- ' ' * ' Plasma Physics for Astrophysics RUSSELL M. KULSRUD PRINCETON UNIVERSITY E;RESS '. ' PRINCETON AND OXFORD,, ', V.
List of Figures Foreword by John N. Bahcall Preface Chapter 1. Introduction 1 1.1 How Do We Describe a Plasma and Its Electromagnetic Fields? 6 References 13 Chapter 2. Particle Motions 14 2.1 Motion in a Uniform Magnetic Field 14 2.2 Motion of a Particle in a Nonuniform Magnetic Field 18 2.3 Magnetic Mirrors 22 2.4 Polarization Drift 25 2.5 Adiabatic Invariants 27 2.6 The Motion of Trapped Particles in the Magnetosphere 31 2.7 Particle Motion and Macroscopic Force Balance 34 2.8 Problems ' 37 References 39 Chapter 3. Magnetohydrodynamics 40 3.1 The Basic Equations 40 3.2 Flux Freezing 46 3.3 Applications of Flux Freezing 50 3.3.1 The Symmetric Cases 50 3.3.2 Stellar Collapse 51 3.3.3 The Solar Wind and the Magnetosphere 53 3.3.4 Stellar Formation and the Angular Momentum Problem \ 56 3.3.5 Magnetic Fields in Turbulence 57 3.4 Io and Jupiter 58 3.5 Motions of Lines of Force in a Vacuum 62 3.6 The Validity of the MHD Equations 63 3.7 Pulsar Magnetospheres 64 3.8 Problems. 67 References 70 Chapter 4. Conservation Relations 71 4.1 Introduction 71 4.2 The Lorentz Force 71 4.3 Conservation of Linear Momentum 74 4.4 Conservation of Angular Momentum 78 4.5 Conservation of Energy 80 4.6 The Virial Theorem 84 4.7 The Action Principle for MHD ' 86 xi xv xvii
viii 4.8 Lundquist's Identity 91 4.9 Axisymmetry 93 4.10 Problems 100 References 102 Chapter 5. MHD Waves 103 5.1 The Basic Equations 103 5.2 The Intermediate Wave, 106 5.3 The Fast and Slow Modes 107 5.3.1 The Nature of the Fast and Slow Modes 108 5.3.2 The Friedricks Diagram 111 5.4 The Number of Modes 113 5.5 Wave Energy and Momentum 11.4 5.6 Waves in Nonuniform Media 118 5.6.1 The Variation in Amplitude 122 5.6.2 Wave Pressure 124 5.7 Problems 126 References 127 Chapter 6. Nonlinear Steepening and Shocks 128 6.1 Nonlinear Steepening 128 6.2 Shocks 135 6.3 MHD Shocks. 140 6.4 The Shock Thickness and Collisionless Shock Waves 147 6.5 Problems 148 References 150 Chapter 7. The Energy Principle and Instabilities 151 7.1 Stability 151 7.2 The Energy Principle 152 7.3 Instabilities 171 7.3.1 The Interchange Instability 171 7.3.2 The Parker Instability. 174 7.3.3 The Interchange without Gravity : 176 7.3.4 Line Tying and Shear 184 7.4 The Magnetorotational Instability (MRI) 186 7.5 Problems 193 References 196 Chapter 8. Collisions and the Braginski Equations 197 8.1 Introduction 197 8.2 Binary Collisions 198 8.3 The Fokker-Planck Equation 203 8.4 Collision Rates 208 8.5 The Space-Dependent Fokker-Planck Equation 210 8.6 The Fluid Equations 213 8.7 Transport Effects 221 8.8 The Braginski Equations 226 8.9 Properties of the Transport Coefficients 228
ix 8.10 Summary 232 8.11 An Example 233 8.12 Maxwellian Collisions 235 8.13 Problems 241 References 244 Chapter 9. Collisionless Plasmas 245 9.1 Introduction 245 9.2 Dispersion Relation for Cold Plasma Waves 245 9.3 Parallel Propagation 248 9.4 The Number of Waves 253 9.5 Perpendicular Propagation 254 9.6 Propagation in a General Direction 257 9.7 The Cold Plasma Approximation 259 9.8 Faraday Rotation and Magnetic Fields 261 9.9 Bremsstrahlung 263 9.10 Wave Energy 264 9.11 Problems 266 References 268 Chapter 10. Collisionless Plasmas: Thermal Effects 269 10.1 Introduction 269 10.2 Ion Acoustic Waves «272 10.3 The Dielectric Constant 273 10.4 Landau Damping 275 10.5 Physical Picture of Landau Damping 286 10.6 Types of Resonances 290 10.7 The Drift Kinetic Equation 291 10.8 Problems 295 References 298 Chapter 11. Nonlinear Phenomena 300 11.1 Introduction, 300 11.2 Wave-Particle Interactions >; 301 11.3 Wave-Wave Interactions 312 11.4 Mode Decay 318 11.5 Nonlinear Landau Damping 323 11.6 Particle Trapping 327 11.7 The Wave Kinetic Equation 329 11.8 Kolmogoroff Turbulence 331 11.9 MHD Turbulence 333 11.9.1 An Exact Solution 334 11.9.2 The Wave Interactions 335 11.9.3 The Goldreich-Sridhar Theory 336 11.10 Problems 339 References 342 Chapter 12. Cosmic Rays 343 12.1 Physical Properties of Cosmic Rays 343
x 12.2 Pitch-Angle Scattering of Cosmic Rays by Alfven Waves 347 12.3 The Cosmic-Ray Alfven-Wave Instability 356 12.4 Quasilinear Diffusion of Cosmic Rays 364 12.5 A Model for Cosmic-Ray Propagation with Sources and Sinks 366 12.6 Cosmic-Ray Pressure and Energy 372 12.7 Fermi Acceleration and Shock Acceleration of Cosmic Rays 376 12.8 Problems 383 References 385 Chapter 13. Astrophysical Dynamos 386 13.1 Introduction 386 13.2 Cowling's Theorem 388 13.3 Parker's Model for the Earth's Dynamo 389 13.4 The Mean Field Dynamo Theory 393 13.4.1 Derivation of the Mean Field Equations 394 13.4.2 The Growth Rate of Dynamo Modes in the Galactic Disk 397 13.5 Protogalactic Origin of the Magnetic Field 403 13.5.1 The Biermann Battery 404 13.5.2 The Protogalactic Dynamo 408 13.6 Small-Scale Fields 412 13.7 Problems 416 References «418 Chapter 14. Magnetic Reconnection 420 14.1 Introduction 420 14.2 The Sweet-Parker Model of Magnetic Reconnection 423 14.3 The Uzdensky Model 427 14.4 Comparison of the Sweet-Parker Model with Observations 436 14.5 Petschek's Model for Magnetic Reconnection 438 14.6 Non-MHD Reconnection 443 14.7 Anomalous Resistivity 446 14.8 Petschek Reconnection Revisited 451 14.9 Which Is the Correct Reconnection Velocity? i ; 452 14.10 The Case When the Guide Field Is Nonzero 453 14.11 Hall Reconnection 453 14.12 Problems 454 References 457 Suggested Further Reading 458 Index 459