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

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• 0%//.)%,&$,/$#-#*'(,&$*-,.0$0.(%&6$%':)$0(%/'$',$4&,0#

-

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• -%5%'4'%,&)$%&$'%5#$(#),-.'%,&$,/$=",-#$*"4%&$,/$#-#*'(,&%*$)%6&4-$+(,*#))%&6- *41#-

- +.-)#$)"4+%&6$

- 0#/%&%'%,&$,/$'%5#$(#/#(&*#$t0$#'*

!1

n

-------2Dx

µE----------=

*,&'(%1.'%,&)$',$+,)%'%,&$(#),-.'%,&


Driftchambers during Construction

>8$?#&'(4-$@#'$?"451#(

• !$8A999$=%(#)

• ','4-$/,(*#$/(,5$=%(#$'#&)%,&$!$B$',&)


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#)

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G'#(#,$J%(#)

451%6.%'%#)

4&4-,6$(#40,.'% !<$!$9K8$55


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

➛


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


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


[Brow

n 1959]Ramsauer Cross Section [from Sauli 1977]

Electron mobilitydepends on cross section[Ramsauer Effect]


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


E-Field/pressureE-Field/pressure

Drift velocity vD

Drift velocity vD

Drift velocity in several argon-methane (CH4) mixtures


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


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


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


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


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 |


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)


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


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


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]


∆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]


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


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


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�

�


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


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


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 ...


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


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


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 ...


Cathodestrip

Anodewire Anode

signal

Cathodesignals

Center of gravitydetermined withσy = 50 - 300 μm

Cathodesignal distribution

Charged particle

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