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1．INTRODUCTION 1

1．General Properties of Plasmas 1

1.1 Definition of a Plasma 1

1.2 Plasma as the Fourth State of Matter 1

1.3 Plasma Production 2

1.4 Particle Interactions and Collective Effects 3

1.5 Some Basic Plasma Phenomena 4

2．Criteria for the Definition of a Plasma 6

2.1 Macroscopic Neutrality 6

2.2 Debye Shielding 7

2.3 The Plasma Frequency 9

3．The Occurrence of Plasmas in Nature 11

3.1 The Sun and its Atmosphere 13

3.2 The Solar Wind 13

3.3 The Magnetosphere and the Van Allen Radiation Belts 14

3.4 The Ionosphere 16

3.5 Plasmas Beyond the Solar System 17

4．Applications of Plasma Physics 17

4.1 Controlled Thermonuclear Fusion 18

4.2 The Magnetohydrodynamic Generator 22

4.3 Plasma Propulsion 23

4.4 Other Plasma Devices 23

5．Theoretical Description of Plasma Phenomena 25

5.1 General Considerations on a Self-Consistent Formulation 25

5.2 Theoretical Approaches 27

Problems 28

2．CHARGED PARTICLE MOTION IN CONSTANT AND UNIFORM ELECTROMAGNETIC FIELDS 33

1．Introduction 33

2．Energy Conservation 34

3．Uniform Electrostatic Field 36

4．Uniform Magnetostatic Field 37

4.1 Formal Solution of the Equation of Motion 37

4.2 Solution in Cartesian Coordinates 40

4.3 Magnetic Moment 44

4.4 Magnetization Current 46

5．Uniform Electrostatic and Magnetostatic Fields 49

5.1 Formal Solution of the Equation of Motion 49

5.2 Solution in Cartesian Coordinates 52

6．Drift Due to an External Force 54

Problems 56

3．CHARGED PARTICLE MOTION IN NONUNIFORM MAGNETOSTATIC FIELDS 59

1．Introduction 59

2．Spatial Variation of the Magnetic Field 61

2.1 Divergence Terms 62

2.2 Gradient and Curvature Terms 64

2.3 Shear Terms 65

3．Equation of Motion in the First-Order Approximation 66

4．Average Force Over One Gyration Period 68

4.1 Parallel Force 70

4.2 Perpendicular Force 72

4.3 Total Average Force 73

5．Gradient Drift 74

6．Parallel Acceleration of the Guiding Center 74

6.1 Invariance of the Orbital Magnetic Moment and of the Magnetic Flux 75

6.2 Magnetic Mirror Effect 77

6.3 The Longitudinal Adiabatic Invariant 81

7．Curvature Drift 84

8．Combined Gradient-Curvature Drift 87

Problems 89

4．CHARGED PARTICLE MOTION IN TIME-VARYING ELECTROMAGNETIC FIELDS 95

1．Introduction 95

2．Slowly Time-Varying Electric Field 95

2.1 Equation of Motion and Polarization Drift 95

2.2 Plasma Dielectric Constant 97

3．Electric Field with Arbitrary Time Variation 100

3.1 Solution of the Equation of Motion 100

3.2 Physical Interpretation 102

3.3 Mobility Dyad 105

3.4 Plasma Conductivity Dyad 105

3.5 Cyclotron Resonance 106

4．Time-Varying Magnetic Field and Space-Varying Electric Field 108

4.1 Equation of Motion and Adiabatic Invariants 108

4.2 Magnetic Heating of a Plasma 112

5．Summary of Guiding Center Drifts and Current Densities 115

5.1 Guiding Center Drifts 115

5.2 Current Densities 115

Problems 116

5．ELEMENTS OF PLASMA KINETIC THEORY 122

1．Introduction 122

2．Pbase Space 123

2.1 Single-Particle Phase Space 123

2.2 Many-Particle Phase Space 123

2.3 Volume Elements 124

3．Distribution Function 126

4．Number Density and Average Velocity 128

5．The Boltzmann Equation 129

5.1 Collisionless Boltzmann Equation 129

5.2 Jacobian of the Transformation in Phase Space 132

5.3 Effects of Particle Interactions 133

6．Relaxation Model for the Collision Term 135

7．The Vlasov Equation 136

Problems 138

6．AVERAGE VALUES AND MACROSCOPIC VARIABLES 141

1．Average Value of a Physical Quantity 141

2．Average Velocity and Peculiar Velocity 142

3．Flux 143

4．Particle Current Density 146

5．Momentum Flow Dyad or Tensor 147

6．Pressure Dyad or Tensor 148

6.1 Concept of Pressure 148

6.2 Force per Unit Area 149

6.3 Force per Unit Volume 151

6.4 Scalar Pressure and Absolute Temperature 152

7．Heat Flow Vector 154

8．Heat Flow Triad 154

9．Total Energy Flux Triad 155

10．Higher Moments of the Distribution Function 157

Problems 157

7．THE EQUILIBRIUM STATE 161

1．The Equilibrium State Distribution Function 161

1.1 The General Principle of Detailed Balance and Binary Collisions 162

1.2 Summation Invariants 164

1.3 Maxwell-Boltzmann Distribution Function 165

1.4 Determination of the Constant Coefficients 166

1.5 Local Maxwell-Boltzmann Distribution Function 169

2．The Most Probable Distribution 169

3．Mixture of Various Particle Species 170

4．Properties of the Maxwell-Boltzmann Distribution Function 171

4.1 Distribution of a Velocity Component 171

4.2 Distribution of Speeds 174

4.3 Mean Values Related to the Molecular Speeds 176

4.4 Distribution of Thermal Kinetic Energy 178

4.5 Random Particle Flux 178

4.6 Kinetic Pressure and Heat Flux 181

5．Equilibrium in the Presence of an External Force 181

6．Degree of Ionization in Equilibrium and the Saha Equation 184

Problems 187

8．MACROSCOPIC TRANSPORT EQUATIONS 193

1．Momens of the Boltzmann Equation 193

2．General Transport Equation 194

3．Conservation of Mass 197

3.1 Derivation of the Continuity Equation 197

3.2 Derivation by the Method of Fluid Dynamics 198

3.3 The Collision Term 200

4．Conservation of Momentum 200

4.1 Derivation of the Equation of Motion 200

4.2 The Collision Term 203

5．Conservation of Energy 204

5.1 Derivation of the Energy Transport Equation 204

5.2 Physical Interpretation 207

5.3 Simplifying Approximations 207

6．The Cold Plasma Model 210

7．The Warm Plasma Model 211

Problems 212

9．MACROSCOPIC EQUATIONS FOR A CONDUCTING FLUID 219

1．Macroscopic Variables for a Plasma as a Conducting Fluid 219

2．Continuity Equation 222

3．Equation of Motion 223

4．Energy Equation 224

5．Electrodynamic Equations for a Conducting Fluid 227

5.1 Maxwell Curl Equations 228

5.2 Conservation of Electric Charge 228

5.3 Generalized Ohm's Law 229

6．Simplified Magnetohydrodynamic Equations 234

Problems 236

10．PLASMA CONDUCTIVITY AND DIFFUSION 238

1．Introduction 238

2．The Langevin Equation 238

3．Linearization of the Langevin Equation 240

4．DC Conductivity and Electron Mobility 242

4.1 Isotropic Plasma 242

4.2 Anisotropic Magnetoplasma 243

5．AC Conductivity and Electron Mobility 247

6．Conductivity with Ion Motion 249

7．Plasma as a Dielectric Medium 250

8．Free Electron Diffusion 251

9．Electron Diffusion in a Magnetic Field 254

10．Ambipolar Diffusion 256

11．Diffusion in a Fully Ionized Plasma 260

Problems 262

11．SOME BASIC PLASMA PHENOMENA 269

1．Electron Plasma Oscillations 269

2．The Debye Shielding Problem 273

3．Debye Shielding Using the Vlasov Equation 278

4．Plasma Sheath 279

4.1 Physical Mechanism 280

4.2 Electric Potential on the Wall 281

4.3 Inner Structure of the Plasma Sheath 282

5．Plasma Probe 288

Problems 291

12．SIMPLE APPLICATIONS OF MAGNETOHYDRODYNAMICS 299

1．Fundamental Equations of Magnetohydrodynamics 299

1.1 Parker Modifled Momentum Equation 300

1.2 The Double Adiabatic Equations of Chew,Goldberger,and Low(CGL) 302

1.3 Special Cases of the Double Adiabatic Equations 305

1.4 Energy Integral 307

2．Magnetic Viscosity and Reynolds Number 309

3．Diffusion of Magnetic Field Lines 311

4．Freezing of Magnetic Field Lines to the Plasma 312

5．Magnetic Pressure 316

6．Isobaric Surfaces 318

7．Plasma Confinement in a Magnetic Field 319

Problems 322

13．THE PINCH EFFECT 325

1．Introduction 325

2．The Equilibrium Pinch 326

3．The Bennett Pinch 332

4．Dynamic Model of the Pinch 335

5．Instabilities in a Pinched Plasma Column 341

6．The Sausage Instability 342

7．The Kink Instability 345

8．Convex Field Configurations 346

Problems 348

14．ELECTROMAGNETIC WAVES IN FREE SPACE 351

1．The Wave Equation 351

2．Solution in Plane Waves 352

3．Harmonic Waves 354

4．Polarization 358

5．Energy Flow 363

6．Wave Packets and Group Velocity 366

Problems 370

15．MAGNETOHYDRODYNAMIC WAVES 375

1．Introduction 375

1.1 Alfvén Waves 376

1.2 Magnetosonic Waves 377

2．MHD Equations for a Compressible Nonviscous Conducting Fluid 379

2.1 Basic Equations 379

2.2 Development of an Equation for the Fluid Velocity 381

3．Propagation Perpendicular to the Magnetic Field 382

4．Propagation Parallel to the Magnetic Field 383

5．Propagation at Arbitrary Directions 384

5.1 Pure Alfvén Wave 386

5.2 Fast and Slow MHD Waves 387

5.3 Phase Velocities 387

5.4 Wave Normal Surfaces 388

6．Effect of Displacement Current 390

6.1 Basic Equations 392

6.2 Equation for the Fluid Velocity 392

6.3 Propagation Across the Magnetostatic Field 393

6.4 Propagation Along the Magnetostatic Field 393

7．Damping of MHD Waves 394

7.1 Alfén Waves 395

7.2 Sound Waves 396

7.3 Magnetosonic Waves 396

Problems 397

16．WAVES IN COLD PLASMAS 400

1．Introduction 400

2．Basic Equations of Magnetoionic Theory 401

3．Plane Wave Solutions and Linearization 402

4．Wave Propagation in Isotropic Electron Plasmas 403

4.1 Derivation of the Dispersion Relation 403

4.2 Collisionless Plasma 405

4.3 Time-Averaged Poynting Vector 407

4.4 The Effect of Collisions 410

5．Wave Propagation in Magnetized Cold Plasmas 413

5.1 Derivation of the Dispersion Relation 414

5.2 The Appleton-Hartree Equation 418

6．Propagation Parallel to B0 419

7．Propagation Perpendicular to B0 423

8．Propagation at Arbitrary Directions 430

8.1 Resonances and Reflection Points 430

8.2 Wave Normal Surfaces 432

8.3 The CMA Diagram 434

9．Some Special Wave Phenomena in Cold Plasmas 439

9.1 Atmospheric Whistlers 439

9.2 Helicons 442

9.3 Faraday Rotation 444

Problems 447

17．WAVES IN WARM PLASMAS 453

1．Introduction 453

2．Waves in a Fully Ionized Isotropic Warm Plasma 453

2.1 Derivation of the Equations for the Electron and Ion Velocities 453

2.2 Longitudinal Waves 456

2.3 Transverse Wave 458

3．Basic Equations for Waves in a Warm Magnetoplasma 460

4．Waves in a Warm Electron Gas in a Magnetic Field 462

4.1 Derivation of the Dispersion Relation 462

4.2 Wave Propagation Along the Magnetic Field 463

4.3 Wave Propagation Normal to the Magnetic Field 466

4.4 Wave Propagation at Arbitrary Directions 469

5．Waves in a Fully Ionized Warm Magnetoplasma 470

5.1 Derivation of the Dispersion Relation 471

5.2 Wave Propagation Along the Magnetic Field 473

5.3 Wave Propagation Normal to the Magnetic Field 477

5.4 Wave Propagation at Arbitrary Directions 479

6．Summary 479

Problems 481

18．WAVES IN HOT ISOTROPIC PLASMAS 483

1．Introduction 483

2．Basic Equations 483

3．General Results for a Plane Wave in a Hot Isotropic Plasma 485

3.1 Perturbation Charge Density and Current Density 485

3.2 Solution of the Linearized Vlasov Equation 486

3.3 Expression for the Current Density 488

3.4 Separation into the Various Modes 489

4．Electrostatic Longitudinal Wave in a Hot Isotropic Plasma 491

4.1 Development of the Dispersion Relation 491

4.2 Limiting Case of a Cold Plasma 492

4.3 High Phase Velocity Limit 493

4.4 Dispersion Relation for Maxwellian Distribution Function 494

4.5 Landau Damping 500

5．Transverse Wave in a Hot Isotropic Plasma 503

5.1 Development of the Dispersion Relation 503

5.2 Cold Plasma Result 504

5.3 Dispersion Relation for Maxwellian Distribution Function 504

5.4 Landau Damping of the Transverse Wave 505

6．The Two-Stream Instability 506

7．Summary 508

7.1 Longitudinal Mode 508

7.2 Transverse Mode 509

Problems 510

19．WAVES IN HOT MAGNETIZED PLASMAS 515

1．Introduction 515

2．Wave Propagation Along the Magnetostatic Field in a Hot Plasma 516

2.1 Linearized Vlasov Equation 516

2.2 Solution of the Linearized Vlasov Equation 517

2.3 Perturbation Current Density 522

2.4 Separation into the Various Modes 524

2.5 Longitudinal Plasma Wave 525

2.6 Transverse Electromagnetic Waves 526

2.7 Temporal Damping of the Transverse Electromagnetic Waves 529

2.8 Cyclotron Damping of the RCP Transverse Wave 531

2.9 Instabilities in the RCP Transverse Wave 532

3．Wave Propagation Across the Magnetostatic Field in a Hot Plasma 534

3.1 Solution of the Linearized Vlasov Equation 536

3.2 Current Density and the Conductivity Tensor 538

3.3 Evaluation ofthe Integrals 540

3.4 Separation into the Various Modes 544

3.5 Dispersion Relations 545

3.6 The Quasistatic Mode 546

3.7 The TEM Mode 550

4．Summary 552

4.1 Propagation Along B0 in Hot Magnetoplasmas 552

4.2 Propagation Across B0 in Hot Magnetoplasmas 553

Problems 554

20．PARTICLE INTERACTIONS IN PLASMAS 560

1．Introduction 560

2．Binary Collisions 561

3．Dynamics of Binary Collisions 566

4．Evaluation of the Scattering Angle 569

4.1 Two Perfectly Elastic Hard Spheres 570

4.2 Coulomb Interaction Potential 570

5．Cross Sections 572

5.1 Differential Scattering Cross Section 574

5.2 Total Scattering Cross Section 576

5.3 Momentum Transfer Cross Section 577

6．Cross Sections for the Hard Sphere Model 578

6.1 Differential Scattering Cross Section 578

6.2 Total Scattering Cross Section 579

6.3 Momentum Transfer Cross Section 579

7．Cross Sections for the Coulomb Potential 580

7.1 Differential Scattering Cross Section 580

7.2 Total Scattering Cross Section 581

7.3 Momentum Transfer Cross Section 581

8．Screening of the Coulomb Potential 582

Problems 586

21．THE BOLTZMANN AND THE FOKKER-PLANCK EQUATIONS 589

1．Introduction 589

2．The Boltzmann Equation 590

2.1 Derivation of the Boltzmann Collision Integral 590

2.2 Jacobian of the Transformation 594

2.3 Assumptions in the Derivation of the Boltzmann Collision Integral 596

2.4 Rate of Change of a Physical Quantity as a Result of Collisions 597

3．The Boltzmann's H Function 598

3.1 Boltzmann's H Theorem 599

3.2 Analysis of Boltzmann's H Theorem 601

3.3 Maximum Entropy or Minimum H Approach for Deriving the Equilibrium Distribution Function 604

3.4 Mixture of Various Particle Species 606

4．Boltzmann Collision Term for a Weakly Ionized Plasma 607

4.1 Spherical Harmonic Expansion of the Distribution Function 607

4.2 Approximate Expression for the Boltzmann Collision Term 609

4.3 Rate of Change of Momentum Due to Collisions 611

5．The Fokker-Planck Equation 612

5.1 Derivation of the Fokker-Planck Collision Term 612

5.2 The Fokker-Planck Coefficients for Coulomb Interactions 616

5.3 Application to Electron-Ion Collisions 621

Problems 621

22．TRANSPPRT PROCESSES IN PLASMAS 628

1．Introduction 628

2．Electric Conductivity in a Nonmagnetized Plasma 629

2.1 Solution of the Boltzmann Equation 629

2.2 Electric Current Density and Conductivity 630

2.3 Conductivity for Maxwellian Distribution Function 633

3．Electric Conductivity in a Magnetized Plasma 634

3.1 Solution of Boltzmann Equation 634

3.2 Electric Current Density and Conductivity 637

4．Free Diffusion 640

4.1 Perturbation Distribution Function 640

4.2 Particle Flux 641

4.3 Free Diffusion Coefficient 641

5．Diffusion in a Magnetic Field 643

5.1 Solution of Boltzmann Equation 643

5.2 Particle Flux and Diffusion Coefficients 645

6．Heat Flow 647

6.1 General Expression for the Heat Flow Vector 647

6.2 Thermal Conductivity for a Constant Kinetic Pressure 648

6.3 Thermal Conductivity for the Adiabatic Case 649

Problems 650

APPENDIX A　Useful Vector Relations 655

APPENDIX B　Useful Relations in Cartesian and in Curvilinear Coordinates 658

APPENDIX C　Physical Constants(MKSA) 662

APPENDIX D　Conversion Factors for Physical Units 663

APPENDIX E　Some Important Plasma Parameters 664

APPENDIX F　Approximate Magnitudes in Some Typical Plasmas 667

INDEX 669