Table Of ContentElectron
Impact Ionization
Edited by
T. D. Miirk and G. H. Dunn
Springer- Verlag Wien GmbH
Prof. Dr. Tilmann D. Mark
Institut fiir Experimentalphysik, Universitiit Innsbruck, Austria
Prof. Dr. Gordon H. Dunn
Joint Institute for Laboratory Astrophysics,
National Bureau of Standards and University of Colorado, Boulder, Colorado, U.S.A.
This work is subject to copyright.
All rights are reserved, whether the whole or part of the material is concerned,
specifically those of translation, reprinting, re-use of illustrations, broadcasting,
reproduction by photocopying machine or similar means, and storage in data banks.
© 1985 by Springer-Verlag Wien
Originally published by Springer-Verlag Wien New York in 1985
Softcover reprint of the hardcover 1st edition 1985
With 156 Figures
Library of Congress Cataloging in Publication Data. Main entry under title: Electron impact ionization. Includes index. 1. Electron impact
ionization. I. Miirk,T.D.(Ti1mannD.), 1944- . II. Dunn,G.H.(GordonH.), 1932- . QC702.7.E38E44.1985.537.5"32. 84-23595.
ISBN 978-3-7091-4030-7 ISBN 978-3-7091-4028-4 (eBook)
DOI 10.1007/978-3-7091-4028-4
Preface
It is perhaps surprising that a process which was one of the first to be studied on an
atomic scale, and a process which first received attention over seven decades ago,
continues to be the object of diverse and intense research efforts. Such is the case
with the (seemingly) conceptually simple and familiar mechanism of electron
impact ionization of atoms, molecules, and ions. Not only has the multi-body
nature of the collision given ground to theoretical effort only grudgingly, but also
the variety and subtlety of processes contributing to ionization have helped insure
that progress has come only with commensurate work: no pain - no gain.
Modern experimental methods have made it possible to effectively measure and
explore threshold laws, differential cross sections, partial cross sections, inner-shell
ionization, and the ionization of unstable species such as radicals and ions. In most
instances the availability of experimental data has provided impetus and guidance
for further theoretical progress.
If it is surprising that a field so old is still a contemporary, vital research area, it is
then all the more astonishing that no book has provided a comprehensive review on
the varied aspects of the kinetics and dynamics of electron impact ionization. There
is a vast literature of many hundreds (perhaps thousands) of original research
papers. Books by Field and Franklin, by Reed, and by Peterkop, as well as shorter
treatments in chapters of books by Massey and Bur hop, by McDaniel, by Hasted
and by others, are limited in scope or perspective and are not comprehensive in their
discussion of the electron-impact ionization process. Indeed, since electron-impact
ionization is so important in the study, analysis, and modeling of physical/chemical
systems ranging from bodies in intergalactic space to analytical mass spectrometers
in the laboratory, many limited treatments of the process have been found in books
on these "user" fields.
For some time we have felt that continued orderly progress in understanding this
important collision mechanism would be enhanced if a comprehensive treatment of
the process were available in a single reference book. Similarly, those in the "user"
fields would also benefit by having a resource that was not limited in scope and
perspective. With these goals in mind, this work was undertaken. We have sought
and obtained participating authors who are experts in the field and who are
distinguished by their original contributions to their areas.
Quantum mechanical, semiclassical, and semiempirical methods for calculating
ionization cross sections are considered in Chapters 1 - 2. Chapter 3 deals with
experimental and theoretical aspects of the threshold behavior of ionization cross
sections. Summaries of today's knowledge about differential, partial, innershell,
and total ionization cross sections make up Chapters 4-7. Chapter 8 deals with the
active subject of electron-ion ionization; and the final chapter, Chapter 9, deals
VI Preface
with applications of quantitative knowledge of the electron ionization process in
various fields: mass spectrometry, plasma diagnostics, astrophysics, fusion re
search, aeronomy, gaseous electronics, and radiation physics. It is our hope and
expectation that researchers and graduate students in these "user" areas as well as
those working to further understand the intricacies of this fascinating process will
find this book an important source of information.
We are grateful to the contributing authors both for the quality of their manuscripts
and for their patience: some in waiting for the process to come to completion and
some in bearing the harassment of the editors to complete their parts. We also
commend the people at Springer Verlag Wien-New York for the quality and speed
with which they put together the finished product, and for their forbearance.
January 1985 T. D. Mark
G. H. Dunn
Contents
1 Quantum Theoretical Methods for Calculating Ionization Cross Sections ....... .
By S. M. Younger
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Theory of Electron Ionization of Atoms and Ions . . . . . . . . . . . . . . . . . . . . . . 2
1.2.1 General Theory.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2.2 Partial Wave Theories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2.3 Resonances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.2.4 Target Electron Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3 Results of Partial Wave Calculations of Electron Ionization Cross Sections 11
1.3.1 One Electron Atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.3.2 Two Electron Atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.3.3 The Neon Isoelectronic Sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.3.4 The Argon Isoelectronic Sequence............................... 16
1.3.5 Indirect Mechanisms for Electron Ionization. . . . . . . . . . . . . . . . . . . . . . 17
1.3.6 Ionization from Inner Shells. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.3. 7 Ionization from Excited States. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.3.8 Electron Ionization of Heavy Atoms and Ions . . . . . . . . . . . . . . . . . . . . 19
1.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
References............... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2 Semi-Empirical and Semi-Classical Approximations for Electron Ionization...... 24
By S.M. Younger and T. D. Miirk
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.2 Empirical and Semi-Empirical Formulae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.2.1 The Lotz Formulae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.2.2 The Seaton Formula for Highly Charged Ions . . . . . . . . . . . . . . . . . . . . 28
2.2.3 The Jain-Khare Formula for Molecules.. . . . . . . . . . . . . . . . . . . . . . . . . 28
2.2.4 Additivity Rule and Maximum Ionization Cross Sections........... 29
2.3 Semi-Classical Formulae............................................ 30
2.3.1 The Binary Encounter Approximation (BEA). . . . . . . . . . . . . . . . . . . . . 30
2.3.2 The Exchange Classical Impact Parameter (ECIP) Approximation... 31
2.3.3 The Scaled Hydrogenic Formula. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.4 Some Comparisons and Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.4.1 Atoms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.4.2 Molecules. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.4.3 Ions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3 Threshold Behaviour of Ionization Cross-sections . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
By F. H. Read
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
VIII Contents
3.2 Classical Wannier Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.2.1 Justification of the Classical Approach. . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.2.2 Collinear Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.2.3 Total Ionization Cross Section. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.2.4 Experimental Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.2.5 Trajectory Integrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.2.6 Core Screening............................................... 57
3.2.7 Multiple Ionization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.3 Semiclassical and Quantum-Mechanical Treatments..................... 60
3.3.1 Semiclassical and WKB-Like Treatments. . . . . . . . . . . . . . . . . . . . . . . . . 60
3.3.2 Quantum-Mechanical Treatments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.3.3 Wavefunction Symmetry Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.4 Differential Ionization Cross Sections................................. 69
3.4.1 Energy Partitioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.4.2 Angular Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.4.3 Angular Momenta . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
3.5 Related Excitation Cross Sections.................................... 77
3.5.1 Differential Excitation Cross Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
3.5.2 Angular Momentum Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
3.6 Wannier-Ridge Resonances. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
3. 7 Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
4 Differential Ionization Cross Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
By P. J. 0. Teubner
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.2 Triple Differential or (e, 2 e) Cross Sections. . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
4.2.1 Symmetric Kinematics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.2.1.1 Theory .......................... .'.................... 93
4.2.1.2 The Experiments....................................... 95
4.2.1.3 Absolute (e, 2e) Cross Sections . . . . . . . . . . . . . . . . . . . . . . . . . . 100
4.2.1.4 Experiments on Atomic Hydrogen . . . . . . . . . . . . . . . . . . . . . . . 102
4.2.1.5 Correlation Effects. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.2.1.6 Molecular (e,2e) Spectroscopy........................... 107
4.2.2 Asymmetric Collisions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
4.2.2.1 Low Energies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ill
4.2.2.2 High Energies .. . . . .. .. .. . . . . . . . . . . .. .. .. .. .. .. . . . . . . . . 116
4.3 Double Differential Cross Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
4.3.1 Low Energy Double Differential Cross Sections. . . . . . . . . . . . . . . . . . . 118
4.3.2 Electron Energy Loss Spectroscopy.............................. 120
4.4 Dissociative Ionization.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
4.4.1 Selection Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
4.4.2 Dissociative Ionization in H2 • . • • . • • • • • • • • • • • • . • • • • • • • • • • • • • . • • • 124
4.4.3 Methods and Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
4.4.3.1 Energy Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
4.4.3.2 Angular Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
4.5 Inner Shell Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
4.5.1 Electron Energy Loss Spectroscopy.............................. 131
4.5.2 Electron Ion Coincidence Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
Contents IX
5 Partial Ionization Cross Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
By T. D. Mark
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
5.1.1 Ionization Processes and Mechanism............................ 138
5.1.2 Types of Individual Ions Produced.............................. 143
5.1.3 Principle oflonization Cross Section Experiment and Definitions.. . . 150
5.2 Experimental Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
5.2.1 Discrimination Effects in Ion Source-Mass Spectrometer Systems.... 151
5.2.2 Other Experimental Considerations...... . . . . . . . . . . . . . . . . . . . . . . . . 162
5.2.3 Some Types of Experiments and Recent Techniques . . . . . . . . . . . . . . . 165
5.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
5.3.1 Atoms....................................................... 175
5.3.2 Diatomic Molecules........................................... 180
5.3.3 Triatomic Molecules. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
5.3.4 Polyatomic Molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
5.3.5 Clusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
5.3.6 Ionization of Excited Neutral Atoms and Molecules.............. . 185
5.3.7 Ionization of Atoms and Molecules into Specific (Excited) Ionic States 186
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
6 Innersbell Ionization Cross Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
By C. J. Powell
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
6.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
6.2.1 Dielectric and Bethe Theories of Inelastic Electron Scattering . . . . . . . 200
6.2.2 Atomic Calculations of Inner-Shell Ionization Cross Sections . . . . . . . 203
6.3 Semi-Empirical and Empirical Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
6.4 Experimental Measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
6.4.1 Techniques for Inner-Shell Cross Section Measurements............ 208
6.4.2 X-Ray Yield Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
6.4.3 Auger-Electron Yield Measurements.... . . . . . . . . . . . . . . . . . . . . . . . . . 212
6.4.4 Electron Energy-Loss Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
6.5 Comparison of Theory and Experiment............................... 213
6.5.1 K-Shell Data................................................. 213
6.5.2 L-Shell Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
6.5.3 Analysis of Experimental Cross Section Data with the Use
of the Bethe Equation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
6.6 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
6.6.1 Bulk Analysis (Electron-Probe Microanalysis).................... . 221
6.6.2 Surface Analysis (Auger-Electron Spectroscopy)................... 222
6.6.3 Thin-Film Analysis (Electron Energy-Loss Spectroscopy). . . . . . . . . . . 223
6.6.4 Materials Analysis (Analytical Electron Microscopy)............... 224
6.6.5 Radiation Damage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
6. 7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22R
7 Total Ionization Cross Sections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
By F. J. de Heer and M. lnokuti
7 .I Experimental Techniques. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
7.1.1 General..................................................... 232
7.1.2 The Condenser-Plate Method................................... 233
X Contents
7.1.3 The Lozier Tube. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237
7.1.4 The Summation Method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
7.1.5 Gas-Filled Counters........................................... 239
7.1.6 Crossed-Beam Methods........................................ 241
7.2 Data: Survey and Critique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250
7.2.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250
7.2.2 The Use of the Bethe Theory and Other Theoretical Constraints..... 252
7.2.3 Atoms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257
7.2.4 Molecules.... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
7.2.5 Systematics of the Total Ionization Cross Section. . . . . . . . . . . . . . . . . . 270
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272
8 Electron-Ion Ionization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277
By G. H. Dunn
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277
8.2 Experimental Methods.............................................. 283
8.2.1 Crossed Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283
8.2.2 Plasma Rate Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287
8.2.3 Trapped Ions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290
8.3 Experimental Cross Sections - Single Ionization....................... 292
8.3.1 Low ZIons (Z ~ 8) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292
8.3.2 Intermediate ZIons (9~Z~l9)................................ 302
8.3.3 Ions of Z~20... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307
8.3.4 General Observations for Single Ionization . . . . . . . . . . . . . . . . . . . . . . . 315
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316
9 Applications. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320
9.1 Application of Electron Impact Ionization to Plasma Diagnostics......... 320
By W. Lindinger and F. H oworka
9.1.1 Introduction................................................. 320
9.1.2 Densities of Fast Electrons in Hollow Cathode Discharges.......... 321
9.1.2.1 Hole Probe Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322
9.1.2.2 Density [e1] Derived from Electron Impact Ionization
Within the Orifice of a Hole Probe . . . . . . . . . . . . . . . . . . . . . . . 322
9.1.2.3 Density [e1] Derived from Measured Ion Density Profiles.... 324
9 .1.3 Neutral Gas Densities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326
9.2 Collisional Ionization: Astrophysical and Fusion Applications . . . . . . . . . . . 327
By J. M. Shull
9.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327
9.2.2 Astrophysical Plasmas................... . . . . . . . . . . . . . . . . . . . . . . 327
9.2.2.1 Coronal Equilibrium... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329
9.2.2.2 Non-Equilibrium Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332
9.2.3 Fusion Plasmas............................................... 333
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334
9.3 Ionization in Gas Discharges: Experiment and Modeling................ 335
By A. V. Phelps
9.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335
9.3.2 Measurement of Ionization Coefficients in Gases. . . . . . . . . . . . . . . . . . 336
9.3.2.1 Spatial Growth Experiments... . . . . . . . . . . . . . . . . . . . . . . . . . . 336
9.3.2.2 Temporal Growth Experiments. . . . . . . . . . . . . . . . . . . . . . . . . . . 337
