Transcript IONIZATION 1

TITLE
F. Sauli-Short Courses-IEEE-NSS 2002-PART 1
RADIATION DETECTION AND MEASUREMENT
Prof. Glenn Knoll, organizer
Short Courses November 10-11
2002 IEEE NSS/MIC
Norfolk, November 10-16, 2002
1
INTRODUCTION
F. Sauli-Short Courses-IEEE-NSS 2002-PART 1
GASEOUS DETECTORS’
FAMILY TREE
TIME
PROJECTION
CHAMBER
CHERENKOV
RING
IMAGING
MULTIWIRE
PROPORTIONAL
CHAMBER
STREAMER
TUBES
TRANSITION
RADIATION
TRACKER
DRIFT
CHAMBERS
COMPTEUR
A
TROUS
STRAWS
PROPORTIONAL
COUNTER
GAS
ELECTRON
MULTIPLIER
MICROWELL
MICROMEGAS
MICROSTRIP
CHAMBERS
MICROGAP
PARALLEL
PLATE
COUTER
AVALANCHE
CHAMBERS
PESTOV
COUNTER
RESISTIVE
PLATE
CHAMBERS
2
PART 1
F. Sauli-Short Courses-IEEE-NSS 2002-PART 1
IONIZATION
DRIFT AND DIFFUSION
CAPTURE LOSSES
AVALANCHE MULTIPLICATION
3
IONIZATION
F. Sauli-Short Courses-IEEE-NSS 2002-PART 1
COULOMB INTERACTIONS OF CHARGED PARTICLES WITH MOLECULES
PRIMARY IONIZATION: ELECTRON-ION PAIRS
Minimum ionizing particles:
Helium Argon
GAS (STP)
dE/ dx (keV/ cm)
n (ion pairs/ cm)
0.32
2.4
6
25
Xenon
6.7
44
CH 4
DME
1.5
16
3.9
55
Statistics of primary ionization:
Poisson:
k
-n
n
=
P
e
k!
n
k
n: average
k: actual number
(Maximum) detection efficiency:
e = 1- e
-n
thickness
e
Helium
1 mm
2 mm
45
70
Argon
1 mm
2 mm
91.8
99.3
GAS (STP)
4
IONIZATION
F. Sauli-Short Courses-IEEE-NSS 2002-PART 1
SECONDARY AND TOTAL IONIZATION
CLUSTERS AND DELTA ELECTRONS:
GAS (STP)
n (ion pairs/cm)
cm)
N (ion pairs/cm)
Helium
Argon
Xenon
CH 4
DME
6
25
44
16
55
8
90
300
53
160
N: total ion-electron pairs
n
_ ~3
N
CLUSTER SIZE DISTRIBUTION:
P (m) ~
W
m2
H. Fischle et al,
Nucl. Instr. and Meth.
A301(1991)202
5
IONIZATION
F. Sauli-Short Courses-IEEE-NSS 2002-PART 1
CONSEQUENCES OF ENERGY LOSS STATISTICS
LANDAU DISTRIBUTION OF ENERGY LOSS:
Counts
4 cm Ar-CH4 (95-5)
5 bars
6000
PARTICLE IDENTIFICATION
Requires statistical analysis of hundreds of samples
N = 460 i.p.
4000
FWHM~250 i.p.
Counts
15 GeV/c
6000
protons
2000
electrons
4000
0
0
500
1000
N (i.p.)
2000
For a Gaussian distribution: sN ~ 21 i.p.
FWHM ~ 50 i.p.
0
0
500
1000
N (i.p)
I. Lehraus et al, Phys. Scripta 23(1981)727
6
IONIZATION
F. Sauli-Short Courses-IEEE-NSS 2002-PART 1
LOCALIZATION ACCURACY IN DRIFT CHAMBERS
WORSENED BY LONG-RANGE ELECTRONS:
Drift Time
5% of events!
F. Sauli, Nucl. Instr. and Meth. 156(1978)147
7
IONIZATION
F. Sauli-Short Courses-IEEE-NSS 2002-PART 1
CENTER OF GRAVITY OF INDUCED CHARGE READOUT
STRONG ANGULAR DEPENDENCE OF POSITION ACCURACY
Position accuracy as a function
of the track angle to the normal
to the chamber:
G. Charpak et al, Nucl. Instr. and Meth. 167 (1979) 455
8
IONIZATION
F. Sauli-Short Courses-IEEE-NSS 2002-PART 1
ANGULAR DEPENDENCE OF POSITION ACCURACY IN MICRO-STRIP CHAMBERS:
F. Van den Berg et al, Nucl. Instr. and Meth. A349 (1994) 438
9
IONIZATION
F. Sauli-Short Courses-IEEE-NSS 2002-PART 1
DECLUSTERING EFFECT IN TIME PROJECTION CHAMBERS:

B=1.5 T
B offset

Drift
Data: D. Decamp et al, Nucl. Instr. and Meth. A269(1990)121
Simulation: A. Sharma, CERN
10
IONIZATION
F. Sauli-Short Courses-IEEE-NSS 2002-PART 1
LIMITED TIME RESOLUTION OF WIRE AND MICROPATTERN CHAMBERS:
Space distribution of the cluster closer to an electrode:
A1n (x) = ne -n x
Time distribution of the cluster closer to an electrode:
A1n (t) = ne -n w t
w: drift velocity
50
w = 5 cm/µs
A1n(t)
40
30
20
6 ns
3 ns
25 ip/cm
10
0
0
50 ip/cm
5
10
20
15
Time (ns)
11
IONIZATION
F. Sauli-Short Courses-IEEE-NSS 2002-PART 1
PARALLEL PLATE CHAMBERS: SUB-NANOSECOND RESOLUTION
FAST SIGNAL INDUCTION DURING AVALANCHE DEVELOPMENT:
Useful gap
R. Arnaldi et al, Nucl. Phys. B 78(1999)84
12
DRIFT
F. Sauli-Short Courses-IEEE-NSS 2002-PART 1
DRIFT AND DIFFUSION OF CHARGES IN GASES
ELECTRIC FIELD E = 0: THERMAL DIFFUSION
ELECTRIC FIELD E > 0: CHARGE TRANSPORT AND DIFFUSION
IONS
ELECTRONS
E
13
DRIFT
F. Sauli-Short Courses-IEEE-NSS 2002-PART 1
DRIFT AND DIFFUSION OF IONS (CLASSIC KINETIC THEORY OF GASES)
Ions remain thermal up to very high fields
Maxwell energy distribution:
-
F(e ) = C e e
e
KT
Average (thermal) energy:
eT = KT  0.025 eV
Diffusion equation
Fraction of ions at distance x after time t:
2
dN
1
=
N
4 Dt
x
e 4 Dt
dx
D: diffusion coefficient
RMS of linear diffusion:
s x = 2Dt
Molecules diffuse rapidly in the available volume
(leaks!)
14
DRIFT
F. Sauli-Short Courses-IEEE-NSS 2002-PART 1
IONS DRIFT VELOCITY
(Almost) linear function of field
Mobility:
  = w E
~ constant for a given gas (at fixed P and T)
GAS
Ar
CH4
Ar-CH4 80-20
ION
Ar+
CH4+
CH4+
µ+ (cm2 V-1 s-1) @STP
1.51
2.26
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
IONS DIFFUSION (Einstein’s law):
D
KT
s x = 2Dt

e
2 KT x
Same for all ions!
sx =
e E
=
E. McDaniel and E. Mason
The mobility and diffusion of ions in gases (Wiley 1973)
15
DRIFT
F. Sauli-Short Courses-IEEE-NSS 2002-PART 1
DRIFT AND DIFFUSION OF ELECTRONS IN GASES
Electric
Field
Electron Swarm Drift
Ds, Dt
s
Drift velocity:
w=
Ds
Dt
Space diffusion rms:
s = 2Dt = 2D
s
w
s x = s1 x
Townsend expression:
w=
e
E
2m
 : mean collision time
E 
w
=
w
 
Drift velocity and diffusion are gas and field dependent:
P 
1 E 
E 
s
=
F  
D = g 
P
P 
P 
P : pressure
16
DRIFT
F. Sauli-Short Courses-IEEE-NSS 2002-PART 1
LARGE RANGE OF DRIFT VELOCITIES AND DIFFUSIONS
DRIFT VELOCITY:
DIFFUSION:
17
DRIFT
F. Sauli-Short Courses-IEEE-NSS 2002-PART 1
ELECTRON TRANSPORT THEORY
BALANCE BETWEEN ENERGY ACQUIRED FROM THE FIELD AND COLLISION LOSSES
Energy distribution probability:
F0 (e ) = C e e
le (e ) =
-
3e (e ) de
e E le (e ) 2
1
(e)
Drift velocity:
w=
Mean free path between collisions
N s (e )
2 e
E  e le (e )
3m
s: electron-molecule cross section)
Fractional energy loss in collisions

F0 (e )

e
de
v=
2e
m
Diffusion coefficient:
D= 
le (e )
v F0 (e ) de
3
Frost and Phelps, Phys. Rev. 127(1962)1621
V. Palladino and B. Sadoulet, Nucl. Instr. and Meth. 128(1975)323
G. Shultz and J. Gresser, Nucl. Instr. and Meth. 151(1978)413
S. Biagi, Nucl. Instr. and Meth. A283(1989)716
18
DRIFT
F. Sauli-Short Courses-IEEE-NSS 2002-PART 1
CHARGE TRANSPORT DETERMINED BY ELECTRON-MOLECULE CROSS SECTION:
MAGBOLTZ
S. Biagi, Nucl. Instr. and Meth. A421 (1999) 234
http://consult.cern.ch/writeup/magboltz/cross/
http://cpa94.ups-tlse.fr/operations/operation_03/POSTERS/BOLSIG/
19
DRIFT
F. Sauli-Short Courses-IEEE-NSS 2002-PART 1
COMPUTED DRIFT VELOCITY IN MIXTURES
http://consult.cern.ch/writeup/garfield/examples/gas/trans2000.html#elec
20
DRIFT
F. Sauli-Short Courses-IEEE-NSS 2002-PART 1
LONGITUDINAL DIFFUSION (// E)
E Field
LONGITUDINAL DIFFUSION:
sL
Drift
TRANSVERSE DIFFUSION:
Transverse diffusion ( µm for 1 cm drift)
Longitudinal diffusion ( µm for 1 cm drift)
SMALLER THAN TRANSVERSE DIFFUSION:
sT
http://consult.cern.ch/writeup/garfield/examples/gas/Welcome.html
21
DRIFT
F. Sauli-Short Courses-IEEE-NSS 2002-PART 1
DRIFT TIME ACCURACY: DEPENDS ON IONIZATION DENSITY
Anode Wire
Drift
sL
Single electron
Several electrons
Many electrons
Detection threshold
Error on first electron electron:
s1 ~

2 3 ln N
sL
N=100
s1~ 0.4 sL
RESOLUTION LIMITS OF DRIFT TUBES:
G. Scherberger et al, Nucl. Instr. and Meth. A424(1999)495
W. Riegler et al, Nucl. Instr. and Meth. A443(2000)156
22
DRIFT
F. Sauli-Short Courses-IEEE-NSS 2002-PART 1
EFFECTS OF MAGNETIC FIELD
THE SWARM IS ROTATED BY AN ANGLE B
IN THE PLANE PERPENDICULAR TO E AND B
THE MAGNETIC DRIFT VELOCITY IS wB  w0
THE TRANSVERSE DIFFUSION IS REDUCED
B
E

E^ B
tan B =  
B
wB =
E

wB
wB
E

B 1  2  2
 : mean collision time
 = eB / m
E // B
sT
E
sL
r
B
wB
Larmor frequency
wB = w0
sL = s 0
sT =
s0
1  2 2
23
DRIFT
F. Sauli-Short Courses-IEEE-NSS 2002-PART 1
DRIFT IN MAGNETIC FIELD: SIMPLE MODEL:
 = 0
0 =
2mw0
eE
24
DRIFT
F. Sauli-Short Courses-IEEE-NSS 2002-PART 1
TRANSVERSE DIFFUSION IN SEVERAL GASES
transv diff gases bis
1000
DRIFT
MULTIPLICATION
Ar
600
Ar-CH 90-10
REDUCTION IN MAGNETIC FIELD // E
4
400
2
200
Ar-CO 70-30
2
CO
2
0
102
103
P10 diff usion vs mag f ield log bis
800
Ar-CO 90-10
104
E (V/cm)
105
Diffusion for 1 cm (µm)
s for 1 cm (µm)
T
800
Argon-Methane 90-10
700
DRIFT
MULTIPLICATION
600
sT (B=0)
500
400
sL
300
sT (B=2.5 T)
200
sT (B=5 T)
100
0
102
103
104
105
E (V/cm)
25
DRIFT
F. Sauli-Short Courses-IEEE-NSS 2002-PART 1
COMPUTED FROM TRANSPORT THEORY (MAGBOLTZ)
26
DRIFT
F. Sauli-Short Courses-IEEE-NSS 2002-PART 1
MAGNETIC FIELD EFFECTS:
DISTORSIONS IN DRIFT CHAMBERS
W. de Boer et al, Nucl. Instr. and Meth. 156(1978)249
27
DRIFT
F. Sauli-Short Courses-IEEE-NSS 2002-PART 1
MAGNETIC FIELD EFFECT:
COORDINATE DISTORSIONS IN MICRO-STRIP CHAMBERS
F. Angelini et al, Nucl. Instr. and Meth. A347(1994)441
28
DRIFT
F. Sauli-Short Courses-IEEE-NSS 2002-PART 1
TRANSVERSE DIFFUSION: SUBSTANTIALLY REDUCED IN SOME GASES
TIME PROJECTION CHAMBER:
Center-of-gravity of cathode signal
B=0
E // B
B>0
D. Nygren, TPC proposal (PEP4, 1976)
29
DRIFT
F. Sauli-Short Courses-IEEE-NSS 2002-PART 1
STABILITY OF OPERATION
VOLTAGE AND PRESSURE
THE DRIFT VELOCITY IS A FUNCTION OF REDUCED FIELD E/P
E 
w = f  
P 
DRIFT VELOCITY SATURATION:
INSENSITIVE TO VARIATIONS OF E AND P
E
P
30
DRIFT
F. Sauli-Short Courses-IEEE-NSS 2002-PART 1
STABILITY OF OPERATION
TEMPERATURE
Dw DT 3.4 10 -3
=

w
T
C
AT LOW FIELDS (THERMAL ELECTRONS):
At high fields, the thermal coefficient in some gases decreases and even becomes negative:
Dw/w/ºC
CO2
4
Methylal
3
2
C4H10
A-C4H10-Methylal
66-30-4
A
1
0
CH4
-1
100
500
1000
2000
E (V/cm)
G. Shultz and J. Gresser, Nucl. Instr. and Meth. 151(1978)413
31
CAPTURE
F. Sauli-Short Courses-IEEE-NSS 2002-PART 1
ELECTRON CAPTURE LOSSES ON ELECTRONEGATIVE GASES
Attachmant coefficient of oxygen:
Electrons surviving after 20 cm drift (E = 200 V/cm):
The attachment cross section is
energy-dependent, therefore
strongly depends on the gas
composition and electric field
32
CAPTURE
F. Sauli-Short Courses-IEEE-NSS 2002-PART 1
ELECTRON CAPTURE - VERY SENSITIVITE TO GAS MIXTURE
Energy resolution of a proportional counter with two gas fillings (and some leaks!):
5.9 keV X-rays
“Hot” gas
ARGON-ETHANE 50-50
“Cold” gas
DIMETHYLETHER
R. Openshaw, TRIUMF (private, 2000)
33
DRIFT
F. Sauli-Short Courses-IEEE-NSS 2002-PART 1
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
34
CAPTURE
F. Sauli-Short Courses-IEEE-NSS 2002-PART 1
ELECTRON CROSS SECTIONS IN CF4
http://consult.cern.ch/writeup/magboltz/cross/
35
MULTIPLICATION
F. Sauli-Short Courses-IEEE-NSS 2002-PART 1
INCREASING THE FIELD TOWARDS CHARGE MULTIPLICATION
Electrons energy distribution at increasing fields:
Excitation Ionization
10.5 eV
15.5 eV
0.2 kV/cm
IONIZATION 15.7 eV
5 kV/ cm
EXCITATION 11.6 eV
1 kV/ cm
0
5
10
15
20
25
30
Electron energy (eV)
36
MULTIPLICATION
IONIZATION CROSS SECTION
AND TOWNSEND COEFFICIENT
F. Sauli-Short Courses-IEEE-NSS 2002-PART 1
Mean free path for ionization
=
1
Ns
N: molecules/cm3
Townsend coefficient
=
1

Ionizing collisions/cm
S.C. Brown, basic data of plasma physics (MIT press, 1959)
37
MULTIPLICATION
F. Sauli-Short Courses-IEEE-NSS 2002-PART 1
AVALANCHE MULTIPLICATION IN UNIFORM FIELD
Combined cloud chamber-avalanche chamber:
E

x
Ions
dn = n  dx
n(x) = n0e x
Multiplication factor or Gain
n
x
M(x) = = e
n0
Electrons
H. Raether
Electron avalanches and breakdown in gases
(Butterworth 1964)
38
MULTIPLICATION
F. Sauli-Short Courses-IEEE-NSS 2002-PART 1
MEASUREMENT OF THE TOWNSEND COEFFICIENT
Current vs voltage for constant charge injection in a parallel plate counter:
Radiation
M
V
1
s
I
=
ln M
s
39
MULTIPLICATION
F. Sauli-Short Courses-IEEE-NSS 2002-PART 1
TOWNSEND COEFFICIENT IN GAS MIXTURES
ARGON-CH4:
in Argon
A. Sharma and F. Sauli, Nucl. Instr. and Meth. A334(1993)420
40
MULTIPLICATION
F. Sauli-Short Courses-IEEE-NSS 2002-PART 1
SIGNAL DEVELOPMENT
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
41
MULTIPLICATION
F. Sauli-Short Courses-IEEE-NSS 2002-PART 1
PARALLEL PLATE COUNTERS: SIGNAL DEVELOPMENT (CHARGE COLLECTION ONLY)
Single charge +Q:
CATHODE
Charge induced on each electrode by +Q moving
through the difference of potential dV:
V= -V0
dq = Q
s
s0
+Q
dV
ds
=Q
V0
s0
Integrating over s (or time t):
ANODE
q(s) =
V=0
Q
s
s0
q(t ) =
Q
wt
s0
w: drift velocity
Electrons- ion pair (-Q and +Q) released at the same distance s from the cathode :
w-t wt 
q(t ) = Q
 s  s 
 0  t  T
 0
0 
s - s wt 

0
q(t ) = Q
 s  s 
 T  t  T
 0
0 
q(t )
Q
w- (w+ ) : electron (ion) drift velocity
T- (T+ ) : total electron (ion) drift time
Total signal:

q(T ) = Q
Q
s0 - s
s0
(+Q on cathode , -Q on anode)
T-
T
t
42
MULTIPLICATION
F. Sauli-Short Courses-IEEE-NSS 2002-PART 1
PARALLEL PLATE COUNTERS: SIGNAL DEVELOPMENT (CHARGE MULTIPLICATION)
-V0
During the avalanche development, the increase in
the number of charges after a path ds is:
s
n = n0e
s
s0
and the total after a path s:
dn = n ds
0
The incremental charge induction due to electrons after a path s:
dq- = -en0es
Integrating over s:
ds
s0
en0 s
en0 s en0 w-t
q (s) =
(e -1) 
e =
e
s0
s0
s0
-
and the corresponding current :
dq- en0w - w-t en0 w-t
i (t ) =
=
e
= - e
dt
s0
T
-
The current signal iduced by the ions is instead given by:
en0  w-t w*t 
 0  t  T i (t ) =  e
-e

T 
en0  s w* t  
 T  t  T 
i (t ) =  e - e

T 

1
w*
=
1
1
w
w-


43
MULTIPLICATION
F. Sauli-Short Courses-IEEE-NSS 2002-PART 1
PARALLEL PLATE COUNTERS: SIGNAL DEVELOPMENT (CHARGE MULTIPLICATION)
Fas electron signal
Slow ion tail
44
MULTIPLICATION
F. Sauli-Short Courses-IEEE-NSS 2002-PART 1
SIGNAL DEVELOPMENT
WIRE PROPORTIONAL COUNTERS:
Thin anode wire coaxial with cathode
Cathode radius b
Electric field:
CV0 1
E(r) =
2e 0 r
C=
2e 0
ln b a
Anode radius a
Avalanche development around a thin wire:
+
+
+
+
+
+
+
+
+
45
MULTIPLICATION
F. Sauli-Short Courses-IEEE-NSS 2002-PART 1
PROPORTIONAL COUNTERS: GAIN CHARACTERISTICS
ln M
Streamer
Saturation
Breakdown
Multiplication
Collection
Attachment
n1
n2
IONIZATION
CHAMBER
PROPORTIONAL
COUNTER
Voltage
46
MULTIPLICATION
F. Sauli-Short Courses-IEEE-NSS 2002-PART 1
PROPORTIONAL COUNTERS: SIGNAL DEVELOPMENT
Incremental charge induced by Q moving through dV:
dQ =
Q
Q dV
dV =
dr
V0
V0 dr
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 a  dV
QC a  
q =

dr = ln
V0 a dr
2e0
a
-
Q b dV
QC
b
q =

dr = ln
V0 a  dr
2e0 a  

and
QC b
ln = -Q on the anode
2e0 a
q - ln( a   ) - ln a
=
The ratio of electron and ion contributions:

ln b - ln( a   )
q
The total induced signal is
q = q-  q = -
For a counter with a=10µm, b=10 m: q-/q+ ~1%
( Q on the cathode)
The electron-induced signal is negligible
Neglecting electrons, and assuming all ions leave from the wire surface:
t
QC r(t)
q(t ) = q (t ) = -  dq = ln
2
e
a
0
0

dr
 CV0 1

= E =
dt
2e 0 r
QC   CV0 
QC  t 
q(t ) = ln 1
t = ln 1 
2 
2e0 
2
e
 2e0a 
0  t 0 
Total ions drift time:
e0 (b2 - a2 )
T =
 CV0

i(t ) = -
 CV0
r(t) = a 
t
2e0
2
QC 1
2e0 t0 t
q(T  ) = -Q
47
MULTIPLICATION
F. Sauli-Short Courses-IEEE-NSS 2002-PART 1
CHARGE SIGNAL:
q(t)
q(t)
Q
0
0.2
0.4
0.6
0.8
1.0
t (µs)
0
100
200
300
400
500
t (µs) T+
AMPLIFIER TIME CONSTANT;
50 ns
q(t)
CURRENT SIGNAL:
i(t)
100 ns
300 ns
0
20
40
60
80
100
t (ns)
0
100
200
300
400
500
t (ns)
48