Particle Detection with Drift Chambers

By: Walter Blum, Werner Riegler, Luigi Rolandi

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Hardcover | 26 August 2008 | Edition Number 2

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468 Pages

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24.13 x 15.88 x 3.18

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A drift chamber is an apparatus for measuring the space coordinates of the trajectory of a charged particle. This is achieved by detecting the ionization electrons produced by the charged particle in the gas of the chamber and by measuring their drift times and arrival positions on sensitive electrodes. When the multiwire proportional chamber, or 'Charpak chamber' as we used to call it, was introduced in 1968, its authors had already noted that the time of a signal could be useful for a coordinate determination, and rst studies with a drift ch- ber were made by Bressani, Charpak, Rahm and Zupanci c in 1969. When the rst operational drift-chamber system with electric circuitry and readout was built by Walenta, Heintze and Schurlein ? in 1971, a new instrument for particle experiments had appeared. A broad study of the behaviour of drifting electrons in gases began in laboratories where there was interest in the detection of particles.

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Non-Fiction Science Physics Nuclear Physics Engineering & Technology Energy Technology & Engineering Nuclear Power & Engineering Particle & High-Energy Physics Atomic & Molecular Physics Technology in General Instruments & Instrumentation Engineering Engineering Measurement & Calibration

Electronics & Communications Engineering Electronics Engineering

Gas Ionization by Charged Particles and by Laser Rays	p. 1
Gas Ionization by Fast Charged Particles	p. 1
Ionizing Collisions	p. 1
Different Ionization Mechanisms	p. 3
Average Energy Required to Produce One Ion Pair	p. 4
The Range of Primary Electrons	p. 7
The Differential Cross-section d[sigma]/dE	p. 7
Calculation of Energy Loss	p. 9
Force on a Charge Travelling Through a Polarizable Medium	p. 9
The Photo-Absorption Ionization Model	p. 11
Behaviour for Large E	p. 15
Cluster-Size Distribution	p. 15
Ionization Distribution on a Given Track Length	p. 16
Velocity Dependence of the Energy Loss	p. 24
The Bethe-Bloch Formula	p. 29
Energy Deposited on a Track - Restricted Energy Loss	p. 32
Localization of Charge Along the Track	p. 35
A Measurement of N[subscript eff]	p. 37
Gas Ionization by Laser Rays	p. 38
The nth Order Cross-Section Equivalent	p. 38
Rate Equations for Two-Photon Ionization	p. 39
Dependence of Laser Ionization on Wavelength	p. 42
Laser-Beam Optics	p. 44
References	p. 46
The Drift of Electrons and Ions in Gases	p. 49
An Equation of Motion with Friction	p. 49
Case of E Nearly Parallel to B	p. 52
Case of E Orthogonal to B	p. 52
The Microscopic Picture	p. 53
Drift of Electrons	p. 53
Drift of Ions	p. 56
Inclusion of Magnetic Field	p. 64
Diffusion	p. 67
Electric Anisotropy	p. 70
Magnetic Anisotropy	p. 72
Electron Attachment	p. 75
Results from the Complete Microscopic Theory	p. 79
Distribution Function of Velocities	p. 79
Drift	p. 81
Inclusion of Magnetic Field	p. 82
Diffusion	p. 83
Applications	p. 83
Determination of [sigma]([epsilon]) and [lambda]([epsilon]) from Drift Measurement	p. 83
Example: Argon-Methane Mixture	p. 85
Experimental Check of the Universal Drift Velocity for Large [omega tau]	p. 88
A Measurement of Track Displacement as a Function of Magnetic Field	p. 89
A Measurement of the Magnetic Anisotropy of Diffusion	p. 89
Calculated and Measured Electron Drift Velocities in Crossed Electric and Magnetic Fields	p. 92
References	p. 94
Electrostatics of Tubes, Wire Grids and Field Cages	p. 97
Perfect and Imperfect Drift Tubes	p. 98
Perfect Drift Tube	p. 99
Displaced Wire	p. 99
Wire Grids	p. 105
The Electric Field of an Ideal Grid of Wires Parallel to a Conducting Plane	p. 105
Superposition of the Electric Fields of Several Grids and of a High-Voltage Plane	p. 108
Matching the Potential of the Zero Grid and of the Electrodes of the Field Cage	p. 110
An Ion Gate in the Drift Space	p. 112
Calculation of Transparency	p. 113
Setting of the Gating Grid Potential with Respect to the Zero-Grid Potential	p. 118
Field Cages	p. 118
The Difficulty of Free Dielectric Surfaces	p. 119
Irregularities in the Field Cage	p. 121
References	p. 124
Amplification of Ionization	p. 125
The Proportional Wire	p. 125
Beyond the Proportional Mode	p. 128
Lateral Extent of the Avalanche	p. 130
Amplification Factor (Gain) of the Proportional Wire	p. 132
The Diethorn Formula	p. 134
Dependence of the Gain on the Gas Density	p. 136
Measurement of the Gain Variation with Sense-Wire Voltage and Gas Pressure	p. 136
Local Variations of the Gain	p. 138
Variation of the Gain Near the Edge of the Chamber	p. 138
Local Variation of the Gain Owing to Mechanical Imperfections	p. 139
Gain Drop due to Space Charge	p. 142
Statistical Fluctuation of the Gain	p. 145
Distributions of Avalanches in Weak Fields	p. 145
Distributions of Avalanches in Electronegative Gases	p. 147
Distributions of Avalanches in Strong Homogeneous Fields	p. 149
Distributions of Avalanches in Strong Non-uniform Fields	p. 151
The Effect of Avalanche Fluctuations on the Wire Pulse Heights	p. 151
A Measurement of Avalanche Fluctuations Using Laser Tracks	p. 152
References	p. 154
Creation of the Signal	p. 157
The Principle of Signal Induction by Moving Charges	p. 157
Capacitance Matrix, Reciprocity Theorem	p. 158
Signals Induced on Grounded Electrodes, Ramo's Theorem	p. 160
Total Induced Charge and Sum of Induced Signals	p. 161
Induced Signals in a Drift Tube	p. 163
Signals Induced on Electrodes Connected with Impedance Elements	p. 165
Application to a Drift Tube and its Circuitry	p. 169
Alternative Methods for the Calculation of the Signal	p. 171
Signals Induced in Multiwire Chambers	p. 172
Signals Induced on Wires	p. 172
Signals Induced on Cathode Strips and Pads	p. 176
References	p. 179
Electronics for Drift Chambers	p. 181
Linear Signal Processing	p. 183
Laplace and Fourier Transforms	p. 183
Transfer Functions, Poles and Zeros, Delta Response	p. 185
CR, RC, Pole-zero and Zero-pole Filters	p. 187
Cascading of Circuit Elements	p. 191
Amplifier Types, Bandwidth, Sensitivity, and Ballistic Deficit	p. 192
Signal Shaping	p. 194
Unipolar and Bipolar Signal Shaping	p. 195
Signal Tail Cancellation	p. 200
Signal Pileup, Baseline Shift, and Baseline Fluctuations	p. 205
Input Circuit	p. 211
Noise and Optimum Filters	p. 213
Noise Characterization	p. 214
Noise Sources	p. 217
Noise in Wire Chambers	p. 225
A Universal Limit on the Signal-to-Noise Ratio	p. 231
Electronics for Charge Measurement	p. 234
Electronics for Time Measurement	p. 235
Influence of Electronics Noise on Time Resolution	p. 237
Influence of Pulse-Height Fluctuations on Time Resolution	p. 239
Influence of Electron Arrival Time Fluctuations on Time Resolution	p. 241
Three Examples of Modern Drift Chamber Electronics	p. 246
The ASDBLR Front-end Electronics	p. 246
The ATLAS CSC Front-end Electronics	p. 247
The PASA and ALTRO Electronics for the ALICE TPC	p. 247
References	p. 248
Coordinate Measurement and Fundamental Limits of Accuracy	p. 251
Methods of Coordinate Measurement	p. 251
Basic Formulae for a Single Wire	p. 253
Frequency Distribution of the Coordinates of a Single Electron at the Entrance to the Wire Region	p. 254
Frequency Distribution of the Arrival Time of a Single Electron at the Entrance to the Wire Region	p. 256
Influence of the Cluster Fluctuations on the Resolution - the Effective Number of Electrons	p. 257
Accuracy in the Measurement of the Coordinate in or near the Wire Direction	p. 261
Inclusion of a Magnetic Field Perpendicular to the Wire Direction: the Wire E x B Effect	p. 261
Case Study of the Explicit Dependence of the Resolution on L and [theta]	p. 263
The General Situation - Contributions of Several Wires, and the Angular Pad Effect	p. 264
Consequences of (7.33) for the Construction of TPCs	p. 268
A Measurement of the Angular Variation of the Accuracy	p. 268
Accuracy in the Measurement of the Coordinate in the Drift Direction	p. 270
Inclusion of a Magnetic Field Parallel to the Wire Direction: the Drift E x B Effect	p. 271
Average Arrival Time of Many Electrons	p. 272
Arrival Time of the Mth Electron	p. 272
Variance of the Arrival Time of the Mth Electron: Contribution of the Drift-Path Variations	p. 273
Variance of the Arrival Time of the Mth Electron: Contribution of the Diffusion	p. 275
Accuracy Limitation Owing to Wire Vibrations	p. 277
Linear Harmonic Oscillator Driven by Random Pulses	p. 278
Wire Excited by Avalanche Ions	p. 279
Accuracy Limitation Owing to Space Charge Fluctuations	p. 281
References	p. 288
Geometrical Track Parameters and Their Errors	p. 291
Linear Fit	p. 292
Case of Equal Spacing Between x[subscript 0] and x[subscript N]	p. 293
Quadratic Fit	p. 294
Error Calculation	p. 295
Origin at the Centre of the Track - Uniform Spacing of Wires	p. 296
Sagitta	p. 298
Covariance Matrix at an Arbitrary Point Along the Track	p. 299
Comparison Between the Linear and Quadratic Fits in Special Cases	p. 300
Optimal Spacing of Wires	p. 302
A Chamber and One Additional Measuring Point Outside	p. 302
Comparison of the Accuracy in the Curvature Measurement	p. 304
Extrapolation to a Vertex	p. 304
Limitations Due to Multiple Scattering	p. 306
Basic Formulae	p. 306
Vertex Determination	p. 309
Resolution of Curvature for Tracks Through a Scattering Medium	p. 310
Spectrometer Resolution	p. 311
Limit of Measurement Errors	p. 311
Limit of Multiple Scattering	p. 312
References	p. 313
Ion Gates	p. 315
Reasons for the Use of Ion Gates	p. 315
Electric Charge in the Drift Region	p. 315
Ageing	p. 318
Survey of Field Configurations and Trigger Modes	p. 318
Three Field Configurations	p. 318
Three Trigger Modes	p. 320
Transparency under Various Operating Conditions	p. 320
Transparency of the Static Bipolar Gate	p. 321
Average Transparency of the Regularly Pulsed Bipolar Gate	p. 323
Transparency of the Static Bipolar Gate in a Transverse Magnetic Field	p. 326
References	p. 329
Particle Identification by Measurement of Ionization	p. 331
Principles	p. 331
Shape of the Ionization Curve	p. 334
Statistical Treatment of the n Ionization Samples of One Track	p. 337
Accuracy of the Ionization Measurement	p. 339
Variation with n and x	p. 339
Variation with the Particle Velocity	p. 340
Variation with the Gas	p. 341
Particle Separation	p. 344
Cluster Counting	p. 345
Ionization Measurement in Practice	p. 347
Track-Independent Corrections	p. 347
Track-Dependent Corrections	p. 348
Performance Achieved in Existing Detectors	p. 349
Wire Chambers Specialized to Measure Track Ionization	p. 349
Ionization Measurement in Universal Detectors	p. 354
References	p. 358
Existing Drift Chambers - An Overview	p. 361
Definition of Three Geometrical Types of Drift Chambers	p. 361
Historical Drift Chambers	p. 362
Drift Chambers for Fixed-Target and Collider Experiments	p. 365
General Considerations Concerning the Directions of Wires and Magnetic Fields	p. 366
The Dilemma of the Lorentz Angle	p. 367
Left-Right Ambiguity	p. 368
Planar Drift Chambers of Type 1	p. 368
Coordinate Measurement in the Wire Direction	p. 368
Five Representative Chambers	p. 369
Type 1 Chambers without Field-Shaping Electrodes	p. 375
Large Cylindrical Drift Chambers of Type 2	p. 377
Coordinate Measurement along the Axis - Stereo Chambers	p. 377
Five Representative Chambers with (Approximately) Axial Wires	p. 377
Drift Cells	p. 380
The UA1 Central Drift Chamber	p. 384
The ATLAS Muon Drift Chambers (MDT)	p. 385
A Large TPC System for High Track Densities	p. 388
Small Cylindrical Drift Chambers of Type 2 for Colliders (Vertex Chambers)	p. 390
Six Representative Chambers	p. 393
Drift Chambers of Type 3	p. 397
Double-Track Resolution in TPCs	p. 398
Five Representative TPCs	p. 399
A Type 3 Chamber with a Radial Drift Field	p. 403
A TPC for Heavy-Ion Experiments	p. 404
A Type 3 Chamber as External Particle Identifier	p. 404
A TPC for Muon-Decay Measurements	p. 406
Chambers with Extreme Accuracy	p. 407
References	p. 409
Drift-Chamber Gases	p. 413
General Considerations Concerning the Choice of Drift-Chamber Gases	p. 413
Inflammable Gas Mixtures	p. 416
Gas Purity, and Some Practical Measurements of Electron Attachment	p. 420
Three-Body Attachment to O[subscript 2], Mediated by CH[subscript 4], i-C[subscript 4]H[subscript 10] and H[subscript 2]O	p. 420
'Poisoning' of the Gas by Construction Materials, Causing Electron Attachment	p. 422
The Effect of Minor H[subscript 2]O Contamination on the Drift Velocity	p. 422
Chemical Compounds Used for Laser Ionization	p. 424
Choice of the Gas Pressure	p. 426
Point-Measuring Accuracy	p. 427
Lorentz Angle	p. 428
Drift-Field Distortions from Space Charge	p. 429
Deterioration of Chamber Performance with Usage ('Ageing')	p. 429
General Observations in Particle Experiments	p. 430
Dark Currents	p. 430
Ageing Tests in the Lower-Flux Regime	p. 433
Ageing Tests in the High-Flux Regime	p. 435
References	p. 439
Index	p. 443
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Particle Detection with Drift Chambers

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