Blum W., Riegler W., Rolandi L. Particle Detection with Drift Chambers
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Index
AC coupling, 198, 209, 210
Accuracy in magnetic field
angular variation, 269
Accuracy of curvature, 298, 304
improvement with wire spacing, 302
track through scattering medium, 310
Admittance matrix, 166
Ageing, 429–439
contaminants to be avoided, 435
effect of a soft tube, 435
total collected charge, 430
Ageing experience (table), 431
Ageing tests
high flux regime, 435–439
low flux regime, 433–435
ALTRO chip, 247
Amplification factor (gain) of proportional
wire, 132–138, see also Avalanches
and gas density, 136
and sense wire voltage, 136
and space charge, 142–144
local variations, 138–144
statistical variations, 145–154
Amplifier
charge, 192
current, 182, 192
integration time of, 199
linear, 181
operational, 182
peaking time of, 192
sensitivity of, 192
voltage, 182, 192
Angular pad effect, 264
Arrival time
average of many electrons, 272
diffusion, 275
drift path variations, 254, 273
of the Mth electron, 272
ASDBLR frontend, 246
ATLAS CSC frontend, 247
ATLAS muon drift chamber, 386
ATLAS muon spectrometer, 387
ATLAS transition radiation tracker TRT, 436
Avalanche force on the wire, 279
Avalanches, 126, see also Amplification factor
(gain)
fluctuations measured with laser tracks, 152
in electronegative gases, 147
in strong homogeneous fields, 149
in strong non-uniform fields, 151
in weak fields, 145
lateral extent, 130
role of photons, 126
Axial stereo chambers, 377
Axial wire chambers, 366, 377
Ballistic deficit, 193, 199
Bandwidth limit, 192
unipolar and bipolar shaper, 197
Baseline shift and fluctuation, 206–211
Bethe-Bloch formula, 29
modified, 32
Blanc’s law, 61
Bloch–Bradbury process, 76
Bragg’s additivity rule, 31
Campbell’s theorem, 207, 209, 218
Capacitance, 160
drift tube, 170
electrode, 168
Capacitance matrix, 158
calculation of, 168
Cathode charge distribution, 176
Cathode deposits, 432
443
444 Index
Cathode radius
equivalent, 175
tube, 163
Cathode signal, 164, 176
Central-limit theorem of statistics, 145
Cerenkov radiation, 26
Chambers without field shaping electrodes,
375
Characteristic energy of electrons, 69
Charge
induced, 161
interpolation of cathode, 179
Charge measurement
electronics for, 234
Charge transfer, 426
Charpak chamber, 362
Cluster counting, 345
Cluster size fluctuations
influence on resolution, 257–261
Cluster-size distribution, 15–18
role of large clusters, 21
Cold gas, 69, 414
Constant charge density in volume, 142
Convolution, 183, 184, 186, 188, 198
Coordinate measurement
accuracy depending on drift length, 263
accuracy in drift direction, 270–277
accuracy in wire direction, 261–270
accuracy of single wire, 253–261
influence of cluster fluctuations
(appendix), 282–288
contribution of several wires, 265
different methods, 251
fundamental limits of accuracy Chap. 7,
251–288
in the wire direction, 368
using pads, 268
CR filter, 187
delta response of, 188
transfer function of, 187
Cross induced signal, 174
Cylindrical drift chambers of type 2, 377–397
Dark currents, 430
DC coupling, 198, 210
Declustering through diffusion, 260, 269, 288
Delta response, 185–187
bipolar and unipolar shaper, 195
CR and RC filter, 188
infinite cusp, 233
Pole-zero filter, 191
Density effect for energy loss, 32
Diethorn formula, 134
Diethorn parameters measured, 136
Diffusion, 67–75
electric anisotropy, 70
limits achievable, 414
magnetic anisotropy, 72, 83
measurement of, 89
measurements, 83
width, 69
widths after 1 cm of drift, 416
Diffusion constant, 67–70
isotropic, 83
Diffusion tensor, 74
Discriminator, 236
Dissociative attachment, 76
Drift cells, 380–383, 393–397
Drift chamber gases Chap. 12, 413–439
Drift Chap. 2, 49, 94
Drift direction, 49
Drift field by electric charges on insulator, 375
Drift field distortions from space charge, 315
Drift tubes, 98–104
perfect, 99
Drift velocity, 49–67, 81–94
and minor H
2
O contamination, 422
in crossed fields, 92
in electromagnetic field, 64–67, 82
of electrons, 53–56
of ions, 56–63
Effective number of electrons, 35, 37
definition, 36
measurement, 37
Effective number of electrons N
eff
, 257
analytic expression, 287
diffusion dependence, 260, 288
measurement, 269
Einstein formula for diffusion, 69
Electric charge in the drift region, 315
Electroluminescence, 408
Electron attachment, 75–79
three–body attachment processes, 76–79
two–body attachment process, 76
Electron attachment and construction material,
422
Electron energy, 54, 68, 415
dependence on electric field, 70, 87
Electron velocity distribution, 79
in magnetic field, 82
Electrostatic wire stability, 104
Energy loss, 9
and dielectric constant, 10
density dependence, 29
density effect, 32
logarithmic divergence, 15
cut-off, 32–34
Index 445
most probable, 34
plateau, 26
relativistic rise, 26
restricted, 32
sample length dependence, 30
velocity dependence, 24, 28
Energy loss dE/dx, see also Ionization
Energy transfer, 14
Equilibrium velocity in electron drift, 54
Equivalent input noise
cathode channel, 225
definition of, 224
transmission line channel, 230
wire channel, 231
Equivalent noise charge (ENC)
cathode channel, 227
definition of, 226
transmission line channel, 230
wire channel, 231
Error propagation into track parameters, 292
Existing Drift Chambers Chap. 11, 361–409
External particle identifier, 404
Extrapolation to a vertex, 302–306
Extreme accuracy, 407
Fermi plateau, see plateau
Field cage
electrode configuration, 120
irregularities, 121
non-linear resistor chain, 121
one wrong resistor, 123
Field cages, 118–124
Field correcting strips, 139
Field wires, 97
First operational drift chamber system, 363
First Townsend coefficient, 133
Flame tests, 417
Free dielectric surfaces, 119
Gain drop
measured in background radiation, 144
near chamber edge, 138
Gain variation
due to mechanical imperfections, 141
with atmospheric pressure, 138
Gas
inflammable mixtures, 416–419
Gas choice, general considerations, 413
Gas pressure
and drift field distortions from space charge,
429
and electric and magnetic fields, 83, 427
and point measuring accuracy, 427
choice of, 426–429
influence on various parameters (table), 428
Gas purity and electron attachment, 420–423
Gating grid, 112–118
asynchronous trigger, 320
bipolar, 319
bipolar in magnetic field, 319
calculation of transparency, 113–117
condition of full transparency, 113
effect on spatial resolution, 328
electron transparency, 117, 320, 327, 328
monopolar, 318
setting the potential, 118
synchronous trigger, 320
transparency under various conditions,
320–328
Geiger mode, 130
Geometrical types 1, 2 and 3 of drift chambers,
361
Gravitational wire sag, 101
electrostatic amplification, 103
maximum stresses in some wire materials,
102
measurement through oscillation, 103
H
2
O contamination and effect on drift velocity,
422
High track densities, 388
History of drift chambers, 362–365
Hot gas, 414
Impedance
amplifier input, 211, 224
cathode channel, 225
chamber, 217
circuit element, 185
noise of a passive, 220
transmission line channel, 229
voltage and current amplifier, 192
voltage buffer input, 191
wire channel, 231
Impedance matrix, 166
Inflammability
and UV absorption power, 419
limits of concentration, 416, 417
Input circuit, 211
Intermediate excited states, 3
Ion drift in gas mixtures, 59
Ion Gates Chap. 9, 315–328
and limitation of space charge, 315
and wire chamber ageing, 318
Ion mobilities, 60, 62
in gas mixtures, 61
Ionization, see also Energy loss dE/dx
average, 21
446 Index
average energy to produce 1 ion pair, 4, 6
by laser rays, 38
chemical compounds used for, 38
corrections to measurement, 347
cross-sections, 1, 3
curve, 334
different mechanisms, 3
distributions, 19
estimator for strength, 338
max. likelihood meth., 338
truncated mean, 338
increase by adding compound, 6
measured pulse height distributions, 25
measurement
accuracy, 339–344
statistical treatment, 337
most probable, 18
number of collisions per cm of track, 2
of electrons to that of pions at 15 GeV/c, 336
primary and secondary, 3
pulseheight distributions
widths, 20, 343
retarded, 7
Ionization amplification Chap. 4, 125–154
Ionization potentials, 6
Isotropic diffusion coefficient, 83
Jesse effect, 4
Jet chamber geometry, 381
Jitter, 237
Kirchhoff’s law, 184
Knock-on electrons
range of, 7, 8
Landau distribution, 22, 23, 34
Langevin equation, 49
Laplace and Fourier Transform
relations for, 184
Laplace and Fourier transform, 183
Large cylindrical drift chambers, performance
of some (tables), 378
Laser ionization
dependence on chemical compounds in the
gas, 38, 424–426
dependence on wavelength, 42
Laser-beam optics, 44
diffraction limitation, 45
Heisenberg’s uncertainty principle, applied
to, 45
Liouville’s theorem applied to, 44
minimum width, 46
phase space diagrams, 44
Left-right ambiguity, 368
Light-tracks simulating particle tracks, 46
Limited streamer, 128
Linear signal processing, 183
Lorentz angle, 367, 413
Magnet spectrometer, typical, 365
Magnetic spectrometer resolution, 311
multiple scattering dominating, 312
Main drift chambers, 366
Malter effect, 430
Maxwell distribution of electron velocities, 80
Mean excitation energy, 29
Mean time between collisions, 54
Metastable state (in ionization), 4
Mobility
of electrons, 50
of ions, 57
Mobility tensor, 50, 82
Momentum resolution in spectrometer, 311
limit of multiple scattering, 312
Multiwire proportional chamber, 361
Muon chambers of L3 experiment, 373
n-th order cross-section equivalent, 38
Nernst–Townsend formula, 69
Noise, 213–234
amplifier, 222
chamber+amplifier, 223
equivalent input, 224
Flicker or 1/f, 221
linear network, 215
parallel and series, 222
passive impedance, 220
power spectrum of, 214
shot, 218
thermal or Johnson, 219
white, 215
zero crossing frequency of, 215
Noise corner time constant, 227, 233
Norton’s theorem, 216
Optimal tracking procedure, 310
Optimum filter, 231, 239
Pad dimension, choice of, 268
Pad response function, 178
Parseval’s theorem, 184
Particle identification Chap. 10
momentum ranges in argon, 334
Particle identification Chap. 10, 331–358
principles, 331–334
Particle mass determination, 331
Particle separation
Index 447
Performance achieved in existing detectors,
349–358
Particle separation power, 333, 344
PASA frontend, 247
Peaking time
definition of, 192
optimum, 238, 240
delta signal, 227
wire chamber signal, 229
tail cancellation and, 203
unipolar and bipolar shaper, 196
Penning effect, 4
Photo-absorption ionization (PAI) model, 11
applications, 335, 340
Photo-ionization cross-section, 12
Pileup of signals, 205
Planar drift chambers of type 1, 368–377
Planar drift chambers of type 1, performance
of some (tables), 370
Plasma frequency for optical dispersion, 27
Plateau of the energy loss, 27
and density of the medium, 27
Poisoning of the gas by construction material,
422
Poisoning times (table), 423
Pole-zero filter, 187
delta response of, 203
tail cancellation with a, 201, 202
transfer function of, 189
Polya functions, 152
Precision drift chamber, 408
Proportional wire, 125–128
Quench gases, 128
Radial drift field chamber, 403
Ramo’s theorem, 160
Ramsauer minimum, 55, 86
Random pulses on wire, 279
Random velocity of drifting electrons, 54
Random velocity of drifting ions, 57
Range of delta rays, 33
Range of primary electrons, 7, 8
RC filter, 187
delta response of, 188
transfer function of, 187
Reciprocity theorem, 158
Reduced electric and magnetic fields, 83
Regime of proportionality, 126
Relativistic rise of energy loss
dependence on gas density, 29, 335
dependence on sample length, 336, 340
Relaxation techniques for electrostatic
calculations, 98
Resolution formula, 341, 343
Rutherford scattering, 15
Safe chamber gas, 418
Safe gas mixtures (tables), 419
Sagitta measuring error, 298
Sagitta of a track, 298
Saturated drift velocity, 413
Secondary electron tracks, 14
Sensitivity
definition of, 192
unipolar and bipolar shaper, 196
Shape of the ionization curve, 334–336
5-parameter form, 336
Shaping, unipolar and bipolar, 195–200, 210
Signal induction, 157–179
cathode strip, 176
current, 160
drift tube, 163
electron, 164
ion, 163, 165
multiwire chamber, 172
principle of, 157
sum of, 161
voltage, 165
Signal to noise ratio, 232
Slope to noise ratio, 238
Small drift chambers of type 2, performance of
some (tables), 391
Space charge fluctuations, 281–282
Spiral projection chamber, 403
Spread of arrival times of electrons, 252
Spread of electrons along the wire, 252
Stability of a linear system, 187
Staggering of sense wires, 368, 380
Step function, 188
Stereo chambers, 377
Sternheimer correction to Bethe-Bloch
formula, 32
Stoichiometric ratio for complete combustion,
416
Streamer charge distribution, 129
Strength of the ionization, 332
Tail cancellation, 200–205
Thevenin’s theorem, 216
Thin-field emission effect, 430
Three-body attachment coefficients, 78, 421
Three-body attachment to O
2
, 420–421
Three-component gas mixtures (diagrams),
418
Time constant t
0
, characteristic, 163, 173
Time measurement
electronics for, 235
448 Index
Time walk, 240
Tonks’ theorem, 52
Townsend (unit), 56
TPC concept, 364
TPC field configuration, 111
TPC’s, performance of some (tables), 400
Track parameters
covariance matrix, 300, 303, 305
loss of accuracy due to magn. field, 300
quadratic fit, 294
straight line fit, 292
Track parameters Chap. 8, 291–313
Transfer function, 185–187
Zero-pole and Pole-zero filter, 189
cascaded elements, 191
CR and RC filter, 189
optimum filter, 233, 235, 239
poles and zeros of, 185
unipolar and bipolar shaper, 195, 196
Truncated mean for ionization measurement,
338
Two-body attachment rate constant, 76
Two-photon ionization, 39
rate equations for, 39–41, 43
Type 1 drift chambers, 361, 368–377
Type 2 drift chambers, 364, 377–397
Type 3 drift chambers (TPC’s), 364, 397–406
UA1 central drift chamber, 384
Van der Waals unstable molecules, 78
Vertex chambers, 366, 390–397
W-values, 4, 24
Weighting field, 161
drift tube, 163
multiwire chamber, 173
time dependent, 171
Weighting potential, 161
Whiskers on electrodes, 432
growth measured (table), 433
Wire E ×B effect, 261
Wire deposits, 430
Wire direction and magnetic field, 366
Wire excitation by avalanches, 279
Wire grids, 105–112
capacitance matrix, 109
superposition, 108
surface charge density, 113
Wire positioning error, 99
Wire pulse heights, 151
Wire signal, 163, 173
Wire vibrations, 277–280
Yule-Furry law, 147
Z-chambers, 377
Zero-pole filter, 187
transfer function of, 189