Table of Contents
1 Introduction 1
1.1 The Roots of Plasma Physics 2
1.2 The Plasma Environment of Our Earth 4
1.2.1 The Energy Source of Stars 4
1.2.2 The Active Sun 5
1.2.3 The Solar Wind 7
1.2.4 Earth's Magnetosphere and Ionosphere 9
1.3 Gas Discharges 12
1.3.1 Lighting 12
1.3.2 Plasma Displays 14
1.4 Dusty Plasmas 15
1.5 Controlled Nuclear Fusion 17
1.5.1 A Particle Accelerator Makes No Fusion Reactor 18
1.5.2 Magnetic Confinement in Tokamaks 19
1.5.3 Experiments with D-T Mixtures 19
1.5.4 The International Thermonuclear Experimental Reactor 20
1.5.5 Stellarators 22
1.5.6 Inertial Confinement Fusion 23
1.6 Challenges of Plasma Physics 24
1.7 Outline of the Book 25
2 Definition of the Plasma State 29
2.1 States of Matter 29
2.1.1 The Boltzmann Distribution 30
2.1.2 The Saha Equation 32
2.1.3 The Coupling Parameter 34
2.2 Collective Behavior of a Plasma 34
2.2.1 Debye Shielding 35
2.2.2 Quasineutrality 39
2.2.3 Response Time and Plasma Frequency 39
2.3 Existence Regimes 40
2.3.1 Strong-Coupling Limit 40
2.3.2 Quantum Effects 42
Problems 43
3 Single Particle Motion in Electric and Magnetic Fields 45
3.1 Motion in Static Electric and Magnetic Fields 45
3.1.1 Basic Equations 45
3.1.2 Cyclotron Frequencies 46
3.1.3 The Earth Magnetic Field 47
3.1.4 E×B Drift 48
3.1.5 Gravitational Drift 49
3.1.6 Application: Confinement of Nonneutral Plasmas 50
3.2 The Drift Approximation 51
3.2.1 The Concept of a Guiding Center 51
3.2.2 Gradient Drift 51
3.2.3 Curvature Drift 53
3.2.4 The Toroidal Drift 53
3.3 The Magnetic Mirror 54
3.3.1 Longitudinal Gradient 55
3.3.2 Magnetic Moment 56
3.4 Adiabatic Invariants 56
3.4.1 The Magnetic Moment as First Invariant 57
3.4.2 The Mirror Effect 57
3.4.3 The Longitudinal and the Flux Invariant 59
3.5 Time-Varying Fields 60
3.5.1 The Polarization Drift 60
3.5.2 Time-Varying Magnetic field 61
3.6 Toroidal Magnetic Confinement 62
3.6.1 The Tokamak Principle 63
3.6.2 The Stellarator Principle 65
3.6.3 Rotational Transform 65
3.7 Electron Motion in an Inhomogeneous Oscillating Electric Field 67
3.7.1 The Ponderomotive Force 67
Problems 69
4 Stochastic Processes in a Plasma 73
4.1 The Velocity Distribution 73
4.1.1 The Maxwell Velocity Distribution in One Dimension 73
4.1.2 The Maxwell Distribution of Speeds 75
4.1.3 Moments of the Distribution Function 75
4.1.4 Distribution of Particle Energies 76
4.2 Collisions 77
4.2.1 Cross Section 77
4.2.2 Mean Free Path and Collision Frequency 78
4.2.3 Rate Coefficients 79
4.2.4 Inelastic Collisions 80
4.2.5 Coulomb Collisions 81
4.3 Transport 83
4.3.1 Mobility and Drift Velocity 83
4.3.2 Electrical Conductivity 84
4.3.3 Diffusion 85
4.3.4 Motion in Magnetic Fields in the Presence of Collisions 89
4.3.5 Application: Cross-Field Motion in a Hall Ion Thruster 92
4.4 Heat Balance of Plasmas 94
4.4.1 Electron Heating in a Gas Discharge 94
4.4.2 Ignition of a Fusion Reaction: The Lawson Criterion 96
4.4.3 Inertial Confinement Fusion 101
Problems 105
5 Fluid Models 107
5.1 The Two-Fluid Model 108
5.1.1 Maxwell's Equations 108
5.1.2 The Concept of a Fluid Description 109
5.1.3 The Continuity Equation 110
5.1.4 Momentum Transport 111
5.1.5 Shear Flows 114
5.2 Magnetohydrostatics 115
5.2.1 Isobaric Surfaces 116
5.2.2 Magnetic Pressure 117
5.2.3 Diamagnetic Drift 119
5.3 Magnetohydrodynamics 120
5.3.1 The Generalized Ohm's Law 121
5.3.2 Diffusion of a Magnetic Field 121
5.3.3 The Frozen-in Magnetic Flux 123
5.3.4 The Pinch Effect 124
5.3.5 Application: Alfvén Waves 125
5.3.6 Application: The Parker Spiral 128
Problems 130
6 Plasma Waves 133
6.1 Maxwell's Equations and the Wave Equation 133
6.1.1 Basic Concepts 134
6.1.2 Fourier Representation 135
6.1.3 Dielectric or Conducting Media 135
6.1.4 Phase Velocity 137
6.1.5 Wave Packet and Group Velocity 137
6.1.6 Refractive Index 139
6.2 The General Dispersion Relation 139
6.3 Waves in Unmagnetized Plasmas 140
6.3.1 Electromagnetic Waves 141
6.3.2 The Influence of Collisions 143
6.4 Interferometry with Microwaves and Lasers 144
6.4.1 Mach-Zehnder Interferometer 145
6.4.2 Folded Michelson Interferometer 148
6.4.3 The Second-Harmonic Interferometer 149
6.4.4 Plasma-Filled Microwave Cavities 150
6.5 Electrostatic Waves 151
6.5.1 The Longitudinal Mode 151
6.5.2 Bohm-Gross Waves 152
6.5.3 Ion-Acoustic Waves 153
6.6 Waves in Magnetized Plasmas 156
6.6.1 The Dielectric Tensor 156
6.6.2 Circularly Polarized Modes and the Faraday Effect 158
6.6.3 Propagation Across the Magnetic Field 162
6.7 Resonance Cones 165
Problems 167
7 Plasma Boundaries 169
7.1 The Space-Charge Sheath 169
7.2 The Child-Langmuir Law 170
7.3 The Bohm Criterion 172
7.3.1 Stability Analysis 173
7.3.2 The Bohm Criterion Imposed by the Sheath 174
7.3.3 The Bohm Criterion as Seen from the Presheath 175
7.4 The Plane Langmuir Probe 176
7.4.1 The Ion Saturation Current 179
7.4.2 The Electron Saturation Current 179
7.4.3 The Electron Retardation Current 180
7.4.4 The Floating Potential 181
7.5 Advanced Langmuir Probe Methods 182
7.5.1 The Druyvesteyn Method 182
7.5.2 A Practical Realization of the Druyvesteyn Technique 184
7.5.3 Double Probes 185
7.5.4 Orbital Motion about Cylindrical and Spherical Probes 186
7.6 Application: Ion Extraction From Plasmas 188
7.7 Double Layers 190
7.7.1 Langmuir's Strong Double Layer 191
7.7.2 Experimental Evidence of Double Layers 193
Problems 195
8 Instabilities 197
8.1 Beam-Plasma Instability 198
8.1.1 Non-Thermal Distribution Functions 198
8.1.2 Dispersion of the Beam-Plasma Modes 199
8.1.3 Growth Rate for a Weak Beam 201
8.1.4 Why is the Slow Space-Charge Wave Unstable? 202
8.1.5 Temporal or Spatial Growth 205
8.2 Buneman Instability 206
8.2.1 Dielectric Function 206
8.2.2 Instability Analysis 207
8.3 Beam Instability in Finite Systems 208
8.3.1 Geometry of the Pierce Diode 208
8.3.2 The Dispersion Relation for a Free Electron Beam 209
8.3.3 The Influence of the Boundaries 209
8.3.4 The Pierce Modes 211
8.3.5 Discussion of the Pierce Model 212
8.4 Macroscopic Instabilities 214
8.4.1 Stable Magnetic Configurations 214
8.4.2 Pinch Instabilities 215
8.4.3 Rayleigh-Taylor Instability 215
Problems 218
9 Kinetic Description of Plasmas 219
9.1 The Vlasov Model 220
9.1.1 Heuristic Derivation of the Vlasov Equation 220
9.1.2 The Vlasov Equation 222
9.1.3 Properties of the Vlasov Equation 223
9.1.4 Relation Between the Vlasov Equation and Fluid Models 224
9.2 Application to Current Flow in Diodes 225
9.2.1 Construction of the Distribution Function 226
9.2.2 Virtual Cathode and Current Continuity 229
9.2.3 Finding a Self-Consistent Solution 229
9.2.4 Discussion of Numerical Solutions 230
9.3 Kinetic Effects in Electrostatic Waves 231
9.3.1 Electrostatic Electron Waves 231
9.3.2 The Meaning of Cold, Warm and Hot Plasma 233
9.3.3 Landau Damping 235
9.3.4 Damping of Ion-Acoustic Waves 237
9.3.5 A Physical Picture of Landau Damping 239
9.3.6 Plasma Wave Echoes 244
9.3.7 No Simple Route to Landau Damping 246
9.4 Plasma Simulation with Particle Codes 246
9.4.1 The Particle-in-Cell Algorithm 247
9.4.2 Phase-Space Representation 249
9.4.3 Instability Saturation by Trapping 251
9.4.4 Current Flow in Bounded Plasmas 252
Problems 256
10 Dusty Plasmas 259
10.1 Charging of Dust Particles 260
10.1.1 Secondary Emission 261
10.1.2 Photoemission 262
10.1.3 Charge Collection 266
10.1.4 Charging Time 268
10.1.5 Charge Fluctuations 270
10.1.6 Influence of Dust Density on Dust Charge 272
10.2 Forces on Dust Particles 276
10.2.1 Levitation and Confinement 276
10.2.2 Neutral Drag Force 283
10.2.3 Thermophoretic Force 283
10.2.4 Ion Wind Forces 284
10.2.5 Interparticle Forces 291
10.3 Plasma Crystals 294
10.3.1 Experimental Observations 295
10.3.2 The Role of Ion Wakes 296
10.3.3 Coulomb and Yukawa Balls 298
10.3.4 A Simple Model for the Structure of Yukawa Balls 300
10.4 Waves in Dusty Plasmas 304
10.4.1 Compressional and Shear Waves in Monolayers 304
10.4.2 Spectral Energy Density of Waves 315
10.4.3 Dust Density Waves 316
10.4.4 Concluding Remarks 319
Problems 320
11 Plasma Generation 323
11.1 DC-Discharges 323
11.1.1 Types of Low Pressure Discharges 323
11.1.2 Regions in a Glow Discharge 324
11.1.3 Processes in the Cathode Region 325
11.1.4 The Hollow Cathode Effect 329
11.1.5 Thermionic Emitters 329
11.1.6 The Negative Glow 330
11.1.7 The Positive Column 331
11.1.8 Similarity Laws 333
11.1.9 Discharge Modes of Thermionic Discharges 334
11.2 Capacitive Radio-Frequency Discharges 335
11.2.1 The Impedance of the Bulk Plasma 336
11.2.2 Sheath Expansion 337
11.2.3 Electron Energetics 340
11.2.4 Self Bias 341
11.2.5 Application: Anisotropic Etching of Silicon 344
11.3 Inductively Coupled Plasmas 345
11.3.1 The Skin Effect 346
11.3.2 E and H-Mode 347
11.3.3 The Equivalent Circuit for an ICP 348
11.4 Concluding Remark 349
Problems 350
Glossary 351
Appendix: Constants and Formulas 359
1 Physical Constants 359
2 List of Useful Formulas 360
2.1 Lengths 360
2.2 Frequencies 360
2.3 Velocities 361
3 Useful Mathematics 361
3.1 Vector Relations 361
3.2 Matrices and Tensors 363
3.3 The Theorems of Gauss and Stokes 364
Solutions 365
References 379
Name Index 389
Subject Index 391
