Gas Detectors - atlas.physics.arizona.eduatlas.physics.arizona.edu/.../Lec7_Gas_Detectors.pdf ·...
Embed Size (px)
Transcript of Gas Detectors - atlas.physics.arizona.eduatlas.physics.arizona.edu/.../Lec7_Gas_Detectors.pdf ·...

Large Volume Particle TrackingGas Detectors

Introduction
Gas
Drifting chargesdue to electric field
Anode[e.g. wire or plane]
Schematic Principleof gas detectors
Particle
Primary IonizationSecondary Ionization (due to δ-electrons)

Introduction
CylindricalDrift Chamber
[H1 Experiment]
[email protected] 21 Par ticle Detectors 2
Intrinsic Position Resolution
!"#$%&'(%&)%*$+,)%'%,&$(#),-.'%,&$%)$%&/-.#&*#0$12$'"(##$#//#*')3
• )'4'%)'%*)$,/$+(%54(2$%,&%)4'%,&3$+,%&'$,/$,(%6%&$,/$+(%54(2$*-.)'#($74(%#)$12$$!899µ5
• 0%//.)%,&$,/$#-#*'(,&$*-,.0$0.(%&6$%':)$0(%/'$',$4&,0#
-
- ;,(#&'<$#//#*'
• -%5%'4'%,&)$%&$'%5#$(#),-.'%,&$,/$=",-#$*"4%&$,/$#-#*'(,&%*$)%6&4-$+(,*#))%&6- *41#-
- +.-)#$)"4+%&6$
- 0#/%&%'%,&$,/$'%5#$(#/#(&*#$t0$#'*
!1
n
-------2Dx
µE----------=
*,&'(%1.'%,&)$',$+,)%'%,&$(#),-.'%,&
[email protected] 22 Par ticle Detectors 2
Driftchambers during Construction
>8$?#&'(4-$@#'$?"451#(
• !$8A999$=%(#)
• ','4-$/,(*#$/(,5$=%(#$'#&)%,&$!$B$',&)
[email protected] 23 Par ticle Detectors 2
Options for Readout of Second Coordinate
+(Z = L/2)
r
Z
"#
O
L
A
Y
01
A
A
Z = +L/2
X
$
Z = L/2
C;$ CD$
<9$ <
(#)%)'%7#$=%(#E$4&4-,6$(#40,.'
?(,))#0$F-4&#)
G#65#&'#0$?4'",0#)
?"4(6#$H%7%),&E$<I12I'%5%&6
G'#(#,$J%(#)
451%6.%'%#)
4&4-,6$(#40,.'% !<$!$9K8$55
[email protected] 24 Par ticle Detectors 2
Time Projection Chamber
L&$'"#$)#7#&'%#)$HKM26(#&$0#7#-,+#0$'"#$!%5#$F(,N#*'%,&$?"451#($O!F?PK$
• -4(6#$64)$7,-.5#$=%'"$,&#$*#&'(4-$#-#*'(,0#
• 5%&%54-$45,.&'$,/$54'#(%4-
• #-#*'(,&)$0(%/'$%&$)'(,&6$#-#*'(%*$/%#-0$,7#($0%)'4&*#$,/$)#7#(4-$5#'#()$',$#&0$=4--)$="#(#$'"#2$*4&$1#$(#6%)'#(#0$/,($#Q45+-#$=%'"$RJF?)$$- (#40,.'$,/$4&,0#$=%(#)$4&0$*4'",0#$+40)$%"QE2
- 0(%/'$'%5#$%"<
- &$$.&451%6.,.)$S0$"%'$5#4).(#5#&')
• 0%//.)%,&$)'(,&6-2$(#0.*#0E$)%&*#$T$UU$V&"#-#*'(,&)$)+%(4-$4(,.&0$TI/%#-0$-%&#)3$;4(5,($(40%.)$W8µ5
• -4)#($*4-%1(4'%,&$/,($+(#*%)#$7H$0#'#(5%&4'%,&
• 7#(2$6,,0$"%'$(#),-.'%,&$4&0$0TX0Q$5#4)K
• -,&6$0(%/'$'%5#)$O!Y9µ)P$&$- (4'#$-%5%'4'%,&
- 7#(2$6,,0$64)$Z.4-%'2$(#Z.%(#0
6. Cylindrical Driftchamber
Gregor Herten / 6. Driftchamber 24
Number of wires: ~ 15000Total force from wire tension: ~ 6 t

Introduction
Alice TPC[View inside]

Introduction
Relevant Parametersfor gas detectors
Ionization energyAverage energy/ion pairAverage number of primary ion pairs [per cm]
Average number of ion pairs [per cm]
: Ei
: Wi
: np
: nT
Gas <Z> ρ [g/cm3] Ei [eV] Wi [eV] dE/dx [keV/cm] np [cm-1] nT [cm-1]
He 2 1.66⋅10–4 24.6 41 0.32 5.9 7.8
Ar 18 1.66⋅10–3 15.8 27 2.44 29.4 94
CH4 19 6.7⋅10–4 13.1 28 1.48 18 53
C4H10 34 2.42⋅10–3 10.6 23 4.50 46 195
Differences due to δ-electrons
�nT � =L ·
�dEdx
�i
Wi
[about 2-6 times np][L: layer thickness]
δ-electrons lead to secondary ionization and limit spatial resolution; typical length scale of secondaryionization: 10 μm. Example: kinetic energy: Tkin = 1 keV; gas: Isobutane ➛ range: R = 20 μm ...[using R [g/cm2] = 0.71 (Tkin)1.72 [MeV]; valid for Tkin < 100 keV]

λ = 1/(neσI)
P (np, �np�) =�np�npe−�np�
np!
Introduction
Also important:Mobility of charges:Influences the timing behavior of gas detectors ...
Diffusion:Influences the spatial resolution ...
Avalanche process via impact ionization:Important for the gain factor of the gas detector ...
Recombination and electron attachment:Admixture of electronegative gases (O2, F, Cl ...) influences detection efficiency ...
Ionization statistics:Mean distance between two ionizations:Mean number of ionizations: �np� = L/λ
np Poissonian distributed:
σI : Ionization x-Sectionne : Electron densityL : Thickness
He 0.25 cmAir 0.052 cmXe 0.023 cm
Mean free path λ:[typical values]
[➛ σI(He) ≈ 100 b]
P(0) = exp(-L/λ) yields λ, σI
using (in)efficiency of gas-detectors

τ = λ(Tkin)/vtherm. = const.�v = �a · τ =e �E
M· τ
�vD = ��v � =12�v =
e| �E|2M
· τ = µ+| �E|
�Tion(E �= 0)� = �Tion(Therm.)� =32kT
Drift and Diffusion in Gases
Ion mobility:With external electric field: ions obtain velocity vD in addition to thermal motion;on average ions move along field lines of electric field E ...
Kinetic energy:
approximately equal to thermal energy, as the (heavy) ions loose typically half their energy when colliding with the non-ionized gas atoms.
Drift velocity vD develops only from one interaction to another ...Assuming vD (t=0) = 0 and collision time τ yields:
since Tkin essentially thermal, and vtherm. thus constant ...
μ+ : ion mobility e.g. μ+ = 0.61 cm2/Vs for C4H10
[E = 1 kV/cm; typical drift distances = few cm ➛ typical ion drift time = few ms]
Temperaturesorry ...
Drift velocity vD for ions proportional to E !

m�x = e �E + e(�v × �B) + m �A(t)
�vD = ��v�
�m�x � = e �E + e(�vD × �B)− m
τ�vD = 0
�x� = 0
�vD =eτ
m�E = µ− �E �vD = µ · �E + ωτ · �vD × �B
�vD =µ| �E|
1 + ω2τ2
��E + ωτ �E × �B + ω2τ2( �E · �B) �B
�
ω =eB
m
µ = µ− =eτ
m
➛
Drift and Diffusion in Gases
Electron mobility:Equation of motion:[in E,B field]
time-dependent stochastic forcem �A(t)instantaneous electron velocity�v = �x
Assume:- E and B field constant between collisions- Time averaged stochastic term can be represented by friction term- Time between collisions small with respect to considered time interval: Δt τ- Drift velocity at fixed E constant, i.e. average acceleration vanishes,
»
[describes collisions with gas atoms]
B = 0: B ≠ 0:
with
Remark: μ+ μ– as M m ...« »
Component ⊥ to E,B
Component in direction of B

�vD = µ �E
µ ∼ τ ∼ 1/σ(E)λ(Te) ∼ λ(E)
µ ≈ const. vD ∝ E
Drift and Diffusion in Gases
Electron mobility: [B = 0]
Consider two situations:
Tkin,e kT gas atoms have only a few low-lying energy levels such that electrons can lose little energy in collisions [hot gases]
Tkin,e ≈ kT gas atoms have many low-lying energy levels such that electrons loose all energy they gain between collisions [cold gases]
»
Electrons accelerated in E-field until sufficient energy is reached ...Higher E-field yields smaller mean free path ➛ constant vD possible ...[Example: vD = 3 – 5 cm/μs for 90% Ar/10% CH4]
μ not constant![If λ ~ 1/E; vD = const]
and
and
Similar to situation with ions ...[Example: μ = 7⋅10-3 cm2/μs V for 90% Ne/10% CO2; vD = 2 cm/μs @ 300 V/cm]
Compare: Electrons: vD of order cm/μs Ions: vD of order cm/ms

Drift and Diffusion in Gases
[Brow
n 1959]Ramsauer Cross Section [from Sauli 1977]
Electron mobilitydepends on cross section[Ramsauer Effect]

Drift and Diffusion in Gases
Drift velocity of electronsin several gases at normal conditions
E-Field/pressure
Use gas mixture to obtain constant vD
Important for applications using drift time to get spatial information

Drift and Diffusion in Gases
E-Field/pressureE-Field/pressure
Drift velocity vD
Drift velocity vD
Drift velocity in several argon-methane (CH4) mixtures

Drift and Diffusion in Gases
Drift velocity in several argon-isobutane (C4H10) mixtures

R21st =
� ∞
0
dt
τe−
tτ · (vt)2
1/τ · e−tτ
σ2(t) = 2λ2 · t
τ= 2Dt
D =σ2(t)2t
D0 =σ2
0(t)2t
=λ2
0
τ
Drift and Diffusion in Gases
time
Diffusionwithout E,B field Electron
cloud
DiffusionCase 1: Thermal motion [E = B = 0]
Ensemble of electrons ...τ : time between collisionsλ : mean free pathv : average thermal velocity; v = λ/τ_ _
=� ∞
0
dt
τe−
tτ · (
λ
τt)2 = 2λ2
... with probabilitythat no collision took place within time t
length ofelectron path squared
Extension of charge cloudat time of first collision
Extension after n = t/τ collisions:
with:
[D: Diffusion coefficient]
Index refers toE = B = 0
and

v = λ/τ
σ(t) =�
D0 2t
σL(t) =�
1/3D0 2t
σx(t) = σy(t) = σz(t) =�
1/3D0 2t
σT (t) =�
2/3D0 2t
N(x) = ζ · exp�− x2
2σ2x
�= ζ · exp
�− x2
4DLt
� ρ + �∇�j = 0
ρ = D ∆ρ
ρ(�r, t) = ζ · exp�− �r 2
4Dt
�➛
D0,L =13
λ20
τ=
13v2τ D0,T =
23
λ20
τ=
23v2τ
D0 =λ2
0
τ=
2�T �m
τ = v2τ
Drift and Diffusion in Gases
Diffusion coefficient without field: �T � =12mv2
Isotropy:
with
v : average thermal velocity
_T : Kin. energy of e–
LongitudinalDiffusion Coefficient
TransverseDiffusion Coefficient
Charge cloud extension after time t:
and
Charge distribution:
1-dim:
3-dim:
Diffusion equation:
No field: �j = −D�∇ρ
N(�r ) = ζ · exp�− �r 2
4Dt
� ➛

�B = B · �ez
DT (B) =D0,T
1 + ω2τ2=
2/3D0
1 + ω2τ2
ϕ
vT = ωr
=�
2/3λ0
τ
⊗
d = 2r sinφ
2φ = s/r
s = vT t
= 2r sins
2r
R21st =
� ∞
0
dt
τe−
tτ ·
�2r sin
vT t
2r
�2
= 2τ2v2
T
1 + ω2τ2
σ2T (B, t) = 2 · t
τ· τ2v2
T
1 + ω2τ2
= 2t · D0,T
1 + ω2τ2
D0,T =23v2τ = v2
T τ
Drift and Diffusion in Gases
DiffusionCase 2: Influence of B-field[B ≠ 0; assume ]
Longitudinal direction:
Transversal direction:
No Lorentz force along B-field direction
r d s
B➙
[Partial Integration]
After first collision:
After time t τ, i.e. n = t/τ collisions:
»
[using: ]
For large B-fields ω = eB/m 1 and thusDT(B) D0,T; e.g: Ar/CH4, B=1.5 T ➛ DT = D0,T/50
»»
B-Field can substantially reduce diffusion in transverse direction ...
DL(B) = D0,L =13D0

Abbildung 7.6: Abhangigkeit von !t von der Driftlange
"E = "0 v =!
3kTm
ist die mittlere Geschwindigkeit der Elektronen im thermodynamischen Gleichgewicht.
"E != 0
Wir hatten gerade gesehen (Kap.7.1.2), daß im thermischen Limit # unabhangig von "E gilt(Beispiel CO2–Gas).
v =!(#)
#=
"2D
#
D =3
2
kT
m· # .
MitvD = µ! | "E | =
e#
m| "E |
giltD =
kT · vD
e | "E |·3
2
und mit der Driftlange $D = vD · t
folgt
!2(t) = 2 · D · t =3kT
e | "E |· $D
Diese Relation gilt nur fur kalte Gase wie CO2, die hinreichend viel Anregungsfreiheitsgradebesitzen. Man spricht vom thermischen Limit. Fur Ar/CH4–Mischungen etwa nimmt vD einMaximum an, wo die Driftgeschwindigkeit unabhangig von | "E | ist. Da dieses Maximumbei der Energie des Ramsauer–Minimum auftritt, ist dort %/# maximal, d.h. D ist groß.Kombiniert man "E, "B, so kann man zwar DT klein halten, aber DL kann groß werden.Diese qualitativen Uberlegungen kann man verscharfen, indem man anstelle des einzelnenElektrons ein durch eine Verteilungsfunktion beschriebenes Elektronenensemble mit Hilfe derBoltzmann–Gleichung untersucht. Zur quantitativen Behandlung benotigt man dann außer-dem die Wirkungsquerschnitte fur den Stoß (Abb.7.7).
129
Drift and Diffusion in Gases
Transverse diffusion as function of drift length for different B fields
0 50 100 L [cm] 0
0.2
0.4
0.6
0.8
σ T2
[a.u
.]
B=0
B=.35 T
B=1.13 T

D0,L =13
· 2�T �m
τ
vD =eτ
m| �E |
σ2L(t) = 2Dt =
2�T �3e| �E |
vDt ∝ LD
| �E |
Drift and Diffusion in Gases
DiffusionCase 3: Influence of E-field[E ≠ 0]
Drift in direction of E field superimposed to statistical diffusion ...
Extra velocity influenceslongitudinal diffusion ...Transverse diffusion not affected ...
Hot gases : DL > DT »
Cold gases : DL ≈ DT
[for large E fields ...]
[Tkin,e ≈ kT]
[Tkin,e kT]
Diffusion:Long.
using:Lower limit:
Longitudinal diffusion in E-field

∂f
∂t+ �v
∂
∂�rf +
∂
∂�v
�e �E
m+ �ω × �v
�f = Q(t)
Drift and Diffusion in Gases
For exact solution:
Solve "transport equation" for electron density distribution : f(t,�r,�v)
diffusion external forces
stochasticcollision term
Typically needs tobe solved numerically ...
AvailablePrograms:
MagboltzGarfield

Λ = pr · n+n−
➥
Loss of Electrons
Electrons maybe lost during drift ...Possible processes:
i. recombination of ions and electrons
ii. electron attachment
Depends on number of charge carriersand recombination coefficient ...
Recombination rate:
Recombinationcoefficient ≈ 10-7 cm3/sGenerally not important ...
Electro-negative gases bind electrons; e.g.: O2, Freon, Cl2, SF6 ... Attachment coefficient h strongly energy dependent ("Ramsauer effect") ...
Example O2: h = 10-4
Collisions of electron per second: 1011
Typical drift time of electron: 10-6 s
Fraction lost: Xloss = 10-4 1011 s-1 10-6 s ⋅ p = 10p Xloss < 1% ➛ p < 10-3, i.e. less than 1 ‰ admixture
Oxygen shouldbe kept out

dn = n · α dx
n = n0eαx
G =n
n0= eαx G =
n
n0= exp
�� x2
x1
α(x)dx
�
Avalanche Multiplication
Sei n(x) = Elektronen am Ort x
dn = n · dx1/!
n = no e!x
Man definiert den Multiplikationsfaktor
M =n
no= e!x
Im inhomogenen Feld gilt ! = ! ( "E) = ! (x).
M = e
! x2
x1!(x) dx
Anwendung : Zahlrohr
!+
!!!!! (x) ist aus Messungen bekannt.Da die Driftgeschwindigkeit vD(e!) ! vD(Ion), erhalt man unter Berucksichtigung derDi!usion und Streuung eine tropfenartige Lawinenform (Abb.7.6)
Anode
Abbildung 7.5: Townsend Lawine in der Nahe des Anodendrahtes eines Zahlrohrs [55]
Man kann bei Detektoren den Multiplikationsfaktor nicht beliebig anwachsen lassen, weil essonst zur Funkenbildung kommt. Nach Raether ist die Grenze der Funkenbildung gegebendurch
! · x = 20 ! M = 108
Diese Grenze beschrankt die naturliche Gasverstarkung eines Detektors. Ublicherweise arbei-ten die Detektoren aber bei wesentlich kleinerem Wert von M (" 104).
126
Large electric field yieldslarge kinetic energy of electrons ...
➛ Avalanche formationLarger mobility of electrons results in liquid drop like avalanche with electrons near head ...
Mean free path: λion[for a secondary ionization]
Probability of an ionization perunit path length: α = 1/λion [1st Townsend coefficient]
n(x) = electrons at location x
Gain:
and more general for α = α(x):
Drop-like shape of an avalancheLeft: cloud champer pictureRight: schematic view
[Raether limit: G ≈ 108; αx = 20; then sparking sets in ...]
Townsend avalanche

Avalanche Multiplication
Ionization Probability
Need about 75-100 eV for high ionization probability
E ≈ 75 kV/cmneeded to reach α/p = 1
Townsend Coefficient
[need to gain this energy within few microns]

=eU0
ln r0/ri
� r2
r1
1r
drdiv �E =
ρ
�0
��E dA =
�ρ
�0d3r
2πr L · | �E| = Q/�0| �E| =λ
2π�0
1r
λ = Q/L
U0 =� r0
ri
E dr =λ
2π�0ln
r0
ri
E =U0
r ln r0/ri
λ
2π�0=
U0
ln r0/ri
➛
=eU0
ln r0/ri
· ln r2/r1
∆Tkin = e∆U = e
� r2
r1
E(r)dr
Avalanche Multiplication
To reach high E fieldsuse a thin wire as anode ...
Close to wire E-field very large ...
ProportionalCounter
Wire
– U0
Kinetic energy:
Reminder Physics II:
➛
linear chargedensity
rir0
const.
Choose ratio aslarge as possible with small Δr ...[Δr should be smaller than typical mean free path ...]

1000 2000 3000 4000 5000
0.05
0.1
0.15
r1 [µm]
Avalanche Multiplication
∆r = r2 − r1 = 50µm
lnr2 /
r1
Need wire thickness of order mean free path ...

| �E| =λ
2π�0
1r
λ = Q/L
V0 =λ
2π�0ln
b
a=
λ
C
C =2π�0ln b
a
Single Wire Proportional Counter
Wire
Particle
Geiger Counter
Wire
E-field:
Voltage:
Capacity:[per unit length]
with:
[linear charge density]
Relations:
[F/m]

Single Wire Proportional Counter
Ionization mode: full charge collection no multiplication; gain ≈ 1
Proportional mode: multiplication of ionization signal proportional to ionization measurement of dE/dx secondary avalanches need quenching; gain ≈ 104 – 105
Limited proportional mode: [saturated, streamer] strong photoemission requires strong quenchers or pulsed HV; gain ≈ 1010
Geiger mode: massive photoemission; full length of the anode wire affected; discharge stopped by HV cut

Single Wire Proportional Counter
Time development of an avalanche in a proportional counter
A single primary electron proceeds towards anode in regions ofincreasingly high fields, experiencing ionizing collisions; due to the lateral
diffusion, a drop-like avalanche, surrounding the wire develops.
a b c
d e

E(r) =CV0
2π�0
1r
C =2π�0ln b/a
dW = qdφ(r)
drdr
dW = l CV0 dV
W = 1/2 l CV 20
lC
qdφ(r)
drdr = l CV0 dV
dV =q
lCV0
dφ(r)dr
dr
➛
φ(r) = −CV0
2π�0ln
r
a
Single Wire Proportional Counter
Pulse formation and shape:
Again, pulse signal is formed by induction due to the movement of charges towards cathode and anode ... +
2b2a
charge
–V0
with
[Capacity per unit length]
Electric field:
Electric potential:
Consider charge q:[Assume fast charge movement ...]
from:
[ Capacity: ! ]
change in potentialenergy
electrostatic energy
No compensationby power supply
Integrate ...

V = V + + V − = − q
lC
C =2π�0ln b/a
V −/V + =ln(a+r�/a)ln(b/a+r�)
= − q
2π�0lln
�a + r�
a
�
V + =q
lCV0
� b
a+r�
dφ(r)dr
dr = − q
2π�0lln
�b
a + r�
�
Single Wire Proportional Counter
Total induced voltagefor electrons:
dV =q
lCV0
dφ(r)dr
dr
Integrate ...
+
2b2a
charge
–V0
with
Ratio of V+ and V–:
Total induced voltagefor ions:
Cross check:
with
With typical numerical values: a = 10 μm, b = 10 mm, r' = 1 μm
V–/V+ = 0.013Signal almost entirelydue to ions ...
V − = − q
lCV0
� a
a+r�
dφ(r)dr
dr = − q
lCV0
�CV0
2π�0ln
�a + r�
a
��
φ(r) = −CV0
2π�0ln
r
a

Dabei nehmen wir an, daß die Ionen bei r = a starten – was wegen der Ausbildung der
Lawine eine sinnvolle Naherung ist –, und daß der Elektronenbeitrag vernachlassigbar ist.
Driftgeschwindigkeit der Ionen :
dr
dt= µ+ | !E | = µ+
C V0
2" #0
·1
r
r!
a
rdr =µ+ C · V0
2" #0
t!
0
dt ! r(t) =
"a2 +
µ+ C V0
" #0
· t .
Einsetzen in V (t) ergibt
V (t) = !Q
2" #0 · L·1
2$n
#1 +
µ+C V0
" #0a2· t
$= !
Q
4" #0
1
L$n
#1 +
t
t0
$
t0 =" #0a2
µ+CV0
ist die charakteristische Zeitkonstante des Systems (Abb.7.10).
V(t)t
400 500 T300200100
=!! =
10µ
µ ss100
= 8!
Abbildung 7.10: Zeitabhangigkeit des Signals eines Zahlrohrs, % = R CK (Abb.7.8) [55]
Die Gesamtdriftzeit T der Ionen ist gegeben durch die Forderung
r (T ) = b
T =" #0
µ+ CV0
(b2 ! a2) = t0
#b2
a2! 1
$
Es giltV
%a
bT
&=
Q
L C·1
2
wobei a
b" 10!3 ,
d.h. in der Zeit 10!3 T wird naherungsweise das halbe Spannungssignal erzeugt. Durch ge-
eignete Wahl des Anodendwiderstands und der Kapazitat CK kann man erreichen, daß das
Signal mit der Zeitkonstanten % = R CK di!erenziert wird.
133
V (t) =� r(t)
r(0)
dV
drdr = − q
2π�0lln
r(t)a
vD =dr
dt= µE(r) =
µCV0
2π�0
1r
r dr =µCV0
2π�0dt
r(t) =�
a2 +µCV0
π�0t
�1/2
V (t) = − q
4π�0lln
�1 +
µCV0
π�0a2t
�= − q
4π�0lln
�1 +
t
t0
�
➛
t0 = π�0a2/µCV0
Single Wire Proportional Counter
Ignoring electron signaland setting r(0) = a ...
Calculation of r(t):
Voltage time dependence:
with:
Unmodified pulse
Differentiatedpulse
Inputsignal
Differentiator: Measure output voltage across resistor ...
V(t) t

r(T ) = b
T =π�0
µCV0
�b2 − a2
�= t0
�b2
a2− 1
�
V (a/b · T ) = − q
4π�0lln
�1 +
a/b · T
t0
�= − q
4π�0lln
�1 + a/b
�b2
a2− 1
��
≈ − q
4π�0lln
�b
a
�= −1
2q
lC
Single Wire Proportional Counter
Total drift time T:
b =�
a2 +µCV0
π�0T
�1/2
t0 = π�0a2/µCV0
with:
Calculation V(a/b⋅T):
C =2π�0ln b/a
with
[Capacity per unit length]Typically a/b ≈ 10-3, i.e. after 10-3 T alreadyhave of the signal voltage is reached ...
Choice of suitable RC-circuit allows short (differentiated) signals ...

LHCb Outer Tracker
OuterTracker
Straw Tubes[double layers]
3 Chambers[4 layers á 18 modules]

LHCb Outer Tracker
Trigger Tracker
T1T2 T3
Long Tracks:
~ 38 track points ~ 24 OT/IT measurem.
Outer Tracker (OT)
InnerTracker (IT)
Outer Tracker Station

Georges Charpak 25
15
Guard strip
Fig. 1: A few construction details of multiwire chambers. The scnsitives anode wires areseparated by 2 mm from each othcr; their diameter is 20 µm. They are stretched between twocathode meshes, in a gas at atmospheric pressure. The edges of the planes are potted inAraldite, allowing only the high voltage to enter and only the pulses to leave to go to a 10 kRamplifier.
Fig. 2: Equipotcntials and electric field lines in amultiwire proportional cbambcr. The effect ofthe slight shifting of one of the wires can bc seen.It has no effect on the field close to the wire.
Fig. 3: Dctail of fig. 2 showing the electric fieldaround a wire (wire spacing 2 mm, diameter 20µm).
Multi-Wire Proportional Chamber (MWPC)
G. CharpakNobel Prize 1992
MWPC construction details from Charpak's nobel lecture [1967 design]Sense wires [∅ = 20 μm] separated by 2 mm; wires lie between two cathode meshes; edges of the planes are potted in Araldite ...

Multi-Wire Proportional Chamber (MWPC)
d
Schematic setup:
L rw
particle track
anode wire
cathode plane
Parameters: Features:d = 2 - 4 mmrw = 20 - 25 μmL = 3 - 6 mmU0 = several kV
Total area: O(m2)
Tracking of charged particlesSome PID capabilities via dE/dxLarge area coverageHigh rate capabilities

Multi-Wire Proportional Chamber (MWPC)
Electric field linesand equipotentials
Small wire displacements reduce field quality ...
Need high mechanical precision both for geometry and wire tension ...
[electrostatics and gravitation; wire sag]near wire: radial fieldfar away: homogeneous field
∆G
G≈ 3
∆a
a
∆G
G≈ 12
∆L
L
Displacement effect

Multi-Wire Proportional Chamber (MWPC)
Space point resolution:Only information about closest wire ➛ σx = d/√12[Not very precise and only one for one dimension ...]
2-dim.: use 2 MWPCs with different orientation ...3-dim.: several layers of such X-Y-MWPC combinations.
Signal generation:Electrons drift to closest wireGas amplification near wire ➛ avalancheSignal generation due to electrons and slow ions ...
Timing resolution: Depends on location of penetrationFor fast response: OR of all channels ...[Typical: σt = 10 ns]
maincontribution
• die Verstarkung so groß ist, daß alle Pulse oberhalb der Schwelle des nachgeschaltetenVerstarkers liegen,
• noch keine Geiger–Entladung bei der gewahlten Spannung eintritt,
• mechanische Toleranzen eingehalten werden, nur so erreicht man uber die gesamte Kam-merflache ein Plateau (Abb.7.10) von 100V . . . 200V .
Wie sieht das Signal als Funktion der Zeit naherungsweise aus (siehe Abb.7.13 a–d) ?
a) b)
c) d)
Abbildung 7.13: Zeitabhangigkeit des Signals einer MWPC a) und b) schematisch, c) Signaleines Einzeldrahtes, d) logisches Oder der Drahte eines Systems (SFM) [55]
Typische Eigenschaften eines Kammersystems in einem Detektor (SFM) :
Zeitauflosung 10 nsPulsbreite 16 nsOrtsauflosung 1 mm
Microstrip Proportional Counters (MSGC) [87], [88]
Die Proportionalkammer (MWPC) hat folgende Nachteile :
• Ortsauflosung ist durch den Anodendrahtabstand begrenzt, der aufgrund mechanischerStabilitat nicht unter 1–2 mm liegen kann.
• Die Ionen wandern nur langsam ab (1 ms), bei hohen Raten sinkt die Verstarkung.
136
• die Verstarkung so groß ist, daß alle Pulse oberhalb der Schwelle des nachgeschaltetenVerstarkers liegen,
• noch keine Geiger–Entladung bei der gewahlten Spannung eintritt,
• mechanische Toleranzen eingehalten werden, nur so erreicht man uber die gesamte Kam-merflache ein Plateau (Abb.7.10) von 100V . . . 200V .
Wie sieht das Signal als Funktion der Zeit naherungsweise aus (siehe Abb.7.13 a–d) ?
a) b)
c) d)
Abbildung 7.13: Zeitabhangigkeit des Signals einer MWPC a) und b) schematisch, c) Signaleines Einzeldrahtes, d) logisches Oder der Drahte eines Systems (SFM) [55]
Typische Eigenschaften eines Kammersystems in einem Detektor (SFM) :
Zeitauflosung 10 nsPulsbreite 16 nsOrtsauflosung 1 mm
Microstrip Proportional Counters (MSGC) [87], [88]
Die Proportionalkammer (MWPC) hat folgende Nachteile :
• Ortsauflosung ist durch den Anodendrahtabstand begrenzt, der aufgrund mechanischerStabilitat nicht unter 1–2 mm liegen kann.
• Die Ionen wandern nur langsam ab (1 ms), bei hohen Raten sinkt die Verstarkung.
136
100 ns
10 ns
OR
Single
Possible improvement: segmented cathode ...

Multi-Wire Proportional Chamber (MWPC)
Cathodestrip
Anodewire Anode
signal
Cathodesignals
Center of gravitydetermined withσy = 50 - 300 μm
Cathodesignal distribution
Charged particle