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- Author: J. A. Bittencourt
- Title: Fundamentals of Plasma Physics
- Amazon Link: https://www.amazon.com/dp/0387209751/?tag=pfamazon01-20
- Prerequisities: Better part of an undergraduate (BS) physics program
- Contents: Undergraduate, advanced upper level (senior); Graduate, introductory
Table of Contents
Code:
1 INTRODUCTION
1. General Properties of Plasmas 1
1.1 Definition of a Plasma
1.2 Plasma as the Fourth State of Matter
1.3 Plasma Production
1.4 Particle Interactions and Collective Effects
1.5 Some Basic Plasma Phenomena
2. Criteria for the Definition of a Plasma 6
2.1 Macroscopic Neutrality
2.2 Debye Shielding
2.3 The Plasma Frequency
3. The Occurrence of Plasmas in Nature 11
3.1 The Sun and its Atmosphere
3.2 The Solar Wind
3.3 The Magnetosphere and the Van Allen Radiation Belts
3.4 The Ionosphere
3.5 Plasmas Beyond the Solar System
4. Applications of Plasma Physics 17
4.1 Controlled Thermonuclear Fusion
4.2 The Magnetohydrodynamic Generator
4.3 Plasma Propulsion
4.4 Other Plasma Devices
5. Theoretical Description of Plasma Phenomena 25
5.1 General Considerations on a Self-Consistent Formulation
5.2 Theoretical Approaches
Problems 28
2 CHARGED PARTICLE MOTION IN CONTSTANT AND UNIFORM
ELECTROMAGNETIC FIELDS
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
4.2 Solution in Cartesian Coordinates
4.3 Magnetic Moment
4.4 Magnetization Current
5. Uniform Electrostatic and Magnetostatic Fields 49
5.1 Formal Solution of the Equation of Motion
5.2 Solution in Cartesian Coordinates
6. Drift Due to an External Force 54
Problems 56
3 CHARGED PARTICLE MOTION IN NONUNIFORM
MAGNETOSTATIC FIELDS
1. Introduction 59
2. Spatial Variation of the Magnetic Field 61
2.1 Divergence Terms
2.2 Gradient and Curvature Terms
2.3 Shear Terms
3. Equation of Motion in the First-Order Approximation 66
4. Average Force Over One Gyration Period 68
4.1 Parallel Force
4.2 Perpendicular Force
4.3 Total Average Force
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
6.2 Magnetic Mirror Effect
6.3 The Longitudinal Adiabatic Invariant
7. Curvature Drift 84
8. Combined Gradient-Curvature Drift 87
Problems 89
4 CHARGED PARTICLE MOTION IN
TIME-VARYING ELECTROMAGNETIC FIELDS
1. Introduction 95
2. Slowly Time-Varying Electric Field 95
2.1 Equation of Motion and Polarization Drift
2.2 Plasma Dielectric Constant
3. Electric Field with Arbitrary Time Variation 100
3.1 Solution of the Equation of Motion
3.2 Physical Interpretation
3.3 Mobility Dyad
3.4 Plasma Conductivity Dyad
3.5 Cyclotron Resonance
4. Time-Varying Magnetic Field and Space-Varying Electric Field 108
4.1 Equation of Motion and Adiabatic Invariants
4.2 Magnetic Heating of a Plasma
5. Summary of Guiding Center Drifts and Current Densities 115
5.1 Guiding Center Drifts
5.2 Current Densities
Problems 116
5 ELEMENTS OF PLASMA KINETIC THEORY
1. Introduction 122
2. Phase Space 123
2.1 Single-Particle Phase Space
2.2 Many-Particle Phase Space
2.3 Volume Elements
3. Distribution Function 126
4. Number Density and Average Velocity 128
5. The Boltzmann Equation 129
5.1 Collisionless Boltzmann Equation
5.2 Jacobian of the Transformation in Phase Space
5.3 Effects of Particle Interactions
6. Relaxation Model for the Collision Term 135
7. The Vlasov Equation 136
Problems 138
6 AVERAGE VALUES AND MACROSCOPIC VARIABLES
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
6.2 Force per Unit Area
6.3 Force per Unit Volume
6.4 Scalar Pressure and Absolute Temperature
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
1. The Equilibrium State Distribution Function 161
1.1 The General Principle of Detailed Balance and Binary Collisions
1.2 Summation Invariants
1.3 Maxwell-Boltzmann Distribution Function
1.4 Determination of the Constant Coefficients
1.5 Local Maxwell-Boltzmann Distribution Function
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
4.2 Distribution of Speeds
4.3 Mean Values Related to the Molecular Speeds
4.4 Distribution of Thermal Kinetic Energy
4.5 Random Particle Flux
4.6 Kinetic Pressure and Heat Flux
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
1. Moments of the Boltzmann Equation 193
2. General Transport Equation 194
3. Conservation of Mass 197
3.1 Derivation of the Continuity Equation
3.2 Derivation by the Method of Fluid Dynamics
3.3 The Collision Term
4. Conservation of Momentum 200
4.1 Derivation of the Equation of Motion
4.2 The Collision Term
5. Conservation of Energy 204
5.1 Derivation of the Energy Transport Equation
5.2 Physical Interpretation
5.3 Simplifying Approximations
6. The Cold Plasma Model 210
7. The Warm Plasma Model 211
Problems 212
9 MACROSCOPIC EQUATIONS FOR A CONDUCTING FLUID
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
5.2 Conservation of Electric Charge
5.3 Generalized Ohm’s Law
6. Simplified Magnetohydrodynamic Equations 234
Problems 236
10 PLASMA CONDUCTIVITY AND DIFFUSION
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
4.2 Anisotropic Magnetoplasma
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 PHENOMENON
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
4.2 Electric Potential on the Wall
4.3 Inner Structure of the Plasma Sheath
5. Plasma Probe 288
Problems 291
12 SIMPLE APPLICATIONS OF MAGNETOHYDRODYNAMICS
1. Fundamental Equations of Magnetohydrodynamics 299
1.1 Parker Modified Momentum Equation
1.2 The Double Adiabatic Equations of Chew, Goldberger, and Low (CGL)
1.3 Special Cases of the Double Adiabatic Equations
1.4 Energy Integral
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
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
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
1. Introduction 375
1.1 Alfv´en Waves
1.2 Magnetosonic Wave
2. MHD Equations for a Compressible Nonviscous Conducting Fluid 379
2.1 Basic Equations
2.2 Development of an Equation for the Fluid Velocity
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 Alfv´en Wave
5.2 Fast and Slow MHD Waves
5.3 Phase Velocities
5.4 Wave Normal Surfaces
6. Effect of Displacement Current 390
6.1 Basic Equations
6.2 Equation for the Fluid Velocity
6.3 Propagation Across the Magnetostatic Field
6.4 Propagation Along the Magnetostatic Field
7. Damping of MHD Waves 394
7.1 Alfv´en Waves
7.2 Sound Waves
7.3 Magnetosonic Waves
Problems 397
16 WAVES IN COLD PLASMA
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
4.2 Collisionless Plasma
4.3 Time-Averaged Poynting Vector
4.4 The Effect of Collisions
5. Wave Propagation in Magnetized Cold Plasmas 413
5.1 Derivation of the Dispersion Relation
5.2 The Appleton-Hartree Equation
6. Propagation Parallel to B0 419
7. Propagation Perpendicular to B0 423
8. Propagation at Arbitrary Directions 430
8.1 Resonances and Reflection Points
8.2 Wave Normal Surfaces
8.3 The CMA Diagram
9. Some Special Wave Phenomena in Cold Plasmas 439
9.1 Atmospheric Whistlers
9.2 Helicons
9.3 Faraday Rotation
Problems 447
17 WAVES IN WARM PLASMA
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
2.2 Longitudinal Waves
2.3 Transverse Wave
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
4.2 Wave Propagation Along the Magnetic Field
4.3 Wave Propagation Normal to the Magnetic Field
4.4 Wave Propagation at Arbitrary Directions
5. Waves in a Fully Ionized Warm Magnetoplasma 470
5.1 Derivation of the Dispersion Relation
5.2 Wave Propagation Along the Magnetic Field
5.3 Wave Propagation Normal to the Magnetic Field
5.4 Wave Propagation at Arbitrary Directions
6. Summary 479
Problems 481
18 WAVES IN HOT ISOTROPIC PLASMA
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
3.2 Solution of the Linearized Vlasov Equation
3.3 Expression for the Current Density
3.4 Separation into the Various Modes
4. Electrostatic Longitudinal Wave in a Hot Isotropic Plasma 491
4.1 Development of the Dispersion Relation
4.2 Limiting Case of a Cold Plasma
4.3 High Phase Velocity Limit
4.4 Dispersion Relation for Maxwellian Distribution Function
4.5 Landau Damping
5. Transverse Wave in a Hot Isotropic Plasma 503
5.1 Development of the Dispersion Relation
5.2 Cold Plasma Result
5.3 Dispersion Relation for Maxwellian Distribution Function
5.4 Landau Damping of the Transverse Wave
6. The Two-Stream Instability 506
7. Summary 508
7.1 Longitudinal Mode
7.2 Transverse Mode
Problems 510
19 WAVES IN HOT MAGNETIZED PLASMA
1. Introduction 515
2. Wave Propagation Along the Magnetostatic Field in a Hot Plasma 516
2.1 Linearized Vlasov Equation
2.2 Solution of the Linearized Vlasov Equation
2.3 Perturbation Current Density
2.4 Separation into the Various Modes
2.5 Longitudinal Plasma Wave
2.6 Transverse Electromagnetic Waves
2.7 Temporal Damping of the Transverse Electromagnetic Waves
2.8 Cyclotron Damping of the RCP Transverse Wave
2.9 Instabilities in the RCP Transverse Wave
3. Wave Propagation Across the Magnetostatic Field in a Hot Plasma 534
3.1 Solution of the Linearized Vlasov Equation
3.2 Current Density and the Conductivity Tensor
3.3 Evaluation of the Integrals
3.4 Separation into the Various Modes
3.5 Dispersion Relations
3.6 The Quasistatic Mode
3.7 The TEM Mode
4. Summary 552
4.1 Propagation Along B0 in Hot Magnetoplasmas
4.2 Propagation Across B0 in Hot Magnetoplasmas
Problems 554
20 PARTICLE INTERACTIONS IN PLASMAS
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
4.2 Coulomb Interaction Potential
5. Cross Sections 572
5.1 Differential Scattering Cross Section
5.2 Total Scattering Cross Section
5.3 Momentum Transfer Cross Section
6. Cross Sections for the Hard Sphere Model 578
6.1 Differential Scattering Cross Section
6.2 Total Scattering Cross Section
6.3 Momentum Transfer Cross Section
7. Cross Sections for the Coulomb Potential 580
7.1 Differential Scattering Cross Section
7.2 Total Scattering Cross Section
7.3 Momentum Transfer Cross Section
8. Screening of the Coulomb Potential 582
Problems 586
21 THE BOLTZMANN AND THE FOKKER-PLANCK EQUATIONS
1. Introduction 589
2. The Boltzmann Equation 590
2.1 Derivation of the Boltzmann Collision Integral
2.2 Jacobian of the Transformation
2.3 Assumptions in the Derivation of the Boltzmann Collision Integral
2.4 Rate of Change of a Physical Quantity as a Result of Collisions
3. The Boltzmann’s H Function 598
3.1 Boltzmann’s H Theorem
3.2 Analysis of Boltzmann’s H Theorem
3.3 Maximum Entropy or Minimum H Approach for Deriving the Equilibrium
Distribution Function
3.4 Mixture of Various Particle Species
4. Boltzmann Collision Term for a Weakly Ionized Plasma 607
4.1 Spherical Harmonic Expansion of the Distribution Function
4.2 Approximate Expression for the Boltzmann Collision Term
4.3 Rate of Change of Momentum Due to Collisions
5. The Fokker-Planck Equation 612
5.1 Derivation of the Fokker-Planck Collision Term
5.2 The Fokker-Planck Coefficients for Coulomb Interactions
5.3 Application to Electron-Ion Collisions
Problems 621
22 TRANSPORT PROCESSES IN PLASMAS
1. Introduction 628
2. Electric Conductivity in a Nonmagnetized Plasma 629
2.1 Solution of the Boltzmann Equation
2.2 Electric Current Density and Conductivity
2.3 Conductivity for Maxwellian Distribution Function
3. Electric Conductivity in a Magnetized Plasma 634
3.1 Solution of Boltzmann Equation
3.2 Electric Current Density and Conductivity
4. Free Diffusion 640
4.1 Perturbation Distribution Function
4.2 Particle Flux
4.3 Free Diffusion Coefficient
5. Diffusion in a Magnetic Field 643
5.1 Solution of Boltzmann Equation
5.2 Particle Flux and Diffusion Coefficients
6. Heat Flow 647
6.1 General Expression for the Heat Flow Vector
6.2 Thermal Conductivity for a Constant Kinetic Pressure
6.3 Thermal Conductivity for the Adiabatic Case
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
Publisher's webpage - http://www.springer.com/physics/atomic,+molecular,+optical+&+plasma+physics/book/978-0-387-20975-3Publisher said:Fundamentals of Plasma Physics is a comprehensive textbook designed to present a logical and unified treatment of the fundamentals of plasma physics based on statistical kinetic theory, with applications to a variety of important plasma phenomena. The clarity and completeness of the text makes it suitable for self-learning.
Throughout the text the emphasis is on clarity, rather than formality. The various derivations are explained in detail and, wherever possible, the physical interpretations are emphasized. The mathematical treatment is set out in great detail, carrying out steps that are usually left to the reader. The problems form an integral part of the text and most of them were designed in such a way as to provide a guideline for the student, stating intermediate steps with answers.
The book is intended primarily for advanced undergraduate and first year graduate students meeting the subject of plasma physics for the first time and is suitable for those who have taken classical mechanics, electrodynamics and mathematics beyond sophomore level.
It is a valuable compendium for any serious student of plasma physics at the level of research student or research worker and it is also of interest to researchers in other related fields, such as space physics and applied electromagnetism.
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