PHYSICS OF IONIZED GASES
BORIS M. SMIRNOV Russian Academy of Sciences
With the editorial collaboration of Howard R. Reiss
A Wiley-lnterscience Publication
JOHN WILEY & SONS, INC.
New York / Chichester / Weinham / Brisbane / Singapore / Toronto
CONTENTS
PREFACE xiii
1 PLASMA IN NATURE AND IN LABORATORY SYSTEMS 1
1.1 Plasma as a State of Matter / 1
1.2 Methods of Plasma Generation / 4
1.3 Plasmas in Laboratory Devices / 7
1.4 Plasma in Contemporary Technology / 1 0
1.5 Terrestrial Atmospheric Plasma / 1 2
1.6 Solar Plasma / 14
1.7 Plasma with a Condensed Phase / 16
2 STATISTICS OF A WEAKLY IONIZED GAS 18
2.1 Distribution Functions / 1 8
2.2 The Boltzmann Distribution / 19
2.3 Statistical Weight of a State and Distributions of Particles in Gases / 21
2.4 The Maxwell Distribution / 23
2.5 The Saha Distribution / 24
2.6 Dissociative Equilibrium in Molecular Gases / 26
2.7 Laws of Blackbody Radiation / 26
2.8 Ionization Equilibrium in an Aerosol Plasma / 28
2.9 Thermoemission of Electrons / 30
v
Vi CONTENTS
2.10 The Treanor Effect / 31
2.11 Normal Distribution / 34
3 THE IDEAL PLASMA 36
3.1 Conditions for an Ideal Plasma / 36
3.2 Charged Particles in a Gas / 37
3.3 Penetration of Electric Fields into Plasmas / 37
3.4 Definition of a Plasma / 39
3.5 Oscillations of Plasma Electrons / 40
3.6 Interactions in Ideal Plasmas / 41
3.7 Beam Plasma / 42
4 ELEMENTARY PLASMA PROCESS 45
4.1 Particle Collisions in Plasmas / 45
4.2 Elastic Collisions / 46
4.3 Hard-Sphere Model / 49
4.4 Capture Cross Section / 50
4.5 Total Scattering Cross Section / 52
4.6 Gaseous-State Criterion / 53
4.7 Slow Inelastic Collisions / 54
4.8 Autoionizing and Autodetaching States in Collision Processes / 56
4.9 Types of Elementary Process / 59
5 PROCESSES INVOLVING CHARGED PARTICLES 63
5.1 Atomic Ionization by Electron Impact / 63
5.2 Collision of Two Charged Particles in a Plasma / 65
5.3 Mutual Recombination of Positive and Negative Ions / 66
5.4 Three-Body Collision Processes / 67
5.5 Three-Body Recombination of Electrons and Ions / 69
5.6 Three-Body Recombination of Positive and Negative Ions / 70
5.7 Stepwise Ionization of Atoms / 7 1
5.8 Dissociative Recombination / 73
5.9 Dielectronic Recombination / 74
5.10 Charge-Exchange Processes / 75
RAREFIED AND DENSE PLASMAS
6.1 Criteria for an Ideal Plasma / 77
6.2 Conditions for Ideal Equilibrium Plasmas / 79
6.3 Instability of Two-Component Strongly Coupled Plasmas / 80
6.4 Special Features of Strongly Coupled Plasmas / 82
6.5 Quantum Plasmas / 83
6.6 Ideal Electron-Gas and Ion-Gas Systems / 86
6.7 Decrease of the Atomic Ionization Potential in Plasmas / 87
6.8 Interactions and Structures in Dusty Plasmas / 89
RADIATIVE PROCESSES IN WEAKLY IONIZED GASES
7.1 Interaction of Radiation with Atomic Systems / 91
7.2 Spontaneous and Stimulated Emission / 92
7.3 Broadening of Spectral Lines / 94
7.4 Impact Broadening of Spectral Lines / 96
7.5 Statistical Broadening of Spectral Lines / 98
7.6 Cross Sections for Photon Emission and Absorption / 101
7.7 The Absorption Coefficient / 102
7.8 Propagation of Resonant Radiation through a Gas / 103
7.9 Self-Reversal of Spectral Lines / 105
7.10 Photoresonant Plasma / 106
7.11 Radiation from the Solar Photosphere / 109
EXCITED ATOMS IN GASES AND PLASMAS
8.1 Excitation and Quenching of Excited States by Electron Impact / 1 1 3
8.2 Equilibrium of Resonantly Excited Atoms in a Plasma / 1 1 5
8.3 Lifetimes of Resonantly Excited Atoms in a Plasma / 1 1 6
8.4 Stepwise Ionization through Resonantly Excited States / 117
8.5 Associative Ionization and the Penning Process / 1 1 8
8.6 Processes Involving Formation of a Long-Lived Complex / 119
8.7 Excimer Molecules / 121
viii CONTENTS
9 PHYSICAL KINETICS OF GASES AND PLASMAS 123
9.1 The Boltzmann Kinetic Equation / 123
9.2 Macroscopic Gas Equations / 125
9.3 Equation of State / 127
9.4 Collision Integral / 129
9.5 Macroscopic Equation for Ion Motion in a Gas / 130
9.6 Collision Integral for Electrons in a Gas / 132
9.7 Electrons in a Gas in an External Electric Field / 134
9.8 Electron Equilibrium in a Gas / 1 3 6
9.9 The Landau Collision Integral / 138
9.10 Excitation of Atoms in a Plasma / 142
10 TRANSPORT PHENOMENA IN GASES 147
10.1 Transport of Particles in Gases / 147
10.2 Diffusive Particle Motion / 149
10.3 Diffusion of Electrons in Gases / 150
10.4 The Einstein Relation / 152
10.5 Heat Transport / 153
10.6 Thermal Conductivity Due to Internal Degrees of Freedom / 154
10.7 Thermal Capacity of Molecules / 155
10.8 Momentum Transport / 157
10.9 The Navier-Stokes Equation / 157
10.10 Thermal Diffusion of Electrons / 158
10.11 Electron Thermal Conductivity / 160
11 CHARGED-PARTICLE TRANSPORT IN GASES 164
11.1 Mobility of Charged Particles / 1 6 4
11.2 Mobility of Ions in a Foreign Gas / 165
11.3 Mobility of Ions in the Parent Gas / 166
11.4 Energetic Townsend Coefficient / 1 6 8
11.5 Conductivity of a Weakly Ionized Gas / 170
11.6 Conductivity of a Strongly Ionized Plasma / 170
11.7 Ambipolar Diffusion / 171
11.8 Electrophoresis / 173
11.9 Recombination of Ions in Dense Gases / 174
11.10 Gas-density Dependence of the Ionic Recombination Coefficient / 175
CONTENTS IX
12 SMALL PARTICLES IN PLASMAS 177
12.1 Plasmas with Dispersed Inclusions / 1 7 7
12.2 Polarizability of Small Particles / 179
12.3 Absorption Cross Section for Small Particles / 180
12.4 Mobility of Large Clusters / 183
12.5 Recombination Coefficient of Small Charged Clusters / 184
12.6 Multicharged Clusters in Hot Gases and Plasmas / 184
12.7 Charging of Small Particles in a Plasma / 186
12.8 Charged Particles in an Aerosol Plasma / 187
12.9 Electric Fields in Aerosol Plasmas / 190
12.10 Electric Processes in Clouds / 190
12.11 Size Distribution of Clusters in Gases / 192
12.12 Critical Size of Clusters / 194
12.13 Clusters in Hot, Weakly Ionized Gas / 195
12.14 Kinetics of Cluster Processes in the Parent Vapor / 196
12.15 Coagulation of Clusters in Expanding Gas / 200
12.16 Metallic Clusters in Arc Plasmas / 201
12.17 Instability in a Cluster Plasma / 203
13 PLASMA IN EXTERNAL FIELDS 205
13.1 Motion of an Electron in a Gas in External Fields / 205
13.2 Conductivity of a Weakly Ionized Gas / 206
13.3 Dielectric Constant of a Weakly Ionized Gas / 207
13.4 Plasma in a Time-Dependent Electric Field / 208
13.5 The Hall Effect / 210
13.6 Cyclotron Resonance / 212
13.7 Motion of Charged Particles in a Nonuniform Magnetic Field / 213
13.8 Excitation of a Weakly Ionized Gas by External Fields / 216
13.9 Magnetohydrodynamic Equations / 218
13.10 High-Conductivity Plasma in a Magnetic Field / 219
13.11 Pinch Effect / 221
13.12 Skin Effect / 222
13.13 Reconnection of Magnetic Lines of Force / 223
X CONTENTS
14 INSTABILITIES OF EXCITED GASES 225
14.1 Convective Instability of Gases / 225
14.2 The Rayleigh Problem / 226
14.3 Convective Movement of Gases / 229
14.4 Convective Heat Transport / 230
14.5 Instability of Convective Motion / 232
14.6 Thermal Explosion / 234
14.7 Thermal Waves / 236
14.8 Vibrational-Relaxation Thermal Waves / 242
14.9 Ozone-Decomposition Thermal Waves / 245
15 WAVES IN PLASMAS 249
15.1 Acoustic Oscillations / 249
15.2 Plasma Oscillations / 251
15.3 Ion Sound / 253
15.4 Magnetohydrodynamic Waves / 255
15.5 Propagation of Electromagnetic Waves in Plasmas / 256
15.6 The Faraday Effect for Plasmas / 257
15.7 Whistlers / 259
16 PLASMA INSTABILITIES 262
16.1 Damping of Plasma Oscillations in Ionized Gases / 262
16.2 Interaction between Plasma Oscillations and Electrons / 263
16.3 Attenuation Factor for Waves in Plasmas / 265
16.4 Beam-Plasma Instability / 267
16.5 The Buneman Instability / 269
16.6 Hydrodynamic Instabilities / 270
17 NONLINEAR PHENOMENA IN PLASMAS 272
17.1 The Lighthill Criterion / 272
17.2 The Korteweg-de Vries Equation / 273
17.3 Solitons / 275
17.4 Langmuir Soliton / 276
17.5 Nonlinear Ion Sound / 277
17.6 Parametric Instability / 279
CONTENTS Xi
18 IONIZATION INSTABILITIES AND PLASMA STRUCTURES 284
18.1 Drift Waves / 284 18.2 Ionization Instability from Thermal Effects / 285 18.3 Ionization Instability of a Plasma in a Magnetic
Field / 287 18.4 Attachment Instability of a Molecular Gas / 289 18.5 Electric Domain / 291 18.6 Striations / 294 18.7 Characteristics of Striation Formation / 298 18.8 Current-Convective Instability / 301
19 ATMOSPHERIC PLASMAS 304
19.1 Special Features of Atmospheric Plasmas / 304 19.2 The Earth as an Electrical System / 307 19.3 Lightning / 309 19.4 Prebreakdown Phenomena in the Atmosphere / 311 19.5 Ionosphere / 313 19.6 Atomic Oxygen in the Upper Atmosphere / 316 19.7 Ions in the Upper Atmosphere / 318
20 GAS-DISCHARGE PLASMAS 321
20.1 Properties of Gas-Discharge Plasmas / 321 20.2 Electrons in the Positive Column of a Glow
Discharge / 322 20.3 Double Layer / 325 20.4 Thermal Regime of Gas Discharges / 326 20.5 Positive Column of a Gas Discharge at High
Pressure / 327 20.6 Positive Column of Low-Pressure Discharges / 334 20.7 Ignition Conditions for Low-Current Discharges / 338 20.8 Breakdown of Gases / 340 20.9 Cathode Region of a Glow Discharge / 342 20.10 Contraction of the Positive Column of a Glow
Discharge / 346 20.11 Plasma Hardening / 347
21 PLASMA INTERACTIONS WITH SURFACES 350
21.1 Cathode Sputtering and Its Uses / 350 21.2 Laser Vaporization / 353
xii CONTENTS
21.3 Etching / 357 21.4 Explosive Emission / 358 21.5 Secondary Electron Emission / 361 21.6 Quenching of Excited Particles on Walls / 362
22 CONCLUSIONS 366
APPENDICES 367
BIBLIOGRAPHY 374
INDEX 377
