Blum W., Riegler W., Rolandi L. Particle Detection with Drift Chambers

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Particle Detection with Drift Chambers

Particle Acceleration and Detection

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Walter Blum · Werner Riegler · Luigi Rolandi

Particle Detection

with Drift Chambers

123

Walter Blum Werner Riegler

MPI f¨ur Physik CERN

Werner-Heisenberg-Institut 1211 Geneve 23

F¨ohringer Ring 6 Switzerland

80805 M¨unchen werner.riegler@cern.ch

Germany

walter.blum@cern.ch

Luigi Rolandi

CERN

1211 Geneve 23

Switzerland

luigi.rolandi@cern.ch

ISBN: 978-3-540-76683-4 e-ISBN: 978-3-540-76684-1

Library of Congress Control Number: 2007940836

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Preface to the First Edition

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 ﬁrst studies with a drift cham-

ber were made by Bressani, Charpak, Rahm and Zupan

c in 1969. When the ﬁrst

operational drift-chamber system with electric circuitry and readout was built by

Walenta, Heintze and Sch

urlein 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.

Diffusion and drift of electrons and ions in gases were at that time well-established

subjects in their own right. The study of the inﬂuence of magnetic ﬁelds on these

processes was completed in the 1930s and all fundamental equations were con-

tained in the article by W.P. Allis in the Encyclopedia of Physics [ALL 56]. It

did not take very long until the particle physicists learnt to apply the methods of

the Maxwell–Boltzmann equations and of the electron-swarm experiments that had

been developed for the study of atomic properties. The article by Palladino and

Sadoulet [PAL 75] recorded some of these methods for use with particle-physics

instruments.

F. Sauli gave an academic training course at CERN in 1975/76, in order to inform

a growing number of users of the new devices. He published lecture notes [SAU 77],

which were a major source of information for particle physicists who began to work

with drift chambers.

When the authors of this book began to think about a large drift chamber for

the ALEPH experiment, we realized that there was no single text to introduce us to

those questions about drift chambers that would allow us to determine their ultimate

limits of performance. We wanted to have a text, not on the technical details, but

on the fundamental processes, so that a judgement about the various alternatives

for building a drift chamber would be on solid ground. We needed some insight

vi Preface to the First Edition

into the consequences of different geometries and how to distinguish between the

behaviour of different gases, not so much a complete table of their properties. We

wanted to understand on what trajectories the ionization electrons would drift to the

proportional wires and to what extent the tracks would change their shape.

Paths to the literature were also required – just a few essential ones – so that an

entry point to every important subject existed; they would not have to be a compre-

hensive review of ‘everything’.

In some sense we have written the book that we wanted at that time. The text

also contains a number of calculations that we made concerning the statistics of

ionization and the fundamental limits of measuring accuracy that result from it,

geometrical ﬁts to curved tracks, and electrostatics of wire grids and ﬁeld cages.

Several experiments that we undertook during the construction time of the ALEPH

experiment found their way into the book; they deal mainly with the drift and diffu-

sion of electrons in gases under various ﬁeld conditions, but also with the statistics

of the ionization and ampliﬁcation processes.

The book is nonetheless incomplete in some respects. We are aware that it lacks

a chapter on electronic signal processing. Also some of the calculations are not yet

backed up in detail by measurements as they will eventually have to be. Especially

the parameter N

eff

of the ionization process which governs the achievable accuracy

should be accurately known and supported by measurements with interesting gases.

We hope that workers in this ﬁeld will direct their efforts to such questions. We

would welcome comments about any other important omissions.

It was our intention to make the book readable for students who are interested

in particle detectors. Therefore, we usually tried to explain in some detail the ar-

guments that lead up to a ﬁnal result. One may say that the book represents a cross

between a monograph and an advanced textbook. Those who require a compendious

catalogue of existing or proposed drift chambers may ﬁnd useful the proceedings of

the triannual Vienna Wire Chamber Conferences [VIE] or of the annual IEEE Sym-

posia on Instrumentation for Nuclear Science [IEE].

Parts of the material have been presented in summer schools and guest lectures,

and we thank H.D. Dahmen (Herbstschule Maria Laach), E. Fernandez (Universita

Autonoma, Barcelona) and L. Bertocchi (ICTP, Trieste) for their hospitality.

We thank our colleagues from the ALEPH TPC group, and especially J. May

and F. Ragusa, for many stimulating discussions on the issues of this book. We are

also obliged to H. Spitzer (Hamburg) who read and commented on an early version

of the manuscript. Special thanks are extended to Mrs. Heininger in Munich who

produced most of the drawings.

Geneva W. Blum

1 April 1993 L. Rolandi

Preface to the Second Edition

The ﬁrst edition has continuously served many students and researchers in the ﬁeld.

Now we have enlarged and improved the book, essentially in three ways: (1) The

chapter on electronic signal processing was added, and (2) the chapter on the cre-

ation of the signal was rewritten and based on the principle of current induction.

This was made possible because our team was complemented with a new young

co-author (W.R.). (3) Also there are various modernizations throughout the book in-

cluding some of the recent chambers capable to measure tracks at very high ﬂuences

that one could not imagine 15 years ago. Four of the chapters were left untouched.

The development of drift chambers in the last 15 years was driven by the idea that

their performance should be pushed towards the limits of the laws of physics. The

concept of the book matches very well this trend because it is the basic principles

of drift chambers rather than their technical design solutions that are in focus. The

most modern design solutions, among them the ones developed for the experiments

of the Large Hadron Collider, can be found e.g. in the proceedings of the IEEE

Symposia [IEE] and of the Vienna Wire Chamber Conferences [VIE].

During the last two decades, the development and optimization of drift cham-

bers has increasingly relied on simulation programs, which in some sense ’encode’

the physics processes described in this book. The program GARFIELD, written by

Rob Veenhof, is the most widely used tool for drift chamber simulation. It allows

calculation of electric ﬁelds, electron and ion drift lines, induced signals, electro-

static wire displacements and many more features of drift chambers. For calculation

of the primary ionization of fast particles in gases, the program HEED, written by

Igor Smirnov, is widely used. A very popular program for calculation of electron

transport properties in different gas mixtures is the program MAGBOLTZ, writ-

ten by Steve Biagi. MAGBOLTZ and HEED are directly interfaced to GARFIELD,

which therefore allows a complete simulation of the drift chamber processes, from

the passage of the charged particle to the detector output signal. Clearly a thorough

understanding of drift chambers, which is subject of this book, is a necessary pre-

condition for efﬁcient use of these simulation programs.

Despite the development of the ﬁne grained silicon detectors which now out-

perform the wire chambers near the interaction point, the large detector volumes

vii

viii Preface to the Second Edition

surrounding modern experiments have to rely on drift chambers because of their

simplicity and also because their measurement accuracy in relation to their size is

better than it is in any other instrument. Time Projection Chambers with electron

drift lengths up to 2.5 m are the most important tools for studying heavy ion col-

lisions, because of their very low material budget, channel number economy and

particle identiﬁcation capabilities. TPCs are also studied as principle detectors for

future electron colliders. 36 years after the ﬁrst working drift chamber, these instru-

ments are still going strong.

Geneva W. Blum

April 2008 W. Riegler

L. Rolandi

References

[ALL 56] W.P. Allis, Motions of ions and electrons, in Handbuch der Physik, ed. by S. Fl

ugge

(Springer, Berlin 1956) Vol. XXI, p. 383

[IEE] The symposia are usually held in the fall of every year and are published in consec-

utive volumes of the IEEE Transactions in Nuclear Science in the ﬁrst issue of the

following year

[PAL 75] V. Palladino and B. Sadoulet, Application of classical theory of electrons in gases to

drift proportional chambers, Nucl. Instrum. Methods 128, 323 (1975)

[SAU 77] F. Sauli, Principles of operation of multiwire proportional and drift chambers, Lec-

tures given in the academic training programme of CERN 1975–76 (CERN 77-09,

Geneva 1977), in Experimental Techniques in High Energy Physics, ed. by T. Ferbel

(Addison-Wesley, Menlo Park 1987)

[VIE] The Vienna Wire Chamber Conferences were held in February of the years 1978,

1980, 1983, 1986, 1989, 1992, 1995, 1998, 2001, 2004, 2007, and they were published

mostly the same years in Nuclear Instruments and Methods in the following volumes:

135, 176, 217, A 252, A 283, A 323, A 367, A 419, A 478, A 535. Since 2001 they

are called Vienna Conference on Instrumentation.

Contents

1 Gas Ionization by Charged Particles and by Laser Rays ............ 1

1.1 GasIonizationbyFastChargedParticles....................... 1

1.1.1 Ionizing Collisions . .................................. 1

1.1.2 Different Ionization Mechanisms ....................... 3

1.1.3 Average Energy Required to Produce One Ion Pair . . . ..... 4

1.1.4 The Range of Primary Electrons . ....................... 7

1.1.5 The Differential Cross-section d

/dE ................... 7

1.2 CalculationofEnergyLoss .................................. 9

1.2.1 Force on a Charge Travelling Through a Polarizable Medium 9

1.2.2 The Photo-Absorption Ionization Model . ................ 11

1.2.3 Behaviour for Large E ................................ 15

1.2.4 Cluster-SizeDistribution.............................. 15

1.2.5 Ionization Distribution on a Given Track Length . . . . . ..... 16

1.2.6 Velocity Dependence of the Energy Loss ................ 24

1.2.7 The Bethe–Bloch Formula . ........................... 29

1.2.8 Energy Deposited on a Track – Restricted Energy Loss . . . . 32

1.2.9 LocalizationofChargeAlongtheTrack ................. 35

1.2.10 A Measurement of N

eff

............................... 37

1.3 GasIonizationbyLaserRays ................................ 38

1.3.1 The nthOrderCross-SectionEquivalent................. 38

1.3.2 Rate Equations for Two-Photon Ionization . . . ............ 39

1.3.3 Dependence of Laser Ionization on Wavelength . . . . . . ..... 42

1.3.4 Laser-BeamOptics................................... 44

References . .................................................... 46

2 The Drift of Electrons and Ions in Gases .......................... 49

2.1 AnEquationofMotionwithFriction .......................... 49

2.1.1 Case of E Nearly Parallel to B ......................... 52

2.1.2 Case of E Orthogonal to B ............................ 52

2.2 The Microscopic Picture . . . .................................. 53

2.2.1 DriftofElectrons .................................... 53

x Contents

2.2.2 DriftofIons ........................................ 56

2.2.3 Inclusion of Magnetic Field ........................... 64

2.2.4 Diffusion .......................................... 67

2.2.5 ElectricAnisotropy .................................. 70

2.2.6 Magnetic Anisotropy . . . . . . ........................... 72

2.2.7 Electron Attachment . . . . . . ........................... 75

2.3 Results from the Complete Microscopic Theory . ................ 79

2.3.1 Distribution Function of Velocities . . . . . . ................ 79

2.3.2 Drift............................................... 81

2.3.3 Inclusion of Magnetic Field ........................... 82

2.3.4 Diffusion........................................... 83

2.4 Applications............................................... 83

2.4.1 Determination of

(

) and λ(

) from Drift Measurement . . 83

2.4.2 Example: Argon–Methane Mixture . . . . . ................ 85

2.4.3 Experimental Check of the Universal Drift Velocity

for Large

ωτ

........................................ 88

2.4.4 A Measurement of Track Displacement as a Function

of Magnetic Field . . .................................. 89

2.4.5 A Measurement of the Magnetic Anisotropy of Diffusion . . . 89

2.4.6 Calculated and Measured Electron Drift Velocities

in Crossed Electric and Magnetic Fields . ................ 92

References . .................................................... 94

3 Electrostatics of Tubes, Wire Grids and Field Cages ................ 97

3.1 Perfect and Imperfect Drift Tubes . . ........................... 98

3.1.1 PerfectDriftTube.................................... 99

3.1.2 Displaced Wire . . . . .................................. 99

3.2 WireGrids ................................................105

3.2.1 The Electric Field of an Ideal Grid of Wires Parallel

to a Conducting Plane . . . . . ...........................105

3.2.2 Superposition of the Electric Fields of Several Grids

andofaHigh-VoltagePlane ...........................108

3.2.3 Matching the Potential of the Zero Grid and of the

Electrodes of the Field Cage ...........................110

3.3 An Ion Gate in the Drift Space. . . . . ...........................112

3.3.1 CalculationofTransparency ...........................113

3.3.2 Setting of the Gating Grid Potential with Respect

totheZero-GridPotential .............................118

3.4 Field Cages . . .............................................118

3.4.1 The Difﬁculty of Free Dielectric Surfaces . . . . ............119

3.4.2 Irregularities in the Field Cage . . .......................121

References . ....................................................124