f. sauli-short courses-ieee-nss 2002-part 1 1 title radiation detection and measurement prof. glenn...
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F. Sauli-Short Courses-IEEE-NSS 2002-PART 1
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TITLE
RADIATION DETECTION AND MEASUREMENTProf. Glenn Knoll, organizerShort Courses November 10-112002 IEEE NSS/MICNorfolk, November 10-16, 2002
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INTRODUCTION
PARALLELPLATE
COUTER
MULTIWIREPROPORTIONAL
CHAMBER
TIME PROJECTION
CHAMBER
DRIFTCHAMBERS
CHERENKOVRING
IMAGING
STREAMERTUBES
STRAWS
PESTOVCOUNTER
RESISTIVEPLATE
CHAMBERS
AVALANCHECHAMBERS
MICROSTRIPCHAMBERS
MICROWELL
MICROGAP
COMPTEURA
TROUS
GASELECTRONMULTIPLIER
MICROMEGAS
TRANSITIONRADIATIONTRACKER
GASEOUS DETECTORS’FAMILY TREE
PROPORTIONALCOUNTER
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PART 1
IONIZATIONDRIFT AND DIFFUSIONCAPTURE LOSSESAVALANCHE MULTIPLICATION
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IONIZATION
PRIMARY IONIZATION: ELECTRON-ION PAIRS
COULOMB INTERACTIONS OF CHARGED PARTICLES WITH MOLECULES
Minimum ionizing particles:
Argon DME
n (ion pairs/ cm) 25 55dE/ dx (keV/ cm)
GAS (STP)
2.4 3.9
Xenon
6.7
44
CH4
1.5
16
Pkn nk
k!e
n
Statistics of primary ionization:
Poisson: n: averagek: actual number
(Maximum) detection efficiency:
1 e n thickness
Argon
GAS (STP)
1 mm 91.82 mm 99.3
Helium
0.32
6
Helium 1 mm 452 mm 70
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IONIZATION
SECONDARY AND TOTAL IONIZATIONCLUSTERS AND DELTA ELECTRONS:
N: total ion-electron pairs nN
~ 3_
CLUSTER SIZE DISTRIBUTION:
P(m) ~W
m2
H. Fischle et al, Nucl. Instr. and Meth. A301(1991)202
Argon DME
n (ion pairs/cm)cm) 25 55
GAS (STP) Xenon
44
CH416
N (ion pairs/cm) 90 160300 53
Helium
6
8
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IONIZATION
CONSEQUENCES OF ENERGY LOSS STATISTICSLANDAU DISTRIBUTION OF ENERGY LOSS:
For a Gaussian distribution: N ~ 21 i.p.FWHM ~ 50 i.p.
00 500 1000
6000
4000
2000
N (i.p.)
Counts4 cm Ar-CH4 (95-5)5 bars
N = 460 i.p. PARTICLE IDENTIFICATION Requires statistical analysis of hundreds of samples
0 500 1000
6000
4000
2000
N (i.p)
Counts
0
protons electrons
15 GeV/c
I. Lehraus et al, Phys. Scripta 23(1981)727
FWHM~250 i.p.
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IONIZATION
LOCALIZATION ACCURACY IN DRIFT CHAMBERSWORSENED BY LONG-RANGE ELECTRONS:
Drift Time
5% of events!
F. Sauli, Nucl. Instr. and Meth. 156(1978)147
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IONIZATION
STRONG ANGULAR DEPENDENCE OF POSITION ACCURACY
G. Charpak et al, Nucl. Instr. and Meth. 167 (1979) 455
Position accuracy as a function of the track angle to the normal to the chamber:
CENTER OF GRAVITY OF INDUCED CHARGE READOUT
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IONIZATION
F. Van den Berg et al, Nucl. Instr. and Meth. A349 (1994) 438
ANGULAR DEPENDENCE OF POSITION ACCURACY IN MICRO-STRIP CHAMBERS:
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IONIZATION
DECLUSTERING EFFECT IN TIME PROJECTION CHAMBERS:
α
β
Data: D. Decamp et al, Nucl. Instr. and Meth. A269(1990)121 Simulation: A. Sharma, CERN
Drift
B offset
B=1.5 T
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IONIZATION
LIMITED TIME RESOLUTION OF WIRE AND MICROPATTERN CHAMBERS:
50 ip/cm
25 ip/cm
3 ns6 ns
Time (ns)0 5 10 2015
A1n(t)
50
40
30
20
10
0
Space distribution of the cluster closer to an electrode:
Time distribution of the cluster closer to an electrode:
€
A1n(x)=ne−nx
€
A1n(t)=ne−nwt
w: drift velocity
w = 5 cm/µs
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IONIZATION
PARALLEL PLATE CHAMBERS: SUB-NANOSECOND RESOLUTION
FAST SIGNAL INDUCTION DURING AVALANCHE DEVELOPMENT:
Useful gap
R. Arnaldi et al, Nucl. Phys. B 78(1999)84
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DRIFT
ELECTRIC FIELD E = 0: THERMAL DIFFUSION
ELECTRIC FIELD E > 0: CHARGE TRANSPORT AND DIFFUSION
E
IONS ELECTRONS
DRIFT AND DIFFUSION OF CHARGES IN GASES
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DRIFT
DRIFT AND DIFFUSION OF IONS (CLASSIC KINETIC THEORY OF GASES)
Ions remain thermal up to very high fieldsMaxwell energy distribution:
Average (thermal) energy:
€
εT =KT ≈0.025eV
€
F(ε)=C ε e−
εKT
Diffusion equationFraction of ions at distance x after time t:
€
dNN
=14Dt
e−
x2
4Dt dx D: diffusion coefficient
RMS of linear diffusion:
€
σ x = 2Dt
Molecules diffuse rapidly in the available volume(leaks!)
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DRIFT
IONS DRIFT VELOCITY
(Almost) linear function of field
Mobility:
€
μ+ =w+ E
~ constant for a given gas (at fixed P and T)
IONS DIFFUSION (Einstein’s law):
€
Dμ
=KTe
€
σx=2KT
exE
€
σ x = 2Dt
Same for all ions!
E. McDaniel and E. MasonThe mobility and diffusion of ions in gases (Wiley 1973)
GAS ION µ+ (cm2 V-1 s-1) @STP
Ar Ar+ 1.51CH4 CH4
+ 2.26
Ar-CH4 80-20 CH4+ 1.61
MWPC: 1 cm gap, Ar-CH4, 5 kV/cm
Total ions drift time T+ ~ 120 µs
TPC: 1 m drift, Ar-CH4, 200 V/cm
Total ions drift time T+ ~ 300 ms
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DRIFT
DRIFT AND DIFFUSION OF ELECTRONS IN GASES
Electron Swarm Drift
ElectricField
s, tDrift velocity:
€
w=ΔsΔ t
s
Space diffusion rms:
€
σ = 2Dt = 2Dsw
Drift velocity and diffusion are gas and field dependent:
€
w=wEP
⎛
⎝ ⎜
⎞
⎠ ⎟ P : pressure
Townsend expression:
€
w=e
2mE τ : mean collision time
€
D =gEP
⎛
⎝ ⎜
⎞
⎠ ⎟
€
σ =1P
FEP
⎛
⎝ ⎜
⎞
⎠ ⎟
€
σx =σ1 x
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DRIFT
LARGE RANGE OF DRIFT VELOCITIES AND DIFFUSIONS
DRIFT VELOCITY: DIFFUSION:
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DRIFT
ELECTRON TRANSPORT THEORY BALANCE BETWEEN ENERGY ACQUIRED FROM THE FIELD AND COLLISION LOSSES
Energy distribution probability:
€
Λ(ε)
€
le(ε)=1
N σ (ε)
Fractional energy loss in collisions
Mean free path between collisions
: electron-molecule cross section)
€
w=23
em
E ε∫ le(ε)∂
F0(ε)ν
∂εdε
€
v=2εm
Drift velocity:
Diffusion coefficient:
€
D =le(ε)3
∫ vF0(ε) dε Frost and Phelps, Phys. Rev. 127(1962)1621V. Palladino and B. Sadoulet, Nucl. Instr. and Meth. 128(1975)323G. Shultz and J. Gresser, Nucl. Instr. and Meth. 151(1978)413S. Biagi, Nucl. Instr. and Meth. A283(1989)716
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DRIFT
CHARGE TRANSPORT DETERMINED BY ELECTRON-MOLECULE CROSS SECTION:
http://consult.cern.ch/writeup/magboltz/cross/
S. Biagi, Nucl. Instr. and Meth. A421 (1999) 234
http://cpa94.ups-tlse.fr/operations/operation_03/POSTERS/BOLSIG/
MAGBOLTZ
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DRIFT
COMPUTED DRIFT VELOCITY IN MIXTURES
http://consult.cern.ch/writeup/garfield/examples/gas/trans2000.html#elec
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DRIFT
Lon
gitu
dina
l diff
usio
n (
µm
for
1 c
m d
rift)
Tra
nsve
rse
diff
usio
n (
µm
for
1 c
m d
rift
)
LONGITUDINAL DIFFUSION (// E)
DriftE Field
T
L
http://consult.cern.ch/writeup/garfield/examples/gas/Welcome.html
SMALLER THAN TRANSVERSE DIFFUSION:
LONGITUDINAL DIFFUSION: TRANSVERSE DIFFUSION:
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DRIFT
DRIFT TIME ACCURACY: DEPENDS ON IONIZATION DENSITY
Drift
Anode Wire
L
Single electron Several electrons Many electrons
Detection threshold
Error on first electron electron: N=100 1~ 0.4 L
€
σ1 ~π
2 3lnNσ L
RESOLUTION LIMITS OF DRIFT TUBES:G. Scherberger et al, Nucl. Instr. and Meth. A424(1999)495W. Riegler et al, Nucl. Instr. and Meth. A443(2000)156
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DRIFT
EFFECTS OF MAGNETIC FIELD rB
rE
θΒ
rwB
rE
rB
θΒwB
THE SWARM IS ROTATED BY AN ANGLE θB
IN THE PLANE PERPENDICULAR TO E AND B THE MAGNETIC DRIFT VELOCITY IS wB w0
THE TRANSVERSE DIFFUSION IS REDUCED
€
r E
€
r B
€
r E
€
r B
//
€
tanθB =ωτ
€
wB =EB
ωτ
1+ω2τ2
€
wB =w0
€
σL =σ0
€
σT =σ0
1+ω2τ2
: mean collision time
€
ω=eB/m Larmor frequency
rB
L
T
wB
€
r E
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DRIFT
DRIFT IN MAGNETIC FIELD: SIMPLE MODEL:
€
τ =τ0
€
τ0 =2mw0
eE
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DRIFT
0
100
200
300
400
500
600
700
800
102 103 104 105
Diffusion for 1 cm (µm)
E (V/cm)
P10 diffusion vs mag field log bis
T( =0)B
L
T( =2.5 )B T
T( =5 )B T
- 90-10Argon Methane
DRIFT MULTIPLICATION
0
200
400
600
800
1000
102 103 104 105
T
for 1 cm (µm)
E (V/cm)
Ar
Ar-CH4 90-10
Ar-CO2 90-10
Ar-CO2 70-30
CO2
transv diff gases bis
DRIFT MULTIPLICATION
TRANSVERSE DIFFUSION IN SEVERAL GASES
REDUCTION IN MAGNETIC FIELD // E
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DRIFT
COMPUTED FROM TRANSPORT THEORY (MAGBOLTZ)
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DRIFT
MAGNETIC FIELD EFFECTS:DISTORSIONS IN DRIFT CHAMBERS
W. de Boer et al, Nucl. Instr. and Meth. 156(1978)249
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DRIFT
MAGNETIC FIELD EFFECT:COORDINATE DISTORSIONS IN MICRO-STRIP CHAMBERS
F. Angelini et al, Nucl. Instr. and Meth. A347(1994)441
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DRIFT
TRANSVERSE DIFFUSION: SUBSTANTIALLY REDUCED IN SOME GASES
TIME PROJECTION CHAMBER: Center-of-gravity of cathode signal
B=0 B>0
€
r E
€
r B //
D. Nygren, TPC proposal (PEP4, 1976)
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DRIFT
STABILITY OF OPERATION VOLTAGE AND PRESSURE
THE DRIFT VELOCITY IS A FUNCTION OF REDUCED FIELD E/P
€
EP
€
w=fEP
⎛
⎝ ⎜
⎞
⎠ ⎟
DRIFT VELOCITY SATURATION:INSENSITIVE TO VARIATIONS OF E AND P
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DRIFT
STABILITY OF OPERATION TEMPERATURE
AT LOW FIELDS (THERMAL ELECTRONS):
€
Δww
=ΔTT
≅3.410−3
oC
G. Shultz and J. Gresser, Nucl. Instr. and Meth. 151(1978)413
At high fields, the thermal coefficient in some gases decreases and even becomes negative:
100 500 1000
0
-1
1
2
3
4
2000E (V/cm)
A
CO2
Methylal
C4H10
CH4
A-C4H10-Methylal 66-30-4
w/w/ºC
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CAPTURE
ELECTRON CAPTURE LOSSES ON ELECTRONEGATIVE GASES
The attachment cross section is energy-dependent, therefore strongly depends on the gas composition and electric field
Attachmant coefficient of oxygen:
Electrons surviving after 20 cm drift (E = 200 V/cm):
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CAPTURE
ELECTRON CAPTURE - VERY SENSITIVITE TO GAS MIXTURE
ARGON-ETHANE 50-50
DIMETHYLETHER
R. Openshaw, TRIUMF (private, 2000)
5.9 keV X-rays “Hot” gas
“Cold” gas
Energy resolution of a proportional counter with two gas fillings (and some leaks!):
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DRIFT
USE OF CF4 AS QUENCHER REPLACING CH4 IN TPCs
- FAST DRIFT VELOCITY- SMALL DIFFUSION- NO HYDROGEN (REDUCED NEUTRON SENSITIVITY)- NON-FLAMMABLE
L. G. Christophorou et al, Nucl. Instr. and Meth.163(1979)141
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CAPTURE
ELECTRON CROSS SECTIONS IN CF4
http://consult.cern.ch/writeup/magboltz/cross/
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MULTIPLICATION
INCREASING THE FIELD TOWARDS CHARGE MULTIPLICATION
IONIZATION 15.7 eV
EXCITATION 11.6 eV
0 5 10 15 20 25 30
Excitation10.5 eV
Ionization15.5 eV
Electron energy (eV)
0.2 kV/cm
1 kV/cm5 kV/cm
Electrons energy distribution at increasing fields:
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MULTIPLICATION
IONIZATION CROSS SECTIONAND TOWNSEND COEFFICIENT Mean free path for ionization
€
λ =1
NσN: molecules/cm3
Townsend coefficient
€
α =1λ
Ionizing collisions/cm
S.C. Brown, basic data of plasma physics (MIT press, 1959)
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MULTIPLICATION
AVALANCHE MULTIPLICATION IN UNIFORM FIELD
€
n(x) =n0eα x
Multiplication factor or Gain
€
dn=nαdx
€
M(x) =nn0
=eα x
E x
Ions
Electrons
Combined cloud chamber-avalanche chamber:
H. RaetherElectron avalanches and breakdown in gases(Butterworth 1964)
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MULTIPLICATION
MEASUREMENT OF THE TOWNSEND COEFFICIENT
Radiation
V
I
Current vs voltage for constant charge injection in a parallel plate counter:
1
M
€
α =lnM
s
s
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F. Sauli-Short Courses-IEEE-NSS 2002-PART 1
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MULTIPLICATION
A. Sharma and F. Sauli, Nucl. Instr. and Meth. A334(1993)420
TOWNSEND COEFFICIENT IN GAS MIXTURESARGON-CH4:
in Argon
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F. Sauli-Short Courses-IEEE-NSS 2002-PART 1
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MULTIPLICATION
PARALLEL PLATE COUNTERS:
+Q
-Q
-Q
+Q
-Q
-Q
A charge +Q between two conductors induces two negative charge profiles(image charge)
Moving the charge modifies the induced charge profile on the conductors and generates detectable signals
+Q towards an electrode: positive induced signal
Induced signals are equal and opposite on anode and cathode
SIGNAL DEVELOPMENT
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F. Sauli-Short Courses-IEEE-NSS 2002-PART 1
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MULTIPLICATION
ANODE
CATHODE
s0
s+Q
V=0
V= -V0
Charge induced on each electrode by +Q moving through the difference of potential dV:
PARALLEL PLATE COUNTERS: SIGNAL DEVELOPMENT (CHARGE COLLECTION ONLY)
Integrating over s (or time t):
€
dq=QdVV0
=Qdss0
€
q(s)=Qs0
s q(t)=Qs0
wt w: drift velocity
Single charge +Q:
Electrons- ion pair (-Q and +Q) released at the same distance s from the cathode :
€
q(t)=Qw−ts0
+w+ts0
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟ 0≤t ≤T−
€
q(t)=Qs−s0
s0+
w+ts0
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟ T−≤t ≤T+
w- (w+ ) : electron (ion) drift velocity
T- (T+ ) : total electron (ion) drift time
Total signal:
€
q(T+)=Q
(+Q on cathode , -Q on anode)
€
q(t)
€
t
€
Qs0 −s
s0
€
Q
€
T−
€
T+
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MULTIPLICATION
PARALLEL PLATE COUNTERS: SIGNAL DEVELOPMENT (CHARGE MULTIPLICATION)
During the avalanche development, the increase in the number of charges after a path ds is:
and the total after a path s:
The incremental charge induction due to electrons after a path s:
Integrating over s:
€
dn=nαds
€
n=n0eαs
€
dq−=−en0eαsds
s0
€
q−(s)=en0αs0
(eαs −1)≈en0αs0
eαs =en0αs0
eαw−t
and the corresponding current :
€
i−(t)=dq−
dt=
en0w−
s0eαw−t =
en0T− eαw−t
The current signal iduced by the ions is instead given by:
€
i+(t)=en0T+ eαw−t −eαw*t⎛
⎝ ⎜
⎞ ⎠ ⎟ 0≤t ≤T−
€
i+(t)=en0T+ eαs−eαw*t⎛
⎝ ⎜
⎞ ⎠ ⎟ T−≤t ≤T+
€
1
w* =1
w++1
w−
s0
s
-V0
0
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MULTIPLICATION
PARALLEL PLATE COUNTERS: SIGNAL DEVELOPMENT (CHARGE MULTIPLICATION)
Fas electron signal
Slow ion tail
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MULTIPLICATION
WIRE PROPORTIONAL COUNTERS:
+
+
-
+
-
+
+
+
+
+
+
Thin anode wire coaxial with cathode
Electric field:Cathode radius b
Anode radius a
€
E(r)=CV0
2πε0
1r
€
C =2πε0
ln b a( )
Avalanche development around a thin wire:
SIGNAL DEVELOPMENT
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MULTIPLICATION
ln M
Voltage
Attachment
Collection
Multiplication
Streamer
PROPORTIONAL COUNTERS: GAIN CHARACTERISTICS
Breakdown
IONIZATION CHAMBER
PROPORTIONAL COUNTER
Saturation
n1
n2
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F. Sauli-Short Courses-IEEE-NSS 2002-PART 1
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MULTIPLICATION
PROPORTIONAL COUNTERS: SIGNAL DEVELOPMENT
€
dQ=QV0
dV=QV0
dVdr
drIncremental charge induced by Q moving through dV:
Assuming that the total charge of the avalanche Q is produced at a (small) distance from the anode, the electron and ion contributions to the induced charge are:
€
q−=QV0
dVdra
a+λ∫ dr=−
QC2πε0
lna+λ
a
€
q+=QV0
dVdra+λ
b∫ dr=−
QC2πε0
lnb
a+λand
The total induced signal is
€
q=q−+q+=−QC2πε0
lnba
=−Q on the anode ( on the cathode)
€
+Q
The ratio of electron and ion contributions:
€
q−
q+ =ln(a+λ)−lnalnb−ln(a+λ)
For a counter with a=10µm, b=10 m: q-/q+ ~1% The electron-induced signal is negligible
Neglecting electrons, and assuming all ions leave from the wire surface:
€
q(t)=q+(t)=− dq=−QC2πε00
t∫ ln
r(t)a
€
drdt
=μ+E =μ+CV0
2πε0
1r
€
r(t) = a2 +μ+CV0
2πε0t
€
i(t)=−QC2πε0
1t0 +t
Total ions drift time:
€
T+=πε0(b2 −a2)
μ+CV0
q(T+) =−Q
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MULTIPLICATION
0 20 40 60 80 100t (ns)
i(t)
CHARGE SIGNAL:
CURRENT SIGNAL:
0 0.2 0.4 0.6 0.8 1.0t (µs)
q(t) q(t)
0 100 200 300 400 500t (µs)
Q
T+
t (ns)
AMPLIFIER TIME CONSTANT;
0 100 200 300 400 500
q(t)
300 ns
100 ns
50 ns