Transcript Document

TITLE
FUNDAMENTS - 1
PRINCIPLES OF GAS DETECTORS
Fabio Sauli
TERA Foundation
CERN
CH-1211 Geneva Switzerland
Part 1: Fundaments
Part 2: Detectors
[email protected]
http://fabio.home.cern.ch/fabio/
http://gdd.web.cern.ch/GDD/
F. Sauli - Gas Detectors - KEK March 14, 2009
BASIC BIBLIOGRAPHY
FUNDAMENTS - 2
D.H. Wilkinson: Ionization Chambers and Counters (Cambridge Univ. Press, 1950)
S.A. Korff: Electron and Nuclear Counters (Van Nostrand, 1955)
P. Rice-Evans: Spark, Streamer, Proportional and Drift Chambers (Richelieu, 1974)
F. Sauli: Principles of Operation of Multiwire Proportional and Drift Chambers (CERN 77-09, 1977)
Th. Ferbel, Editor: Techniques and Concepts of High-energy Physics (Plenum, 1983)
R.C. Fernow: Introduction to Experimental Particle Physics (Cambridge Univ. Press, 1986)
W.R. Leo: Techniques for Nuclear and Particle Physics Experiments (Springer, 1987)
C. Fabjan and J. Pilcher, ed.: Instrumentation in Elementary Particle Physics (World Scientific, 1988)
C.F.G. Delaney and E.C. Finch: Radiation Detectors (Clarendon Press, 1992)
R. Gilmore: Single Particle Detection and Measurement (Taylor and Francis, 1992)
F. Sauli, ed.: Instrumentation in High Energy Physics (World Scientific, 1992)
K. Grupen: Particle Detectors (Cambridge Monographs on Part. Phys. 1996)
K. Kleinknecht: Detectors for Particle Radiation (Cambridge Univ. Press 1998)
G.F. Knoll: Radiation Detection and Measurements, 3d Ed. (Wiley, 2000)
W. Blum, W. Riegler and L. Rolandi: Particle Detection with Drift Chambers, 2d Ed. (Springer 2008)
F. Sauli - Gas Detectors - KEK March 14, 2009
ENERGY LOSS
FUNDAMENTS - 3
DIFFERENTIAL ENERGY LOSS OF CHARGED PARTICES (Z=1) IN MATERIALS:
Expressed in MeV g-1 cm2, the differential
energy loss is equal within a factor of two
for all materials (except H2):
 (g cm 2 )   (g cm 3 ) l(cm)



dE 1 dE

d  dx
 : density
dE
~ 1.5 MeV g 1 cm2
d
SEE:
Review of Particle Physics
Physics Letters B 667(2008)1-1340
http://pdgLive.lbl.gov
F. Sauli - Gas Detectors - KEK March 14, 2009
PHYSICAL PROPERTIES OF GASES
FUNDAMENTS - 4
DIFFERENTIAL ENERGY LOSS, PRIMARY AND TOTAL IONIZATION FOR MINIMUM
IONIZING, Z=1 PARTICLES
NORMAL TEMPERATURE AND PRESSURE (NTP: 20°C, 1 ATMOSPHERE)
GAS
Ne
Ar
Xe
CH4
C2H6
i-C4H10
CO2
CF4
Density
g cm-2
0.839 10-3
1.66 10-3
5.495 10-3
0.667 10-3
1.26
2.49 10-3
1.84 10-3
3.78 10-3
EX
eV
16.7
11.6
8.4
8.8
8.2
7
10
EI
eV
21.6
15.7
12.1
12.6
11.5
10.6
13.8
16
WI
eV
30
25
22
30
26
26
34
54
dE/dx
keV cm-1
1.45
2.65
6.87
1.61
2.91
5.67
3.35
6.38
NP
cm-1
13
25
41
37
48
90
35
63
NT
cm-1
50
106
312
54
112
220
100
120
Z : atomic number ; A : atomic mass;
: density
Ex, Ei : first excitation and ionization potentials
wi: average energy per ion pair
nP , nT : primary and total ion pairs per cm
(From various sources)
F. Sauli - Gas Detectors - KEK March 14, 2009
PRIMARY IONIZATION
FUNDAMENTS - 5
ELECTRON-ION PAIR PRODUCTION
Coulomb interactions between the electric field of the particle and of
the molecules of the medium produce electron-ion pairs.
Multiple ionizing collisions follow Poisson’s statistics:
n k n
P  e
k!
n
k
Detection efficiency:

n: average
k: actual number
 1 P0n 1 en
Minimum ionizing particles in argon NTP (nP: 25 cm-1)

s (mm)
(%)
1
91.8
2
99.3
Distribution of the electron closest to an electrode:
A1n (x)  nenx
A1n (t)  nenwt
w: drift velocity (~ 5 cm µs-1)
Limit in time resolution of
proportional counters:
arrival at anode wire of the
closest electron.
F. Sauli - Gas Detectors - KEK March 14, 2009
SECONDARY AND TOTAL IONIZATION
FUNDAMENTS - 6
CLUSTER SIZE PROBABILITY IN ARGON
Primary electrons can
further ionize the medium
producing local electronion clusters. Occasionally,
the primary electron has
enough energy to produce
a long trail (delta
electron).
Total number of ion pairs:
nT 
E
E: energy loss
wi
wi : average energy per ion pair
The average ionization energy is about the same in all gases
 energy and type of particles.
and does not depend from
For minimum ionizing particles in Argon:
E = 2.4 keV/cm
wi = 26 eV
nT ≈ 90 ion pairs/cm
nT
3
nP
H. Fischle et al,
Nucl. Instr. and Meth. A301 (1991) 202
F. Sauli - Gas Detectors - KEK March 14, 2009
ELECTRONS RANGE IN MATERIALS
FUNDAMENTS - 7
Due to multiple scattering and ionizing
collisions, the penetration of electrons in
materials is shorter than the integrated
range along the path; the practical range is
the extrapolated thickness of material
absorbing all the electrons.
Practical range
Integrated path
Fit to experimental data (light elements):
r = 10 E
R
r

1.7
r : practical range in µg cm-2
E : electron energy in keV
R : range in cm
 : density in µg cm-3
H. Kanter, Phys. Rev. 121(1961)461
F. Sauli - Gas Detectors - KEK March 14, 2009
APPROXIMATE EXPRESSION FOR ELECTRON RANGE
FUNDAMENTS - 8
PRACTICAL ELECTRON RANGE IN GASES AT NTP
A 2 keV delta electron in argon STP has a
practical range of ~ 200 µm.
The asymmetry in released charge affects the
localization accuracy in detectors exploiting the
measurement of the center of gravity (Time
projection Chambers):
180 µm
REAL
COG
2 keV
F. Sauli - Gas Detectors - KEK March 14, 2009
FUNDAMENTS - 9
HEED
CALCULATION OF PRIMARY IONIZATION AND ELECTRON RANGE
PRIMARY CLUSTERS PER cm (STP):
ELECTRON RANGE IN ARGON (STP):
HEED
2 keV
140 µm
I. B. Smirnov, Nucl. Instr. and Meth. A554(2005)474
HEED:
http://consult.cern.ch/writeup/heed/
F. Sauli - Gas Detectors - KEK March 14, 2009
IONIZATION STASTISTICS - 1
FUNDAMENTS - 10
WIDE ENERGY LOSS SPREAD (LANDAU DISTRIBUTION)
The statistics of the energy loss, with wide fluctuations and a long tail (due to delta electrons) requires
statistical analysis of hundreds of samples for determination of the average (as done in Time Projection
Chambers)
I. B. Smirnov, Nucl. Instr. and Meth. A554(2005)474
F. Sauli - Gas Detectors - KEK March 14, 2009
IONIZATION STATISTICS - 2
FUNDAMENTS - 11
The presence of long range delta electrons can substantially
affect the localization accuracy:
DRIFT
Coordinate deduced from drift time:
~5%
CENTER OF GRAVITY
Coordinate from cathode induced charge
F. Sauli, Nucl. Instr. and Meth. 156 (1978) 147
G. Charpak et al, Nucl. Instr. and Meth. 167 (1979) 455
F. Sauli - Gas Detectors - KEK March 14, 2009
ELECTRONS DRIFT AND DIFFUSION
FUNDAMENTS - 12
Drift velocity and diffusion of electrons vary in a wide range, depending the gas mixture:
2k x
x 
e E
k : characteristic energy
x: drift distance
E: electric field
x 
Thermal limit:
The diffusion at equal E/P depends on the inverse square root of pressure:

DRIFT VELOCITY:
x 
2 KT x
e E
2k
e
P
E
x
P
DIFFUSION:

1.5 mm
250 µm
F. Sauli - Gas Detectors - KEK March 14, 2009
TRANSPORT THEORY OF ELECTRON DRIFT
FUNDAMENTS - 13
Charge transport processes are determined by electron-molecule cross sections:
MAGBOLTZ:
Montecarlo program to compute electron
drift and diffusion
S. Biagi, Nucl. Instr. and Meth. A421(1999)234
http://rjd.web.cern.ch/rjd/cgi-bin/cross
F. Sauli - Gas Detectors - KEK March 14, 2009
MIXTURES
FUNDAMENTS - 14
Addition to a noble gas of even small percentages of a molecular gas has dominant effect on the
electron cross section:
CO2 100
Ar 100
CO210
CO2 2
F. Sauli - Gas Detectors - KEK March 14, 2009
DRIFT VELOCITY
FUNDAMENTS - 15
ELECTRON DRIFT VELOCITY IN ARGON-METHANE MIXTURES:
(Computed with MAGBOLTZ)
F. Sauli - Gas Detectors - KEK March 14, 2009
FUNDAMENTS - 16
LONGITUDINAL AND TRANSVERSE DIFFUSION
At low electric fields, the diffusion is symmetric. At
moderate to high fields however the longitudinal diffusion
(in the direction of drift) is reduced.
TRANSVERSE DIFFUSION:
T
E Field
L
Drift
LONGITUDINAL DIFFUSION:
In drift chambers, the dispersive factor is the longitudinal diffusion (measured time in the direction of
the electric field)
In time projection chambers, the dispersive factor is the transverse diffusion (center of gravity of
charge induced on pad rows)
F. Sauli - Gas Detectors - KEK March 14, 2009
MAGNETIC FIELD
FUNDAMENTS - 17
B
The drifting electrons swarm is rotated by an angle B in
the plane perpendicular to E and B; the magnetic drift
velocity is wB ≤ w0
r r
E B
E

tan B   
B
wB 
E
wB
r r
E B
L   0
T 
w
 : mean collision time
wB  w0
s w
L B
r
B

E

B 1  2  2
  eB / m Larmor frequency
s
T
E
EB

wB
0
1  2 2


e

ExB
2 2 B(E  B)
E







m 1   2  2 
B
B 2 
Drift velocity
unchanged
The transverse
diffusion is reduced
Friction force theory
F. Sauli - Gas Detectors - KEK March 14, 2009
TRANSVERSE DIFFUSION IN MAGNETIC FIELD
FUNDAMENTS - 18
IN SOME GASES THE TRANSVERSE DIFFUSION IS STRONGLY REDUCED
Improves the precision of the projected coordinate measurement in Time Projection Chambers
r r
E B
200 V/cm
600 µm

50 µm
F. Sauli - Gas Detectors - KEK March 14, 2009
ELECTRON ATTACHMENT
FUNDAMENTS - 19
Electrons are lost by radiative or non-radiative capture to resulting in the formation of negative ions: e
+ a -> A- (+h). The attachment cross section is gas and energy-dependent, therefore strongly depends
on the gas composition and electric field. For equal amount of oxygen contamination, capture losses are
much more severe in “cold” gases. In the example, a 5% loss is observed for 20 cm drift for 15 ppm of
oxygen in A-CO2 or 800 ppm in Ar-CH4.
ELECTRONS SURVIVING AFTER 20 CM
DRIFT (E = 200 V/cm):
OXYGEN ATTACHMENT COEFFICIENT:
F. Sauli - Gas Detectors - KEK March 14, 2009
EXCITATION AND CHARGE MULTIPLICATION
FUNDAMENTS - 20
Electrons on the high side of the energy distribution reach the excitation and ionization levels,
inducing inelastic collisions.
CROSS SECTIONS AT HIGH ELECTRIC
FIELDS:
ELECTRONS ENERGY DISTRIBUTION IN
ARGON AT INCREASING FIELDS:
Ex=10.6 eV Ei=15.7 eV
EXCITATION 11.6 eV
IONIZATION
15.7 eV
F. Sauli - Gas Detectors - KEK March 14, 2009
INELASTIC COLLISION PROCESSES IN MIXTURES
FUNDAMENTS - 21
Radiative processes with the emission of a
short wavelength photon can induce various
kinds of secondary effects, as internal
reconversion to charge on of molecules with
low ionization potential or emission of
photoelectron at cathodes. Addition to noble
gases of molecular additives reduce these
effects directly, quenching the emissions, or
by absorption.
MAJOR PROCESSES:
Radiative recombination:
Radiative capture:
Dissociative capture:
Three-body collision:
Excimer formation and decay:
Penning effect:
A++ B -> AB + h
J.Meek and J. D. Cragg, Electrical
e + M -> M + h
Breakdown of Gases (Clarendon, 1953)
e + AB -> AB -> A + B
e + A = B -> A- + B
A* + A -> A*2 -> A + A + h
A*+ B -> A + B* + e [Ei(B) < Ex(A)]
F. Sauli - Gas Detectors - KEK March 14, 2009
PHOTON EMISSION SPECTRA IN NOBLE GASES
FUNDAMENTS - 22
The emission spectra after excitation and dimers formation of noble gases are peaked in the far
ultraviolet. The low ionization potential vapors used in Cherenkov ring imaging detectors, as
Triethylamine (TEA) and Tetrakis-dimethylamino ethylene (TMAE), added to noble gases, act as
internal wavelength shifters and result in the emission of photons at longer wavelengths:
Relative light yield 15
1.0
10
0.8
5
Kr
4
3
Energy (eV )
2
TEA
TMAE
0.6
Ar
0.4
Xe
0.2
0
100
200
300
400
500
600
W avelength (nm)
IMAGING CHAMBERS
SCINTILLATING PROPORTIONAL COUNTERS
F. Sauli - Gas Detectors - KEK March 14, 2009
COLLISIONAL IONIZATION: TOWNSEND COEFFICIENT
FUNDAMENTS - 23
Electrons acquiring enough energy from the field can have ionizing collisions with molecules, resulting in
with creation of an electron-ion pair.
Mean free path for ionization:
First Townsend coefficient:


1

1
N
N: molecules/cm3
Ionizing collisions/cm
TOWNSEND COEFFICIENT FOR NOBLE
GASES:
TOWNSEND COEFFICIENT FOR Ar-CH4:
(MAGBOLTZ)
F. Sauli - Gas Detectors - KEK March 14, 2009
AVALANCHE MULTIPLICATION IN UNIFORM FIELD
E
FUNDAMENTS - 24
VISUALIZATION OF AVALANCHES
COMBINING A CLOUD CHAMBER
WITH AN AVALANCHE CHAMBER:
l
x
Ions
Electrons
At each mean free path for ionization, electrons create an
electron-ion pair; results an exponential increase of charge,
with fast electrons on the front and slow ions left behind.
Incremental increase of the number of electrons in the
avalanche:
n(x)  n0e x
dn  n  dx
Multiplication factor or Gain:
n
x
M(x)   e
n0
Maximum Avalanche size before discharge (Raether limit):
QMAX ≈ 107 e
H. Raether, Electron Avalanches and
Breakdown in Gases (Butterworth 1964)
F. Sauli - Gas Detectors - KEK March 14, 2009
SIGNAL INDUCTION ON ELECTRODES
FUNDAMENTS - 25
The multiplying and moving charges in the
avalanche induce signals on the electrodes.
The incremental charge induction due to electrons
after a path s:
dq  en0es
ds
s0
Integrating over s:
en0 s
en0 s en0 wt

q (s) 
(e 1) 
e 
e
s0
s0
s0
and the corresponding current :
dq en0 w w  t en0 w  t
i (t) 

e
  e
dt
s0
T

The current signal induced by ions is given by:
en0  wt w*t 

 0  t  T 
i (t )   e
e

1
1
T 
*
w
en0  s w* t  



i (t )   e  e
T  t T

T 


w

Fast electron signal

1
w
Slow ion tail
J. Townsend, Electrons in Gases
(Hutchinson 1947)
F. Sauli - Gas Detectors - KEK March 14, 2009
AVALANCHE STATISTICS IN UNIFORM FIELDS
FUNDAMENTS - 26
In constant electric field, the probability of an avalanche started by a single electron to have a size N is
given by Furry’s law:
N
1 N
P(N)  e
N
SIZE DISTRIBUTIONS FOR AVALANCHES
STARTED BY 1, 2,... 10 ELECTRONS:
N  e s : average multiplication factor
on the gap s

The maximum probability is for N=0 (no
multiplication!).
N 
P ,n
N 
The Furry distribution has a variance equal to

the average:
N
N
1
For an avalanche started by n electrons:

N 
P(n, N )   
N 
n1

N
N
N N
e
(n 1)!

H. Genz, Nucl. Instr. and Meth. 112(1973)83

F. Sauli - Gas Detectors - KEK March 14, 2009
AVALANCHE SIZE DISTRIBUTION
At large gains (high fields) the
avalanche distribution is described
by a Polya function:
(k  1) k1 k (k1)z z  N
P(z) 
z e
N
(k  1)
for k integer
FUNDAMENTS - 27
AVALANCHE SIZE
DISTRIBUTIONS AT
INCREASING FIELDS:
POLYA DISTRIBUTIONS:
(k  1)  (k)!
of the Polya
The relative variance
distribution is:

2
 N  1
1
1
 bb
   
 N  N 1  k N
For k=0 the distributions reduce to
a Furry law.
• The shape of the single electron avalanche distribution has
a major relevance in determining the energy resolution of
proportional counters
• A peaked single electron pulse height distribution provides
efficient detection (RICH)
H. Sclumbohm,
Zeit. Physik 151(1958)563
F. Sauli - Gas Detectors - KEK March 14, 2009
PROPORTIONAL COUNTER
FUNDAMENTS - 28
Thin anode wire of radius a, coaxial with a cylindrical cathode of radius b
Potential:
C
2 0
ln b 
a

CV0 1
2 0 r
CV0 r
V (r) 
ln
20 a
E(r) 
V (b)  V0
capacitance per unit length

AVALANCHE REGION
V(a)  0
ELECTRIC FIELD
Electric field:
DRIFT AND COLLECTION REGION
Cathode radius b
THRESHOLD FIELD FOR
MULTIPLICATION
Anode radius a
a
DISTANCE FROM CENTER
F. Sauli - Gas Detectors - KEK March 14, 2009
PROPORTIONAL COUNTER: AVALANCHE DEVELOPMENT
Electrons approach the anode; on reaching
a critical value of field strength, they start
an avalanche multiplication, continuing
until the front reaches the wire. Ions are
left behind in a characteristic drop shape.
The extent by which the avalanche
surrounds the wire depends on gas,
geometry and gain.
+
+
-
+
ln M
GAIN CHARACTERISTICS:
At increasing fields, to a region of
charge collection (ionization chamber)
follows a region of multiplication with
the detected charge proportional to the
initial ionization. At higher voltage
follow a region of limited
proportionality, saturation (with the
output charge independent from initial
ionization), streamer formation and
breakdown.
+
+
-
+
FUNDAMENTS - 29
+
+
+
Streamer
Breakdown
Saturation
Multiplication
Collection
Attachment
n1
n2
IONIZATION PROPORTIONAL
CHAMBER COUNTER
Voltage
F. Sauli - Gas Detectors - KEK March 14, 2009
PROPORTIONAL COUNTERS: INDUCED SIGNALS
FUNDAMENTS - 30
For an avalanche starting at a small distance  from the anode, the electron and ion contributions to the
induced charge are:
INDUCED CHARGE:
a

Q
dV
QC a  
q 

dr  
ln
q(t)
V0 a dr
20
a
q 
Q b dV
QC
b

dr  
ln
V0 a  dr
20 a  
Total induced signal on anode:
QC b
q  q  q  
ln  Q
20 a
Q
(+Q on cathode)
Ratio of electron and ion signals:
q  ln( a   )  ln a
~1% for typical geometry


ln b  ln( a   )
q
Time development of the signal on anode:
0
100
300
400 500
t (µs) T+
FAST SIGNAL DIFFERENTIATION:
50 ns
q(t)
100 ns
QC   CV0 
QC  t 

q(t )  
ln 
1
t


ln 1 
2 
20 
 20a  20  t 0 
Total ions drift time:
0 (b2  a2 )

T 
q(T  )  Q

 CV0
200
300 ns
t(ns)
0
100
200
300
400
500
F. Sauli - Gas Detectors - KEK March 14, 2009
PROPORTIONAL COUNTERS: ENERGY RESOLUTION
FUNDAMENTS - 31
The energy resolution is a convolution of ionization
statistics, avalanche spread and electronics noise:
 E   N   M   el 
          
 E   N   M  M 
2
2
For soft X-rays:
2
 N2  FN
Gain variance:
 M 2 1  A 2
    
 M  
N  A 
A
A
F: Fano factor
Single electron
avalanche variance
for a Polya avalanche distribution
2
 E  1
  (F  b)
 E  N
GAS
 Ar
Ar-CH4
RESOLUTION %
2
A
A
F(exp)
0.17
0.19
0.17
0.19
Xe
AVALANCHE
NOISE
b

F(calc)
TOTAL
IONIZATION
GAIN
PULSE HEIGHT SPECTRUM FOR 5.9 keV
X-RAYS IN P10 (Ar-CH4 90-10):

1.3
 0.22 fwhm E  9%
5.9
E
<0.17
Ne+0.5%Ar
0.05

fwhm 1.3 keV
For 5.9 keV X-rays (N~220):
E
E
 7%
for b=1
F. Sauli - Gas Detectors - KEK March 14, 2009
SCINTILLATING PROPORTIONAL COUNTERS
FUNDAMENTS - 32
In noble gases, at moderate electric fields before multiplication, there is a large emission of scintillation
photons. In proportional scintillation counters the detection of these photons eliminate the dispersion due
to the avalanches and achieve the best energy resolution (close to the statistical)
 E 2 F
  
 E  N
CHARGE AND LIGHT YIELD VS VOLTAGE:
SPHERICAL ANODE COUNTER:

Xe 99.95%
1030 torr
CHARGE
LIGHT
A.J.P.L. Policarpo et al, Nucl. Instr. and Meth. 102(1972)337
F. Sauli - Gas Detectors - KEK March 14, 2009
ENERGY RESOLUTION OF SCINTILLATION COUNTERS
55Fe
FWHM
E
 8.5%
 3.6%
E
E
X-RAYS (5.898 keV):
R
Xe 99.95%
1030 torr
Primary statistics limit:

E
E
241Am
FWHM 500 eV
FUNDAMENTS - 33

F
 2.8%
N
ENERGY SPECTRUM:

A.J.P.L. Policarpo et al,
Nucl. Instr. and Meth. 102(1972)337
H. E. Palmer, IEEE Trans. Nucl. Sci.NS-22(1975)100
Fluorescence analysis
X-Ray Spectroscopy
F. Sauli - Gas Detectors - KEK March 14, 2009
IMAGING CHAMBERS
The light emission in avalanches has been
exploited to detect tracks with simple optical
recorders (solid state cameras).
FUNDAMENTS - 34
COSMIC RAY ACTIVITY IN A 10x10x10
cm3 SENSITIVE VOLUME:
The UV light emission in the avalanches is
converted into the visible using an internal
wavelength shifter (TMAE gas) or a thin WLS
on the semi-transparent anode.
DRIFT VOLUME
AVALANCHE
MULTIPLICATION
M. Suzuki et al, Nucl. Instr. and Meth. A263(1988)237
F. Sauli - Gas Detectors - KEK March 14, 2009
3-D OPTICAL IMAGING CHAMBER
FUNDAMENTS - 35
IMAGES OF NUCLEAR DECAYS:
Optical imaging chamber with
recording of the projected image
using a CCD camera, and the time
profile of the emitted light with a
photomultiplier.
Simultaneous recording of
projection and time development of
the emission permits a 3-D
reconstruction of tracks.
Tested with radioactive ion beams
stopping in the gas volume.
K. Miernik et al, Nucl. Instr. and Meth. A581(2007)194
F. Sauli - Gas Detectors - KEK March 14, 2009