ln -β
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Cooling + Energy straggling ...
pRFcτ 3 2
s
αλ1β =
β γ eV cosφ 2π mc
Energy spread E cooling equation:
2
1ncmr4E
g2
ds
d 22
e
22ee
2E2
dsdE
L2E
2rmsμ cτL L
Lμ
d ΔEdp βdε g= - ε +
ds p ds 2 ds
Longitudinal Emittance Cooling equation:
Longitudinal Cooling requires:Positive gL (η, “wedge”), Strong bunching (βcτ small)
Large Vrf, small λrf
MeVμ μ MeVmrf
mμ 0
Δp (m βγ) 105.66V » >> = = 0.16
L L βγ 660Energy loss/recovery
Before decay requires:
2βp e 2
2L μ
σ 1-m= ×
p 2g m log[]-β
Equilibrium σp:
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μ Cooling Regimes
Efficient cooling requires:
Frictional Cooling (<1MeV/c) Σg=~3
Ionization Cooling (~0.3GeV/c) Σg=~2
Radiative Cooling (>1TeV/c) Σg=~4
Low-εt cooling Σg=~2β2
(longitudinal heating)
~ 0
dEdx
E
2 2 22 2
2 2
214 ln 1
( ) 2e
A e e
m cdE ZN r m c
ds A I Z
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Focusing for Cooling Strong focussing needed – magnetic quads, solenoids, Li lens ? Solenoids have been used in most (recent) studies
Focus horizontally and vertically Focus both + and -
rB2
Br
2
,equil.
2Bρβ =
B
Strong focussing possible: β = 0.13m for B=10T, p = 200 MeV/c
β = 0.0027m for B=50T, p = 20 MeV/c
But: Solenoid introduces angular motion L damped by cooling + field flips No chromatic correction (yet) B within rf cavities ?
( )
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Solenoidal Focusing and Angular Momentum
Angular motion with focusing complicates cooling Energy loss in absorbers reduces P, including P
Orbits cool to Larmor centers, not r = 0
Solution: Flip magnetic fields; new Larmor center is near r=0
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More complete coupled cooling equations:
( ) / 2s x y
( ) / 2a x y
θD, θW are dispersion, wedge angles
Scattering terms
Wang and Kim, (MuCOOL 240) have developed coupledcooling equations including dispersion, wedges, solenoids,and symmetric focussing (βx = βy = βT)
2 26 D x y xy zL
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Cooling with exchange and solenoids (Wang and Kim)
dsd
x21
LdsdP
21
dsd
xdsdP
xx
2rms
2rms HL
PPg
ds
d
2rms
dP dPy dθds ds1
y Lds 2
dε= - ε +β + β θ L
ds P P
dsd
21
dsd
z21
zdsdP
Lz
2rms
z
22rms
Pg
ds
d
ds
dH)(
PL
P)1(
ds
dL 2rms
LyxLdsdP
21ds
dP
2g
Example: rms Cooling equations with dispersion and wedges (at ==) in x-plane:
The additional correlation and heating terms are “small” in “well-designed” systems.
2
xx
ηH =
β
L
B eBθ = =
2Bρ 2P
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Study 2 Cooling Channel (for MICE)
Cell contains Rf for acceleration/bunching H2 absorbers
Solenoidal magnets
sFOFO 2.75m cells
108 m cooling channel consists of:
16 2.75m cells + 40 1.65m cells
Focusing increases along channel:
Bmax increases from 3 T to 5.5 T
Simulation Results
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Study2 cooling channel Focusing function at absorbers: 0.5m→0.2m
Total length of channel 100+m Cools to ~0.002m
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Study 2A cooling channel Lattice is weak-focusing
Bmax = 2.5T, solenoidal
β ≅ 0.8m
Cools transversely from ~0.018 to ~0.007m
in ~70mBefore After cooling
-0.4m +0.4m
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RFOFO ring cooler performance Example cools longitudinally
more than transversely Can be adjusted for more
transverse cooling
E-ct before and after
Transverse before and after
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RF Problem: cavity gradient in magnetic field is limited?
Vacuum Cavities800 MHz results: 40MV/m→13MV/m
Muons, Inc. results: 50+ MV/m no change with B
Rf breakdown field decreases in magnetic fields? Solenoidal focussing gives large B at cavities But gas in cavity suppresses breakdown
10% of liquid H2
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Helical 6-D Cooler (Derbenev)
Magnetic field is solenoid B0+ dipole + quad + …
System is filled with H2 gas, includes rf cavities
Cools 6-D (large E means longer path length)
Key parameters:a, k=2π/λ, solenoid field B0, transverse field b(a)
2 21 ( ) 1 ( )( ) ( )
ka kap a B b a
k ka
-12
L 2 2T
1 (ka) a dpΔg = =
γ 1+ (ka) p da
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Comments on Helical Wiggler parameters
1/T2 ≅ 0.67 for equal cooling at ∑g=2
Energy loss at liquid H2 density is ~30MV/m (800atm-e gas)
Typical simulations have used ~ 15MV/m energy loss
Need more rf gradient: ~22MV/m (could use less if needed…)
P 200 MeV/c (0.67T-m)
λ 1.0m
a 0.16m
=ka= P/Pz 1
B 5.5T (Bρ/B=0.12m)
b(a) 1.28T (Bρ/b=0.52m)
b'(a) -0.46T/m
D(a)- dispersion 0.29m
Δg =1/T2 0.9
Typical case
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Helical Wiggler 3-D Cooling (Pµ=250MeV/c)
Cooling factor
~ 50,000 ×
Yonehara, et al.
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Helical wiggler R&D Need Magnet design
Solenoid, dipole + quad
Displaced solenoid coils can provide needed field
Matching in/out
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+- Collider Cooling Scenarios +- Collider
requires energy cooling and emittance exchange (and anti-exchange) to obtain small L, εx, εy emittances required for high-luminosity
Start with large beam from target, compress and cool, going to stronger focussing and bunching as the beam gets smaller …
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Updated Scenario (Palmer-5-1-06)
PIC?
Low EmttanceMuon Collider
REMEX?
“Guggenheim” 6D cooler
800 MHz 6D cooler
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Palmer scenario to do: Matching from section to section Buncher/Wiggler – 3D dynamics Reoptimization
Phase rotation buncher is ν-Factory case (not Collider optimum) Tapered Guggenheims
Final cooler Matching in/out Rf match in/out “realistic” field models
Reacceleration scenario from low-emittance Lower frequency rf + buncher
Can PIC/REMEX or … get us to smaller emittance?
PIC-Parametric-resonance Ionization Cooling (JLab, Y. Derbenev) (also Balbekov, 1997)
Excite ½ integer parametric resonance (in Linac or ring)
Similar to vertical rigid pendulum or ½-integer extraction Elliptical phase space motion becomes hyperbolic Use xx’=const to reduce x, increase x' Use Ionization Cooling to reduce x'
Detuning issues being addressed (chromatic and spherical aberrations, space-charge tune spread). Simulations underway.
First:Then:
IC reduces x’
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PIC/REMEX cooling (Derbenev)
PIC ,eff: 0.6cm 0.1cm
Transverse + longitudinal cooling
Reverse emittance exchange to reduce transverse emittance
(“REMEX”)
Chromaticity correction a problem
Depth of focus a problem Labsorber < ~ β
No “realistic” simulations
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PIC/REMEX examples (Bogacz, Beard, Newsham, Derbenev)
Example: Solenoids + quads + dipoles+rf 2m cells β = 1.4cm, ηx= 0.0m
Problems: Large σp/p (~3%)
Large σθ (>0.1)
Short absorber – 1cm Be = 3MeV
Solution approach: Use simulations to
tune this as a resonant beam line
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Cooling scenario (~Muons, Inc.)
40
Low-Energy “Cooling”=REMEX without wedges
At Pμ = 10 to 200 MeV/c, energy loss heats the beam longitudinally
Transverse cooling can occur emittance exchange
Equilibrium transverse emittance decreases dE/ds scales as 1/β2
βt scales as β
– Solenoid βt p/B
εN,rms Pμ2 ???
Decrease εN,transverse while εlong increases
“wedgeless” emittance exchange
εN,rms × 1/30, εlong ×300 ???
g
P (MeV/c)
gL
0
-1
2
2 3 2
1
2N s
NR
d EdE
ds E ds m c L E
2
, 22 s
N eq dEt R ds
E
g m c L
41
Low-Energy “cooling”-emittance exchange
dPμ/ds varies as ~1/β3
“Cooling” distance becomes very short:
for H at Pμ=10MeV/c
Focusing can get quite strong: Solenoid:
β=0.002m at 30T, 10MeV/c
εN,eq= 1.5×10-4 cm at 10MeV/c
Small enough for “low-emittance” collider
116dP
cmP ds
22
0.3
PB
B B
Pµ
Lcool
200MeV/c
10
0.1 cm
2
, 22 s
N eq dEt R ds
E
g m c L
100 cm
11
cool
dPL
P ds
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Emittance exchange: solenoid focusing Solenoid focusing(30T)
0.002m
Momentum (30→10 MeV/c) L ≈ 5cm R < 1cm Liquid Hydrogen (or gas)
2
, 22 s
N eq dEt R ds
E
g m c L
Pµ
Lcool
200MeV/c
10
0.1cm
Use gas H2 if cooling length too short
11
cool
dPL
P dsεN,eq= 1.5×10-4 cm at 10MeV/c
-Will need rf to change p to z
43
Li-lens cooling Lithium Lens provides strong-
focusing and low-Z absorber in same device
Liquid Li-lens may be needed for highest-field, high rep. rate lens
BINP (Silvestrov) was testing prototype liquid Li lens for FNAL
But FNAL support was stopped - and prototypes were not successful ...
-Cooling Li lens parameters B(T) B (T/m) radius(cm) Length(m) I (MA) (=0.7r)
10 1000 1 1 0.50 0.25ms
15 3000 0.5 1 0.375 64s 20 8000 0.25 1 0.25 16s
0.3
PB
B B
β =0.026m (200 MeV/c, 1000 T/m)β =0.004m (40 MeV/c, 8000 T/m)
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Summary Cooling for neutrino factory is practical Collider cooling scenario needs considerable
development: Longitudinal cooling by large factors … Transverse cooling by very large factors Final beam compression with reverse emittance
exchange Reacceleration and bunching from low energy
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Linac-area MuCool Test Area
Test area for bench test and beam-test of Liquid H2 absorbers
Enclosure complete in ~October 2003 Can test 200 and 805 MHz rf for MuCOOL and
also for Fermilab Assemble and beam test cooling modules
(absorber + rf cavity + solenoid)
46
MTA experimental program Rf: 805, 201 MHz, gas-filled
201MHz just reached 16 MV/m 805 MHz 3T, gas-cavity test
H2 absorbers
47
MICE beam line (Drumm, ISS)
MICE (International Muon Ionization Cooling Experiment) To verify ionization cooling (for a neutrino factory)
with a test of a complete cooling module in a muon beam Muon beam line and test area in RAL-ISIS (Oxford)
Installation Jan. – Oct. 1 2007 Experiment occurs in ~2007-2009 time frame
MICE beam line and experimental area (RAL)
T Target Sheffield
A Pion Capture ISIS
B Decay Solenoid EID
C Muon Transport Channel
Liverpool?
D Diffuser Oxford
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Incoming muon beam
Diffusers 1&2
Beam PIDTOF 0
CherenkovTOF 1
Trackers 1 & 2 measurement of emittance in and out
Liquid Hydrogen absorbers 1,2,3
Downstreamparticle ID:
TOF 2 Cherenkov
Calorimeter
RF cavities 1 RF cavities 2
Spectrometer solenoid 1
Matching coils 1&2
Focus coils 1 Spectrometer solenoid 2
Coupling Coils 1&2
Focus coils 2 Focus coils 3Matching coils 1&2
10% cooling of 200 MeV muons requires ~ 20 MV of RF single particle measurements =>out/ in ) = 10-3
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MICE Experiment
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Last Slide
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Postdoc availability – Front end Optimization