Plasma Physics: An Introduction to the Theory of Astrophysical, Geophysical and Laboratory Plasmas

Front cover......Page 1
Title page......Page 3
Date-line......Page 4
Contents......Page 5
Preface......Page 9
1 Introduction......Page 11
2.1 Collective effects......Page 16
2.2 Charge neutrality and the Debye length......Page 17
2.3 Debye shielding......Page 19
2.4 The plasma parameter......Page 21
2.5 Plasma oscillations......Page 24
Problems......Page 27
3.1 Particle motion in a static, uniform magnetic field......Page 29
3.2 Particle motion in electric and magnetic fields......Page 32
3.3 Particle motion in magnetic and gravitational fields......Page 34
3.4 Particle motion in a time-varying uniform magnetic field......Page 35
Problems......Page 38
4.1 General adiabatic invariants......Page 42
4.2 The first adiabatic invariant: magnetic moment......Page 47
4.3 Relativistic form of the first adiabatic invariant......Page 48
4.4 The second adiabatic invariant: the bounce invariant......Page 50
4.5 Magnetic traps......Page 53
4.6 The third adiabatic invariant......Page 56
Problems......Page 57
5.1 Particle motion in a static inhomogeneous magnetic field......Page 59
5.2 Discussion of orbit theory for a static inhomogeneous magnetic field......Page 63
5.3 Drifts in the Earth\'s magnetosphere......Page 66
5.4 Motion in a time-varying electric field......Page 67
5.5 Particle motion in a rapidly time-varying electromagnetic field......Page 70
Problems......Page 73
6.1 The wave equation......Page 76
6.2 Waves in a cold electron plasma without a magnetic field......Page 78
6.3 Effect of collisions......Page 84
6.4 Electromagnetic waves in a cold magnetized electron plasma......Page 87
6.5 Wave propagation normal to the magnetic field......Page 89
6.6 Propagation parallel to the magnetic field......Page 92
6.7 Faraday rotation......Page 95
6.8 Dispersion of radio waves......Page 99
6.9 Whistlers......Page 101
Problems......Page 103
7.1 The dispersion relation......Page 107
7.2 Wave propagation in an electron plasma......Page 111
Problems......Page 114
8.1 Particle streams of zero temperature......Page 116
8.2 Two-stream instability......Page 119
8.3 Two identical but opposing streams......Page 121
8.4 Stream moving through a stationary plasma......Page 123
Problems......Page 126
9.1 Distribution functions......Page 128
9.2 Linear perturbation analysis of the Vlasov equation......Page 132
9.3 Dispersion relation for a warm plasma......Page 134
9.4 The Landau initial-value problem......Page 135
9.5 Gardner\'s theorem......Page 142
9.6 Weakly damped waves - Landau damping......Page 144
9.7 The Penrose criterion for stability......Page 146
Problems......Page 153
10.1 Lagrange expansion......Page 155
10.2 The Fokker-Planck equation......Page 157
10.3 Coulomb collisions......Page 159
10.4 The Fokker-Planck equation for Coulomb collisions......Page 163
10.5 Relaxation times......Page 169
Problems......Page 177
11.1 The moment equations......Page 179
11.2 Fluid description of an electron-proton plasma......Page 180
11.3 The collision term......Page 181
11.4 Moment equations for each species......Page 182
11.5 Fluid description......Page 183
11.6 Ohm\'s law......Page 185
11.7 The ideal MHD equations......Page 187
11.8 The conductivity tensor......Page 190
Problems......Page 192
12.1 Evolution of the magnetic field......Page 194
12.2 Frozen magnetic field lines......Page 196
12.3 Diffusion of magnetic field lines......Page 201
12.4 The virial theorem......Page 203
12.5 Extension of the virial theorem......Page 204
12.6 Stability analysis using the virial theorem......Page 207
Problems......Page 209
13.1 Introduction......Page 211
13.2 Linear force-free fields......Page 214
13.3 Examples of linear force-free fields......Page 216
13.4 The generating-function method......Page 218
13.5 Calculation of magnetic-field configurations......Page 222
13.6 Linear force-free fields of cylindrical symmetry......Page 224
13.7 Uniformly twisted cylindrical force-free field......Page 226
13.8 Magnetic helicity......Page 230
13.9 Woltjer\'s theorem......Page 233
13.10 Useful relations for semi-infinite force-free magnetic-field configurations......Page 234
Problems......Page 239
14.1 MHD waves in a uniform plasma......Page 243
14.2 Waves in a barometric medium......Page 249
Problems......Page 256
15.1 The linear pinch......Page 258
15.2 Stability analysis......Page 260
15.3 Boundary conditions......Page 261
15.4 Internally homogeneous linear pinch......Page 263
15.5 Application of the boundary conditions......Page 266
Problems......Page 268
16.1 Variation principle for a spatially distributed system......Page 270
16.2 Convection of magnetic field......Page 272
16.3 Variation principle of MHD motion......Page 274
16.4 Small-amplitude disturbances......Page 277
Problems......Page 279
17.2 Current sheet configuration......Page 282
17.3 Evolution of the magnetic field......Page 285
17.4 Equation of motion......Page 287
17.5 The tearing mode......Page 288
17.6 Solution of the differential equations......Page 291
Problem......Page 297
18 Stochastic processes......Page 298
18.1 Stochastic diffusion......Page 299
18.2 One-dimensional stochastic acceleration......Page 304
18.3 Stochastic diffusion, Landau damping and quasilinear theory......Page 307
Problem......Page 309
19.1 Quantum-mechanical description......Page 311
19.2 Transition to the classical limit......Page 314
19.3 The three-state model: emission and absorption......Page 315
19.4 Diffusion equation for the particle distribution function......Page 317
Problem......Page 319
Appendix A Units and constants......Page 321
Appendix B Group velocity......Page 324
Appendix C Amplifying and evanescent waves, convective and absolute instability......Page 329
References......Page 335
Author index......Page 339
Subject index......Page 341
Back cover......Page 346