Fundamentals of Plasma Physics (eBook)

Front Cover 1
Fundamentals of Plasma Physics 4
Copyright Page 5
Table of Contents 6
Preface 18
Chapter 1. INTRODUCTION 20
1. General Properties of Plasmas 20
2. Criteria for the Definition of a Plasma 25
3. The Occurrence of Plasmas in Nature 30
4. Applications of Plasma Physics 36
5. Theoretical Description of Plasma Phenomena 43
Problems 46
Chapter 2. CHARGED PARTICLE MOTION IN CONSTANT AND UNIFORM ELECTROMAGNETIC FIELDS 52
1. Introduction 52
2. Energy Conservation 53
3. Uniform Electrostatic Field 55
4. Uniform Magnetostatic Field 56
5. Uniform Electrostatic and Magnetostatic Fields 70
6. Drift Due to an External Force 75
Problems 77
Chapter 3. CHARGED PARTICLE MOTION IN NONUNIFORM MAGNETOSTATIC FIELDS 80
1. Introduction 80
2. Spatial Variation of the Magnetic Field 82
3. Equation of Motion in the First Order Approximation 87
4. Average Force Over One Gyration Period 89
5. Gradient Drift 94
6. Parallel Acceleration of the Guiding Center 96
7. Curvature Drift 105
8. Combined Gradient-Curvature Drift 108
Problems 110
Chapter 4. CHARGED PARTICLE MOTION IN TIME-VARYING ELECTROMAGNETIC FIELDS 116
1. Introduction 116
2. Slowly Time-Varying Electric Field 116
3. Electric Field with Arbitrary Time Variation 121
4. Time-Varying Magnetic Field and Space Varying Electric Field 130
5. Summary of Guiding Center Drifts and Current Densities 137
Problems 137
Chapter 5. ELEMENTS OF PLASMA KINETIC THEORY 144
1. Introduction 144
2. Phase Space 144
3. Distribution Function 148
4. Number Density and Average Velocity 149
5. The Boltzmann Equation 150
6. Relaxation Model for the Collision Term 157
7. The Vlasov Equation 159
Problems 160
Chapter 6. AVERAGE VALUES AND MACROSCOPIC VARIABLES 164
1. Average Value of a Physical Quantity 164
2. Average Velocity and Peculiar Velocity 165
3. Flux 165
4. Particle Current Density 169
5. Momentum Flow Dyad or Tensor 170
6. Pressure Dyad 171
7. Heat Flow Vector 177
8. Heat Flow Triad 177
9. Total Energy Flux Triad 178
10.Higher Moments of the Distribution Function 180
Problems 181
Chapter 7. THE EQUILIBRIUM STATE 184
1. The Equilibrium State Distribution Function 184
2. The Most Probable Distribution 192
3. Mixture of Various Species of Particles 193
4. Properties of the Maxwell-Boltzmann Distribution Function 194
5. Equilibrium in the Presence of an External Force 205
6. Degree of lonization in Equilibrium - The Saha Equation 208
Problems 212
Chapter 8. MACROSCOPIC TRANSPORT EQUATIONS 217
1. Moments of the Boltzmann Equation 217
2. General Transport Equation 218
3. Conservation of Mass 221
4. Conservation of Momentum 224
5. Conservation of Energy 228
6. The Cold Plasma Model 235
7. The Warm Plasma Model 236
Problems 237
Chapter 9. MACROSCOPIC EQUATIONS FOR A CONDUCTING FLUID 244
1. Macroscopic Variables for a Plasma as a Conducting Fluid 244
2. Continuity Equation 248
3. Equation of Motion 248
4. Energy Equation 250
5. Electrodynamic Equations for a Conducting Fluid 253
6. Simplified Magnetohydrodynamic Equations 260
Problems 262
Chapter 10. PLASMA CONDUCTIVITY AND DIFFUSION 264
1. Introduction 264
2. The Langevin Equation 264
3. Linearization of the Langevin Equation 266
4. DC Conductivity and Electron Mobility 268
5. AC Conductivity and Electron Mobility 274
6. Conductivity with Ion Motion 275
7. The Plasma as a Dielectric Medium 276
8. Free Electron Diffusion 278
9. Electron Diffusion in a Magnetic Field 281
10.Ambipolar Diffusion 283
11.Diffusion in a Fully Ionized Plasma 288
Problems 290
Chapter 11. SOME BASIC PLASMA PHENOMENA 298
1. Electron Plasma Oscillations 298
2. The Debye Shielding Problem 302
3. Debye Shielding using the Vlasov Equation 307
4. Plasma Sheath 309
5. The Plasma Probe 319
Problems 322
Chapter 12. SIMPLE APPLICATIONS OF MAGNETOHYDRODYNAMICS 330
1. Fundamental Equations of Magnetohydrodynamics 330
2. Magnetic Viscosity and Reynolds Number 341
3. Diffusion of Magnetic Field Lines 343
4. Freezing of the Magnetic Field Lines to the Plasma 344
5. Magnetic Pressure 348
6. Plasma Confinement in a Magnetic Field 351
Problems 355
Chapter 13. THE PINCH EFFECT 358
1. Introduction 358
2. The Equilibrium Pinch 359
3. The Bennett Pinch 365
4. Dynamic Model of the Pinch 369
5. Instabilities in a Pinched Plasma Column 374
6. The Sausage Instability 376
7. The Kink Instability 379
8. Convex Field Configurations 380
Problems 381
Chapter 14. ELECTROMAGNETIC WAVES IN FREE SPACE 385
1. The Wave Equation 385
2. Solution in Plane Waves 386
3. Harmonic Waves 387
4. Polarization 390
5. Energy Flow 397
6. Wave Packets and Group Velocity 400
Problems 404
Chapter 15. MAGNETOHYDRODYNAMIC WAVES 409
1. Introduction 409
2. MHD Equations for a Compressible Nonviscous Conducting Fluid 413
3. Propagation Perpendicular to the Magnetic Field 415
4. Propagation Parallel to the Magnetic Field 417
5. Propagation in an Arbitrary Direction 418
6. Effect of Displacement Current 424
7. Damping of MHD Waves 428
Problems 431
Chapter 16. WAVES IN COLD PLASMAS 434
1. Introduction 434
2. Basic Equations of Magnetoionic Theory 435
3. Plane Wave Solutions and Linearization 436
4. Wave Propagation in Isotropie Electron Plasmas 437
5. Wave Propagation in Cold Magnetized Plasmas 447
6. Propagation Parallel to B 453
7. Propagation Perpendicular to B 458
8. Propagation at Arbitrary Directions 463
9. Some Special Wave Phenomena in Cold Plasmas 473
Problems 481
Chapter 17. WAVES IN WARM PLASMAS 488
1. Introduction 488
2. Waves in a Fully Ionized Isotropie Warm Plasma 488
3. Basic Equations for Waves in a Warm Magnetoplasma 496
4. Waves in a Warm Electron Gas in a Magnetic Field 498
5. Waves in a Fully Ionized Warm Magnetoplasma 507
6. Summary 519
Problems 520
Chapter 18. WAVES IN HOT ISOTROPIC PLASMAS 521
1. Introduction 521
2. Basic Equations 521
3. General Results for a Plane Plasma Wave in a Hot Isotropie Plasma 522
4. Electrostatic Longitudinal Wave in a Hot Isotropie Plasma 529
5. Transverse Wave in a Hot Isotropie Plasma 543
6. The Two-Stream Instability 545
7. Summary 548
Problems 550
Chapter 19. WAVES IN HOT MAGNETIZED PLASMAS 555
1. Introduction 555
2. Wave Propagation Along the Magnetostatic Field in a Hot Plasma 555
3. Wave Propagation Across the Magnetostatic Field in a Hot Plasma 576
4. Summary 595
Problems 597
Chapter 20. PARTICLE INTERACTIONS IN PLASMAS 603
1. Introduction 603
2. Binary Collisions 604
3. Dynamics of Binary Collisions 609
4. Evaluation of x for Some Special Cases 613
5. Cross Sections 617
6. Cross Sections for the Hard Sphere Model 622
7. Cross Sections for the Coulomb Potential Field 625
8. Effect of Screening of the Coulomb Potential 626
Problems 631
Chapter 21. THE BOLTZMANN AND THE FOKKER-PLANCK EQUATIONS 635
1. Introduction 635
2. The Boltzmann Equation 635
3. The Boltzmann's H Function 647
4. Boltzmann Collision Term for a Weakly Ionized Plasma 656
5. The Fokker-Planck equation 659
Problems 671
Chapter 22. TRANSPORT PROCESSES IN PLASMAS 677
1. Introduction 677
2. Electric Conductivity in a Nonmagnetized Plasma 677
3. Electric Conductivity in a Magnetized Plasma 683
4. Free Diffusion 691
5. Diffusion in a Magnetic Field 694
6. Heat Flow 699
Problems 703
Appendix I: USEFUL VECTOR RELATIONS 708
Appendix II: USEFUL RELATIONS IN CARTESIAN AND IN CURVILINEAR COORDINATES 711
Appendix III: PHYSICAL CONSTANTS (MKSA) 716
Appendix IV: CONVERSION FACTORS FOR UNITS 717
Appendix V: SOME IMPORTANT PLASMA PARAMETERS 718
Appendix VI: APPROXIMATE MAGNITUDES IN SOME TYPICAL PLASMAS 721
Index 722