Plasma Physics and Engineering

574 Pages·2004·10.29 MB·English

by  Alexander A. Fridman, Lawrence A. Kennedy

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Cover
title: Plasma Physics and Engineering
author: Fridman, Alexander A.; Kennedy, Lawrence A.
publisher: Taylor & Francis Routledge
isbn10 | asin: 1560328487
print isbn13: 9781560328483
ebook isbn13: 9780203334874
language: English
subject Plasma (Ionized gases) , Plasma engineering, Plasma (Gaz
ionisés) , Plasmas, Technique des.
publication date: 2004
lcc: QC718.F77 2004eb
ddc: 530.4/4
subject: Plasma (Ionized gases) , Plasma engineering, Plasma (Gaz
ionisés) , Plasmas, Technique des.
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Page i
Plasma Physics and Engineering
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Plasma Physics and Engineering
Alexander Fridman
Lawrence A.Kennedy
NEW YORK • LONDON
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Denise T.Schanck, Vice President
Robert L.Rogers, Senior Editor
Summers Scholl, Editorial Assistant
Savita Poornam, Marketing Manager
Randy Harinandan, Marketing Assistant
Susan Fox, Project Editor
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Shayna Murry, Cover Designer
Published in 2004 by
Taylor & Francis
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This edition published in the Taylor & Francis e-Library, 2006.
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Published in Great Britain by
Taylor & Francis
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Copyright © 2004 by Taylor & Francis Books, Inc.
All rights reserved. No part of this book may be reprinted or reproduced or utilized in any
form or by any electronic, mechanical, or other means, now known or hereafter invented,
including photocopying and recording, or in any information storage or retrieval system,
without permission in writing from the publishers.
10 9 8 7 6 5 4 3 2 1
Library of Congress Cataloging-in-Publication Data
Fridman, Alexander A., 1953–
Plasma physics and engineering/by Alexander
A.Fridman and Lawrence A.Kennedy
p. cm.
ISBN 1-56032-848-7 (hardcover: alk. paper)
1. Plasma (Ionized gases). 2. Plasma engineering. I. Kennedy, Lawrence A., 1937–
II. Title.
QC718.F77 2004
530.4′4–dc22 2003022820
ISBN 0-203-33487-6 Master e-book ISBN
ISBN 1-56032-848-7 (Print Edition)
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Preface
Plasma enjoys an important role in a wide variety of industrial processes, including material processing;
environmental control; electronic chip manufacturing; light sources; bio-medicine; and space propulsion. It is
also central to understanding most of the universe outside the Earth. As such, the focus of this book is to
provide a thorough introduction to the subject and to be a valued reference that serves engineers and
scientists as well as students. Plasma is not an elementary subject and the reader is expected to have the
normal engineering background in thermodynamics, chemistry, physics, and fluid mechanics upon which to
build an understanding of this subject.
This text has been organized into two parts. Part I addresses the basic physics of plasma. Chapter 2 examines
the elementary processes of charge species in plasma and Chapter 3 provides a thorough introduction to the
elementary processes of excited molecules and atoms in plasmas. Chapter 4 and Chapter 5 examine the
kinetics of charged/excited particles and Chapter 6 gives a thorough introduction to the electrostatics,
electrodynamics, and fluid mechanics of plasma.
Part II addresses the physics and engineering of electric discharges, specifically examining glow and arc
discharges (Chapter 7 and Chapter 8); cold atmospheric pressure discharges typically associated with corona,
dielectric barrier, and spark discharges (Chapter 9); plasma created in high-frequency electromagnetic fields
characterized by radio-frequency, microwave, and optical discharges (Chapter 10); and discharges in aerosols
and dusty plasmas (Chapter 11). The second part of Chapter 12 concludes with discussions on electron beam
plasmas. The authors have drawn upon extensive work in the Russian literature in addition to the more
accessible results from the West. We believe that this will add an important dimension to development of this
subject.
This text is adaptable to a wide range of needs. The material has been taught to graduate and senior-level
students from most engineering disciplines and physics. For the latter, it can be packaged to focus on the
basic physics of plasma with only selections from discharge applications. For graduate courses, a faster pace
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can be set that covers Part I and Part II. Presently, the text is used for a plasma engineering course sequence
(Plasma I, Plasma II) at Drexel University.
We gratefully acknowledge the loving support of our wives, Irene Fridman and Valaree Kennedy; the
governmental research support of the National Science Foundation and the U.S. Department of Energy,
together with our long-term industrial sponsors, Air Liquide, Texaco, Kodak, Georgia Pacific, and Applied
Materials. We especially appreciate John and Chris Nyheim and the Kaplan family for their support of plasma
research at Drexel University and University of Illinois at Chicago. Additionally, we gratefully acknowledge the
invaluable, stimulating discussions with our colleagues, Professors Young Cho, Gary Friedman, Baki Farouk,
Alexei V.Saveliev
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and Alexander Gutsol, and our students. We thank K.Gutsol, A.Fridman, G. Fridman, and A.Chirokov for help
with illustrations.
Alexander Fridman
Lawrence A.Kennedy
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Table of Contents

PART I Fundamentals of Plasma Physics and Plasma Chemistry 1

Chapter Plasma in Nature, in the Laboratory, and in Industry 3
1
1.1 Occurrence of Plasma: Natural and Manmade Plasmas 4
1.2 Gas Discharges 6
1.3 Plasma Applications: Plasmas in Industry 8
1.4 Plasma Applications for Environmental Control 10
1.5 Plasma Applications in Energy Conversion 11
1.6 Plasma Application for Material Processing 13
Chapter Elementary Processes of Charged Species in Plasma 15
2
2.1 Elementary Charged Particles in Plasma and Their Elastic and Inelastic Collisions 15
2.1.1 Electrons 16
2.1.2 Positive Ions 17
2.1.3 Negative Ions 18
2.1.4 Elementary Processes of Charged Particles 19
2.1.5 Fundamental Parameters of Elementary Processes 20
2.1.6 Reaction Rate Coefficients 21
2.1.7 Elementary Elastic Collisions of Charged Particles 22
2.2 Ionization Processes 24
2.2.1 Direct Ionization by Electron Impact 24
2.2.2 Direct Ionization Rate Coefficient 26
2.2.3 Peculiarities of Dissociation of Molecules by Electron Impact: the Frank-Condon Principle 28
and the Process of Dissociative Ionization
2.2.4 Stepwise Ionization by Electron Impact 29
2.2.5 Ionization by High Energy Electron Beams 32
2.2.6 Photoionization Processes 33
2.2.7 Ionization by Collisions of Heavy Particles: Adiabatic Principle and Massey Parameter 34
2.2.8 The Penning Ionization Effect and Process of Associative Ionization 35
2.3 Mechanisms of Electron Losses: Electron-Ion Recombination 36
2.3.1 Different Mechanisms of Electron-Ion Recombination 37
2.3.2 Dissociative Electron-Ion Recombination 38
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2.3.3 Ion Conversion Reactions as a Preliminary Stage of Dissociative Electron-Ion 40
Recombination
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2.3.4 Three-Body Electron-Ion Recombination 40
2.3.5 Radiative Electron-Ion Recombination 42
2.4 Electron Losses due to Formation of Negative Ions: Electron Attachment and Detachment 42
Processes
2.4.1 Dissociative Electron Attachment to Molecules 43
2.4.2 Three-Body Electron Attachment to Molecules 46
2.4.3 Other Mechanisms of Formation of Negative Ions 47
2.4.4 Mechanisms of Negative Ion Destruction: Associative Detachment Processes 48
2.4.5 Electron Impact Detachment 50
2.4.6 Detachment in Collisions with Excited Particles 51
2.5 Ion-Ion Recombination Processes 52
2.5.1 Ion-Ion Recombination in Binary Collisions 52
2.5.2 Three-Body Ion-Ion Recombination: Thomson’s Theory 55
2.5.3 High-Pressure Limit of Three-Body Ion-Ion Recombination: Langevin Model 56
2.6 Ion-Molecular Reactions 58
2.6.1 Ion-Molecular Polarization Collisions: Langevin Rate Coefficient 58
2.6.2 The Ion-Atom Charge Transfer Processes 61
2.6.3 Nonresonant Charge Transfer Processes 64
2.6.4 Ion-Molecular Reactions with Rearrangement of Chemical Bonds 65
2.6.5 Ion-Molecular Chain Reactions and Plasma Catalysis 66
2.6.6 Ion-Molecular Processes of Cluster Growth: the Winchester Mechanism 67
Problems and Concept Questions 69
Chapter Elementary Processes of Excited Molecules and Atoms in Plasma 73
3
3.1 Electronically Excited Atoms and Molecules in Plasma 73
3.1.1 Electronically Excited Particles: Resonance and Metastable States 74
3.1.2 Electronically Excited Atoms 74
3.1.3 Electronic States of Molecules and Their Classification 77
3.1.4 Electronically Excited Molecules and Metastable Molecules 78
3.2 Vibrationally and Rotationally Excited Molecules 81
3.2.1 Potential Energy Curves for Diatomic Molecules: Morse Potential 81
3.2.2 Vibration of Diatomic Molecules: Model of Harmonic Oscillator 84
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3.2.3 Vibration of Diatomic Molecules: Model of Anharmonic Oscillator 86
3.2.4 Vibrationally Excited Polyatomic Molecules: the Case of Discrete Vibrational Levels 88
3.2.5 Highly Vibrationally Excited Polyatomic Molecules: Vibrational Quasi Continuum 92
3.2.6 Rotationally Excited Molecules 94
3.3 Elementary Processes of Vibrational, Rotational, and Electronic Excitation of Molecules in Plasma 96
3.3.1 Vibrational Excitation of Molecules by Electron Impact 96
3.3.2 Lifetime of Intermediate Ionic States during Vibrational Excitation 97
3.3.3 Rate Coefficients of Vibrational Excitation by Electron Impact: Semiempirical Fridman’s 100
Approximation
3.3.4 Rotational Excitation of Molecules by Electron Impact 101
3.3.5 Electronic Excitation of Atoms and Molecules by Electron Impact 103
3.3.6 Rate Coefficients of Electronic Excitation in Plasma by Electron Impact 104
3.3.7 Dissociation of Molecules by Direct Electron Impact 106
3.3.8 Distribution of Electron Energy in Nonthermal Discharges between Different Channels of Excitation 107
and Ionization
3.4 Vibrational (VT) Relaxation; the Landau-Teller Formula 113
3.4.1 Vibrational-Translational (VT) Relaxation: Slow Adiabatic Elementary Process 113
3.4.2 Quantitative Relations for Probability of the Elementary Process of Adiabatic VT Relaxation 115
3.4.3 VT Relaxation Rate Coefficients for Harmonic Oscillators: Landau-Teller Formula 117
3.4.4 Vibrational VT Relaxation of Anharmonic Oscillators 119
3.4.5 Fast Nonadiabatic Mechanisms of VT Relaxation 121
3.4.6 VT Relaxation of Polyatomic Molecules 122
3.4.7 Effect of Rotation on the Vibrational Relaxation of Molecules 124
3.5 Vibrational Energy Transfer between Molecules: VV Relaxation Processes 125
3.5.1 Resonant VV Relaxation 125
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3.5.2 VV Relaxation of Anharmonic Oscillators 127
3.5.3 Intermolecular VV′ Exchange 130
3.5.4 VV Exchange of Polyatomic Molecules 132
3.6 Processes of Rotational and Electronic Relaxation of Excited Molecules 135
3.6.1 Rotational Relaxation 135
3.6.2 Relaxation of Electronically Excited Atoms and Molecules 137
3.6.3 Electronic Excitation Energy Transfer Processes 138
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3.7 Elementary Chemical Reactions of Excited Molecules; Fridman-Macheret α-Model 139
3.7.1 Rate Coefficient of Reactions of Excited Molecules 139
3.7.2 Potential Barriers of Elementary Chemical Reactions: Activation Energy 140
3.7.3 Efficiency α of Vibrational Energy in Overcoming Activation Energy Barrier 142
3.7.4 Fridman-Macheret α-Model 142
3.7.5 Efficiency of Vibrational Energy in Elementary Reactions Proceeding through Intermediate 146
Complexes
3.7.6 Dissociation of Molecules Stimulated by Vibrational Excitation in Nonequilibrium Plasma 149
3.7.7 Dissociation of Molecules in Nonequilibrium Conditions with Essential Contribution of 151
Translational Energy
3.7.8 Chemical Reactions of Two Vibrationally Excited Molecules in Plasma 155
Problems and Concept Questions 155
Chapter Plasma Statistics and Kinetics of Charged Particles 161
4
4.1 Statistics and Thermodynamics of Equilibrium and Nonequilibrium Plasmas: Boltzmann, 161
Saha, and Treanor Distributions
4.1.1 Statistical Distribution of Particles over Different States: Boltzmann Distribution 161
4.1.2 Equilibrium Statistical Distribution of Diatomic Molecules over Vibrational-Rotational States 163
4.1.3 Saha Equation for Ionization Equilibrium in Thermal Plasma 164
4.1.4 Dissociation Equilibrium in Molecular Gases 165
4.1.5 Equilibrium Statistical Relations for Radiation: Planck Formula and Stefan-Boltzmann Law 165
4.1.6 Goncepts of Complete Thermodynamic Equilibrium (CTE) and Local Thermodynamic 167
Equilibrium (LTE) for Plasma Systems
4.1.7 Partition Functions 168
4.1.8 Thermodynamic Functions of Thermal Plasma Systems 168
4.1.9 Nonequilibrium Statistics of Thermal and Nonthermal Plasmas 170
4.1.10 Nonequilibrium Statistics of Vibrationally Excited Molecules: Treanor Distribution 172
4.2 Boltzmann and Fokker-Planck Kinetic Equations: Electron Energy Distribution Functions 176
4.2.1 Boltzmann Kinetic Equation 176
4.2.2 The τ-Approximation of the Boltzmann Kinetic Equation 178
4.2.3 Macroscopic Equations Related to Kinetic Boltzmann Equation 179
4.2.4 Fokker-Planck Kinetic Equation for Determination of Electron Energy Distribution 180
Functions
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4.2.5 Different Specific Electron Energy Distribution Functions: Druyvesteyn Distribution 183
4.2.6 Electron Energy Distribution Functions in Different Nonequilibrium Discharge Conditions 186
4.2.7 Relations between Electron Temperature and Reduced Electric Field 187
4.3 Electric and Thermal Conductivity in Plasma: Diffusion of Charged Particles 189
4.3.1 Isotropic and Anisotropic Parts of Electron Distribution Functions 189
4.3.2 Electron Mobility and Plasma Conductivity 190
4.3.3 Similarity Parameters Describing Electron Motion in Nonthermal Discharges 192
4.3.4 Plasma Conductivity in Perpendicular Static Uniform Electric and Magnetic Fields 193
4.3.5 Conductivity of Strongly Ionized Plasma 195
4.3.6 Ion Energy and Ion Drift in Electric Field 196
4.3.7 Free Diffusion of Electrons and Ions 197
4.3.8 Einstein Relation among Diffusion Coefficient, Mobility, and Mean Energy 199
4.3.9 Ambipolar Diffusion 199
4.3.10 Conditions of Ambipolar Diffusion: Debye Radius 201
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4.3.11 Thermal Conductivity in Plasma 202
4.4 Breakdown Phenomena: Townsend and Spark Mechanisms, Avalanches, Streamers, and Leaders 204
4.4.1 Electric Breakdown of Gases: Townsend Mechanism 204
4.4.2 Critical Breakdown Conditions: Paschen Curves 209
4.4.3 Townsend Breakdown of Larger Gaps: Specific Behavior of Electronegative Gases 211
4.4.4 Sparks vs. Townsend Breakdown Mechanism 213
4.4.5 Physics of Electron Avalanches 214
4.4.6 Cathode- and Anode-Directed Streamers 218
4.4.7 Criterion of Streamer Formation: Meek Breakdown Condition 219
4.4.8 Streamer Propagation Models 221
4.4.9 Concept of a Leader: Breakdown of Multimeter and Kilometer Long Gaps 223
4.5 Steady-State Regimes of Nonequilibrium Electric Discharges 225
4.5.1 Steady-State Discharges Controlled by Volume and Surface Recombination Processes 225
4.5.2 Discharge Regime Controlled by Electron-Ion Recombination 227
4.5.3 Discharge Regime Controlled by Electron Attachment 228
4.5.4 Discharge Regime Controlled by Charged Particle Diffusion to Walls: Engel-Steenbeck Relation 229
4.5.5 Propagation of Electric Discharges 231
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4.5.6 Propagation of Nonthermal Ionization Waves Self-Sustained by Diffusion of Plasma 233
Chemical Products
4.5.7 Nonequilibrium Behavior of Electron Gas: Difference between Electron and Neutral Gas 235
Temperatures
4.5.8 Nonequilibrium Behavior of Electron Gas: Deviations from the Saha Formula—Degree of 236
Ionization
Problems and Concept Questions 237
Chapter Kinetics of Excited Particles in Plasma 243
5
5.1 Vibrational Distribution Functions in Nonequilibrium Plasma: Fokker-Planck Kinetic Equation 243
5.1.1 Nonequilibrium Vibrational Distribution Functions: General Concept of Fokker-Plank 244
Equation
5.1.2 Energy-Space Diffusion-Related VT Flux of Excited Molecules 245
5.1.3 Energy-Space Diffusion-Related VV Flux of Excited Molecules 246
5.1.4 Linear VV Flux along Vibrational Energy Spectrum 247
5.1.5 Nonlinear VV Flux along Vibrational Energy Spectrum 248
5.1.6 Equation for Steady-State Vibrational Distribution Function Controlled by VV and VT 249
Relaxation Processes
5.1.7 Vibrational Distribution Functions: Strong Excitation Regime 250
5.1.8 Vibrational Distribution Functions: Intermediate Excitation Regime 252
5.1.9 Vibrational Distribution Functions: Regime of Weak Excitation 253
5.2 Nonequilibrium Vibrational Kinetics: eV Processes, Polyatomic Molecules, and Non-Steady- 256
State Regimes
5.2.1 eV Flux along Vibrational Energy Spectrum 256
5.2.2 Influence of eV Relaxation on Vibrational Distribution at High Degrees of Ionization 257
5.2.3 Influence of eV Relaxation on Vibrational Distribution at Intermediate Degrees of 258
Ionization
5.2.4 Diffusion in Energy Space and Relaxation Fluxes of Polyatomic Molecules in Quasi 260
Continuum
5.2.5 Vibrational Distribution Functions of Polyatomic Molecules in Nonequilibrium Plasma 263
5.2.6 Non-Steady-State Vibrational Distribution Functions 264
5.3 Macrokinetics of Chemical Reactions and Relaxation of Vibrationally Excited Molecules 265
5.3.1 Chemical Reaction Influence on Vibrational Distribution Function: Weak Excitation Regime 265
5.3.2 Macrokinetics of Reactions of Vibrationally Excited Molecules: Weak Excitation Regime 267
5.3.3 Macrokinetics of Reactions of Vibrationally Excited Molecules in Regimes of Strong and 269
Intermediate Excitation
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5.3.4 Macrokinetics of Reactions of Vibrationally Excited Polyatomic Molecules 270
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5.3.5 Macrokinetics of Reactions of Two Vibrationally Excited Molecules 271
5.3.6 Vibrational Energy Losses Due to VT Relaxation 272
5.3.7 VT Relaxation Losses from Low Vibrational Levels: Losev Formula and Lahdau-Teller Relation 273
5.3.8 VT Relaxation Losses from High Vibrational Levels 273
5.3.9 Vibrational Energy Losses Due to Nonresonance Nature of VV Exchange 275
5.4 Vibrational Kinetics in Gas Mixtures: Isotopic Effect in Plasma Chemistry 276
5.4.1 Kinetic Equation and Vibrational Distribution in Gas Mixture 277
5.4.2 Treanor Isotopic Effect in Vibrational Kinetics 278
5.4.3 Influence of VT Relaxation on Vibrational Kinetics of Mixtures: Reverse Isotopic Effect 280
5.4.4 Influence of eV Relaxation on Vibrational Kinetics of Mixtures and Isotopic Effect 283
5.4.5 Integral Effect of Isotope Separation 285
5.5 Kinetics of Electronically and Rotationally Excited States: Nonequilibrium Translational Distributions: 286
Relaxation and Reactions of “Hot” Atoms in Plasma
5.5.1 Kinetics of Population of Electronically Excited States: Fokker-Planck Approach 286
5.5.2 Simplest Solutions of Kinetic Equation for Electronically Excited States 287
5.5.3 Kinetics of Rotationally Excited Molecules: Rotational Distribution Functions 289
5.5.4 Nonequilibrium Translational Energy Distribution Functions: Effect of “Hot Atoms” 291
5.5.5 Kinetics of Hot Atoms in Fast VT Relaxation Processes: Energy-Space Diffusion Approximation 291
5.5.6 Hot Atoms in Fast VT Relaxation Processes: Discrete Approach and Applications 293
5.5.7 Hot Atom Formation in Chemical Reactions 295
5.6 Energy Efficiency, Energy Balance, and Macrokinetics of Plasma Chemical Processes 297
5.6.1 Energy Efficiency of Quasi-Equilibrium and Nonequilibrium Plasma Chemical Processes 298
5.6.2 Energy Efficiency of Plasma Chemical Processes Stimulated by Vibrational Excitation of Molecules 299
5.6.3 Dissociation and Reactions of Electronically Excited Molecules and Their Energy Efficiency 299
5.6.4 Energy Efficiency of Plasma Chemical Processes Proceeding through Dissociative Attachment 300
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5.6.5 Methods of Stimulation of Vibrational-Translational Nonequilibrium in Plasma 301
Vibrational-Translational Nonequilibrium Provided by High Degree of Ionization 301
Vibrational-Translational Nonequilibrium Provided by Fast Gas Cooling 301
5.6.6 Vibrational-Translational Nonequilibrium Provided by Fast Transfer of Vibrational Energy: 302
Treanor Effect in Vibrational Energy Transfer
5.6.7 Energy Balance and Energy Efficiency of Plasma Chemical Processes Stimulated by 304
Vibrational Excitation of Molecules
5.6.8 Energy Efficiency as Function of Specific Energy Input and Degree of Ionization 306
5.6.9 Components of Total Energy Efficiency: Excitation, Relaxation, and Chemical Factors 309
5.7 Energy Efficiency of Quasi-Equilibrium Plasma Chemical Systems: Absolute, Ideal, and 311
Super-Ideal Quenching
5.7.1 Concepts of Absolute, Ideal, and Super-Ideal Quenching 311
5.7.2 Ideal Quenching of CO2 Dissociation Products in Thermal Plasma 312
5.7.3 Nonequilibrium Effects during Product Cooling: Super-Ideal Quenching 313
5.7.4 Mechanisms of Absolute and Ideal Quenching for H2O Dissociation in Thermal Plasma 315
5.7.5 Effect of Cooling Rate on Quenching Efficiency: Super-Ideal Quenching of H2O 316
Dissociation Products
5.7.6 Mass and Energy Transfer Equations in Multicomponent Quasi Equilibrium Plasma 318
Chemical Systems
5.7.7 Influence of Transfer Phenomena on Energy Efficiency of Plasma Chemical Processes 320
Problems and Concept Questions 324
Chapter Electrostatics, Electrodynamics, and Fluid Mechanics of Plasma 331
6
6.1 Electrostatic Plasma Phenomena: Debye Radius and Sheaths, Plasma Oscillations, and 331
Plasma Frequency
6.1.1 Ideal and Nonideal Plasmas 331
6.1.2 Plasma Polarization, “Screening” of Electric Charges, and External Electric Fields: Debye 332
Radius in Two-Temperature Plasma
6.1.3 Plasmas and Sheaths 333
6.1.4 Physics of DC Sheaths 335
6.1.5 High-Voltage Sheaths: Matrix and Child Law Sheath Models 336
6.1.6 Electrostatic Plasma Oscillations: Langmuir or Plasma Frequency 337
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6.1.7 Penetration of Slow Changing Fields into Plasma: Skin Effect 338
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6.2 Magneto-Hydrodynamics of Plasma 340
6.2.1 Equations of Magneto-Hydrodynamics 340
6.2.2 Magnetic Field “Diffusion” in Plasma: Effect of Magnetic Field Frozen in Plasma 341
6.2.3 Magnetic Pressure: Plasma Equilibrium in Magnetic Field 342
6.2.4 The Pinch-Effect 343
6.2.5 Two-Fluid Magneto-Hydrodynamics: Generalized Ohm’s Law 344
6.2.6 Plasma Diffusion across Magnetic Field 346
6.2.7 Conditions for Magneto-Hydrodynamic Behavior of Plasma: Alfven Velocity and Magnetic Reynolds 348
Number
6.3 Instabilities of Low-Temperature Plasma 349
6.3.1 Types of Instabilities of Low-Temperature Plasmas: Peculiarities of Plasma Chemical Systems 350
6.3.2 Thermal (Ionization-Overheating) Instability in Monatomic Gases 351
6.3.3 Thermal (Ionization-Overheating) Instability in Molecular Gases with Effective Vibrational 353
Excitation
6.3.4 Physical Interpretation of Thermal and Vibrational Instability Modes 355
6.3.5 Nonequilibrium Plasma Stabilization by Chemical Reactions of Vibrationally Excited Molecules 356
6.3.6 Destabilizing Effect of Exothermic Reactions and Fast Mechanisms of Chemical Heat Release 358
6.3.7 Electron Attachment Instability 359
6.3.8 Other Instability Mechanisms in Low-Temperature Plasma 361
6.4 Nonthermal Plasma Fluid Mechanics in Fast Subsonic and Supersonic Flows 362
6.4.1 Nonequilibrium Supersonic and Fast Subsonic Plasma Chemical Systems 363
6.4.2 Gas Dynamic Parameters of Supersonic Discharges: Critical Heat Release 364
6.4.3 Supersonic Nozzle and Discharge Zone Profiling 365
6.4.4 Pressure Restoration in Supersonic Discharge Systems 367
6.4.5 Fluid Mechanic Equations of Vibrational Relaxation in Fast Subsonic and Supersonic Flows of 367
Nonthermal Reactive Plasma
6.4.6 Dynamics of Vibrational Relaxation in Fast Subsonic and Supersonic Flows 369
6.4.7 Effect of Chemical Heat Release on Dynamics of Vibrational Relaxation in Supersonic Flows 372
6.4.8 Spatial Nonuniformity of Vibrational Relaxation in Chemically Active Plasma 373
6.4.9 Space Structure of Unstable Vibrational Relaxation 376
6.5 Electrostatic, Magneto-Hydrodynamic, and Acoustic Waves in Plasma 378
6.5.1 Electrostatic Plasma Waves 378
6.5.2 Collisional Damping of Electrostatic Plasma Waves in Weakly Ionized Plasma 379
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6.5.3 Ionic Sound 380
6.5.4 Magneto-Hydrodynamic Waves 381
6.5.5 Collisionless Interaction of Electrostatic Plasma Waves with Electrons 382
6.5.6 Landau Damping 384
6.5.7 Beam Instability 385
6.5.8 Buneman Instability 386
6.5.9 Dispersion and Amplification of Acoustic Waves in Nonequilibrium Weakly Ionized Plasma: General 387
Dispersion Equation
6.5.10 Analysis of Dispersion Equation for Sound Propagation in Nonequilibrium Chemically Active 389
Plasma
6.6 Propagation of Electromagnetic Waves in Plasma 393
6.6.1 Complex Dielectric Permittivity of Plasma in High-Frequency Electric Fields 393
6.6.2 High-Frequency Plasma Conductivity and Dielectric Permittivity 395
6.6.3 Propagation of Electromagnetic Waves in Plasma 396
6.6.4 Absorption of Electromagnetic Waves in Plasmas: Bouguer Law 398
6.6.5 Total Reflection of Electromagnetic Waves from Plasma: Critical Electron Density 399
6.6.6 Electromagnetic Wave Propagation in Magnetized Plasma 400
6.6.7 Propagation of Ordinary and Extraordinary Polarized Electromagnetic Waves in Magnetized Plasma 402
6.6.8 Influence of Ion Motion on Electromagnetic Wave Propagation in Magnetized Plasma 403
6.7 Emission and Absorption of Radiation in Plasma: Continuous Spectrum 404
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6.7.1 Classification of Radiation Transitions 404
6.7.2 Spontaneous and Stimulated Emission: Einstein Coefficients 405
6.7.3 General Approach to Bremsstrahlung Spontaneous Emission: Coefficients of Radiation Absorption 407
and Stimulated Emission during Electron Collisions with Heavy Particles
6.7.4 Bremsstrahlung Emission due to Electron Collisions with Plasma Ions and Neutrals 408
6.7.5 Recombination Emission 411
6.7.6 Total Emission in Continuous Spectrum 413
6.7.7 Plasma Absorption of Radiation in Continuous Spectrum: Kramers and Unsold-Kramers Formulas 414
6.7.8 Radiation Transfer in Plasma 416
6.7.9 Optically Thin Plasmas and Optically Thick Systems: Black Body Radiation 417
6.7.10 Reabsorption of Radiation, Emission of Plasma as Gray Body, Total Emissivity Coefficient 418
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6.8 Spectral Line Radiation in Plasma 419
6.8.1 Probabilities of Radiative Transitions and Intensity of Spectral Lines 419
6.8.2 Natural Width and Profile of Spectral Lines 420
6.8.3 Doppler Broadening of Spectral Lines 422
6.8.4 Pressure Broadening of Spectral Lines 423
6.8.5 Stark Broadening of Spectral Lines 424
6.8.6 Convolution of Lorentzian and Gaussian Profiles: Voigt Profile of Spectral Lines 425
6.8.7 Spectral Emissivity of a Line: Constancy of a Spectral Line Area 425
6.8.8 Selective Absorption of Radiation in Spectral Lines: Absorption of One Classical Oscillator 426
6.8.9 Oscillator Power 427
6.8.10 Radiation Transfer in Spectral Lines: Inverse Population of Excited States and Principle 428
of Laser Generation
6.9 Nonlinear Phenomena in Plasma 429
6.9.1 Nonlinear Modulation Instability: Lighthill Criterion 430
6.9.2 Korteweg-de Vries Equation 431
6.9.3 Solitones as Solutions of Korteweg-de Vries Equation 432
6.9.4 Formation of Langmuir Solitones in Plasma 433
6.9.5 Evolution of Strongly Nonlinear Oscillations: Nonlinear Ionic Sound 434
6.9.6 Evolution of Weak Shock Waves in Plasma 436
6.9.7 Transition from Weak to Strong Shock Wave 437
Problems and Concept Questions 438

PART II Physics and Engineering of Electric Discharges 445

Chapter Glow Discharge 447
7
7.1 Structure and Physical Parameters of Glow Discharge Plasma, Current-Voltage 447
Characteristics: Comparison of Glow and Dark Discharges
7.1.1 General Classification of Discharges: Thermal and Nonthermal Discharges 447
7.1.2 Glow Discharge: General Structure and Configurations 449
7.1.3 Glow Pattern and Distribution of Plasma Parameters along Glow Discharge 451
7.1.4 General Current-Voltage Characteristic of Continuous Self-Sustained DC Discharges 452
between Electrodes
7.1.5 Dark Discharge Physics 454
7.1.6 Transition of Townsend Dark to Glow Discharge 455
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7.2 Cathode and Anode Layers of Glow Discharge 457
7.2.1 Engel-Steenbeck Model of Cathode Layer 457
7.2.2 Current-Voltage Characteristic of Cathode Layer 458
7.2.3 Normal Glow Discharge: Normal Cathode Potential Drop, Layer Thickness, and Current Density 459
7.2.4 Mechanism Sustaining Normal Cathode Current Density 460
7.2.5 Steenbeck Minimum Power Principle: Application to Effect of Normal Cathode Current Density 463
7.2.6 Glow Discharge Regimes Different from Normal: Abnormal, Subnormal, and Obstructed 464
Discharges
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7.2.7 Negative Glow Region of Cathode Layer: Hollow Cathode Discharge 465
7.2.8 Anode Layer 466
7.3 Positive Column of Glow Discharge 467
7.3.1 General Features of Positive Column: Balance of Charged Particles 467
7.3.2 General Current-Voltage Characteristics of a Positive Column and a Glow Discharge 468
7.3.3 Heat Balance and Plasma Parameters of Positive Column 470
7.3.4 Glow Discharge in Fast Gas Flows 472
7.3.5 Heat Balance and Its Influence on Current-Voltage Characteristics of Positive Columns 473
7.4 Glow Discharge Instabilities 474
7.4.1 Contraction of Positive Column 474
7.4.2 Glow Discharge Conditions Resulting in Contraction 476
7.4.3 Comparison of Transverse and Longitudinal Instabilities: Observation of Striations in Glow 477
Discharges
7.4.4 Analysis of Longitudinal Perturbations Resulting in Formation of Striations 479
7.4.5 Propagation Velocity and Oscillation Frequency of Striations 480
7.4.6 The Steenbeck Minimum Power Principle: Application to Striations 482
7.4.7 Some Approaches to Stabilization of Glow Discharge Instabilities 483
7.5 Different Specific Glow Discharge Plasma Sources 484
7.5.1 Glow Discharges in Cylindrical Tubes, Parallel Plate Configuration, Fast Longitudinal and 484
Transverse Flows
7.5.2 Penning Glow Discharges 484
7.5.3 Plasma Centrifuge 486
7.5.4 Magnetron Discharges 487
7.5.5 Magnetic Mirror Effect in Magnetron Discharges 490
7.5.6 Atmospheric Pressure Glow Discharges 491
7.5.7 Some Energy Efficiency Peculiarities of Glow Discharge Application for Plasma Chemical Processes 492
Problems and Concept Questions 493
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Chapter Arc Discharges 499
8
8.1 Physical Features, Types, Parameters, and Current-Voltage Characteristics of Arc 499
Discharges
8.1.1 General Characteristic Features of Arc Discharges 499
8.1.2 Typical Ranges of Arc Discharge Parameters 500
8.1.3 Classification of Arc Discharges 500
8.1.4 Current-Voltage Characteristics of Arc Discharges 502
8.2 Mechanisms of Electron Emission from Cathode 504
8.2.1 Thermionic Emission: Sommerfeld Formula 504
8.2.2 Schottky Effect of Electric Field on Work Function and Thermionic Emission Current 505
8.2.3 Field Electron Emission in Strong Electric Fields: Fowler-Nordheim Formula 506
8.2.4 Thermionic Field Emission 508
8.2.5 Secondary Electron Emission 509
8.3 Cathode and Anode Layers in Arc Discharges 512
8.3.1 General Features and Structure of Cathode Layer 512
8.3.2 Electric Field in Cathode Vicinity 514
8.3.3 Cathode Energy Balance and Electron Current Fraction on Cathode (S-factor) 516
8.3.4 Cathode Erosion 516
8.3.5 Cathode Spots 517
8.3.6 External Cathode Heating 518
8.3.7 Anode Layer 519
8.4 Positive Column of Arc Discharges 519
8.4.1 General Features of Positive Column of High-Pressure Arcs 519
8.4.2 Thermal Ionization in Arc Discharges: Elenbaas-Heller Equation 521
8.4.3 The Steenbeck “Channel” Model of Positive Column of Arc Discharges 522
8.4.4 Raizer “Channel” Model of Positive Column 524
8.4.5 Plasma Temperature, Specific Power, and Electric Field in Positive Column According to 526
Channel Model
8.4.6 Possible Difference between Electron and Gas Temperatures in Thermal Discharges 528
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