Fundamentals of Plasma Physics Book

CONTENTS
1. General Properties of Plasmas
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 De.nition of a Plasma
2.1 Macroscopic Neutrality
2.2 Debye Shielding
2.3 The Plasma Frequency

3. The Occurrence of Plasmas in Nature
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
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
5.1 General Considerations on a Self-Consistent Formulation
5.2 Theoretical Approaches

Problems
1. Introduction
2. Energy Conservation
3. Uniform Electrostatic Field
4. Uniform Magnetostatic Field
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
5.1 Formal Solution of the Equation of Motion
5.2 Solution in Cartesian Coordinates
6. Drift Due to an External Force Problems

1. Introduction
2. Spatial Variation of the Magnetic Field
2.1 Divergence Terms
2.2 Gradient and Curvature Terms
2.3 Shear Terms
3. Equation of Motion in the First Order Approximation
4. Average Force Over One Gyration Period
4.1 Parallel Force
4.2 Perpendicular Force
4.3 Total Average Force
5. Gradient Drift
6. Parallel Acceleration of the Guiding Center
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
8. Combined Gradient-Curvature Drift Problems

1. Introduction
2. Slowly Time-Varying Electric Field
2.1 Equation of Motion and Polarization Drift
2.2 Plasma Dielectric Constant
3. Electric Field with Arbitrary Time Variation
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
4.1 Equation of Motion and Adiabatic Invariants
4.2 Magnetic Heating of a Plasma
5. Summary of Guiding Center Drifts and Current Densities
5.1 Guiding Center Drifts
5.2 Current Densities Problems

1. Introduction
2. Phase Space
2.1 Single-Particle Phase Space
2.2 Many-Particle Phase Space
2.3 Volume Elements
3. Distribution Function
4. Number Density and Average Velocity
5. The Boltzmann Equation
5.1 Colisionless Boltzmann Equation
5.2 Jacobian of the Transformation in Phase Space
5.3 E.ects of Particle Interactions
6. Relaxation Model for the Collision Term
7. The Vlasov Equation Problems

1. Average Value of a Physical Quantity
2. Average Velocity and Peculiar Velocity
3. Flux
4. Particle Current Density
5. Momentum Flow Dyad or Tensor
6. Pressure Dyad or Tensor
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
8. Heat Flow Triad
9. Total Energy Flux Triad
10. Higher Moments of the Distribution Function Problems

1. The Equilibrium State Distribution Function
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 Coe.cients
1.5 Local Maxwell-Boltzmann Distribution Function
2. The Most Probable Distribution
3. Mixture of Various Particle Species
4. Properties of the Maxwell-Boltzmann Distribution Function
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
6. Degree of Ionization in Equilibrium - The Saha Equation Problems

1. Moments of the Boltzmann Equation
2. General Transport Equation
3. Conservation of Mass
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
4.1 Derivation of the Equation of Motion
4.2 The Collision Term
5. Conservation of Energy
5.1 Derivation of the Energy Transport Equation
5.2 Physical Interpretation
5.3 Simplifying Approximations
6. The Cold Plasma Model
7. The Warm Plasma Model Problems

1. Macroscopic Variables for a Plasma as a Conducting Fluid
2. Continuity Equation
3. Equation of Motion
4. Energy Equation
5. Electrodynamic Equations for a Conducting Fluid
5.1 Maxwell Curl Equations
5.2 Conservation of Electric Charge
5.3 Generalized Ohm's Law
6. Simplified Magnetohydrodynamic Equations Problems

1. Introduction
2. The Langevin Equation
3. Linearization of the Langevin Equation
4. DC Conductivity and Electron Mobility
4.1 Isotropic Plasma
4.2 Anisotropic Magnetoplasma
5. AC Conductivity and Electron Mobility
6. Conductivity with Ion Motion
7. Plasma as a Dielectric Medium
8. Free Electron Diffusion
9. Electron Diffusion in a Magnetic Field
10. Ambipolar Diffusion
11. Diffusion in a Fully Ionized Plasma Problems

1. Electron Plasma Oscillations
2. The Debye Shielding Problem
3. Debye Shielding Using the Vlasov Equation
4. Plasma Sheath
4.1 Physical Mechanism
4.2 Electric Potential on the Wall
4.3 Inner Structure of the Plasma Sheath The Plasma Probe Problems

1. Fundamental Equations of Magnetohydrodynamics
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
3. Diffusion of Magnetic Field Lines
4. Freezing of Magnetic Field Lines to the Plasma
5. Magnetic Pressure
5.1 Concept of Magnetic Pressure
5.2 Isobaric Surfaces
6. Plasma Con.nement in a Magnetic Field Problems

1. Introduction
2. The Equilibrium Pinch
3. The Bennett Pinch
4. Dynamic Model of the Pinch
5. Instabilities in a Pinched Plasma Column
6. The Sausage Instability
7. The Kink Instability
8. Convex Field Con.gurations Problems

1. The Wave Equation
2. Solution in Plane Waves
3. Harmonic Waves
4. Polarization
5. Energy Flow
6. Wave Packets and Group Velocity Problems

1. Introduction
1.1 Alfven Waves
1.2 Magnetosonic Waves
2. MHD Equations for a Compressible Nonviscous Conducting Fluid
2.1 Basic Equations
2.2 Development of an Equation for the Fluid Velocity
3. Propagation Perpendicular to the Magnetic Field
4. Propagation Parallel to the Magnetic Field
5. Propagation at Arbitrary Directions
5.1 Pure Alfven Wave
5.2 Fast and Slow MHD Waves
5.3 Phase Velocities
5.4 Wave Normal Surfaces
6. Effect of Displacement Current
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
7.1 Alfven Waves
7.2 Sound Waves
7.3 Magnetosonic Waves Problems

1. Introduction
2. Basic Equations of Magnetoionic Theory
3. Plane Wave Solutions and Linearization
4. Wave Propagation in Isotropic Electron Plasmas
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
5.1 Derivation of the Dispersion Relation
5.2 The Appleton-Hartree Equation
6. Propagation Parallel to B0
7. Propagation Perpendicular to B0
8. Propagation at Arbitrary Directions
8.1 Resonances and Reflection Points
8.2 Wave Normal Surfaces
8.3 The CMA Diagram
9. Some Special Wave Phenomena in Cold Plasmas
9.1 Atmospheric Whistlers
9.2 Helicons
9.3 Faraday Rotation Problems

1. Introduction
2. Waves in a Fully Ionized Isotropic Warm Plasma
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
4. Waves in a Warm Electron Gas in a Magnetic Field
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
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 Problems

1. Introduction
2. Basic Equations
3. General Results for a Plane Wave in a Hot Isotropic Plasma
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
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
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
7. Summary
7.1 Longitudinal Mode
7.2 Transverse Mode Problems

1. Introduction
2. Wave Propagation Along the Magnetostatic Field in a Hot Plasma
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
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
4.1 Propagation Along B0 in Hot Magnetoplasmas
4.2 Propagation Across B0 in Hot Magnetoplasmas Problems

1. Introduction
2. Binary Collisions
3. Dynamics of Binary Collisions
4. Evaluation of the Scattering Angle
4.1 Two Perfectly Elastic Hard Spheres
4.2 Coulomb Interaction Potential
5. Cross Sections
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
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
7.1 Differential Scattering Cross Section
7.2 Total Scattering Cross Section
7.3 Momentum Transfer Cross Section
8. Screening of the Coulomb Potential Problems

1. Introduction
2. The Boltzmann Equation
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
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
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
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

1. Introduction
2. Electric Conductivity in a Nonmagnetized Plasma
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
3.1 Solution of Boltzmann Equation
3.2 Electric Current Density and Conductivity
4. Free Diffusion
4.1 Perturbation Distribution Function
4.2 Particle Flux
4.3 Free Diffusion Coefficient
5. Di.usion in a Magnetic Field
5.1 Solution of Boltzmann Equation
5.2 Particle Flux and Di.usion Coefficients
6. Heat Flow
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

A. Useful Vector Relations B. Useful Relations in Cartesian and in Curvilinear Coordinates C. Physical Constants (MKSA)
D. Conversion Factors for Physical Units E. Some Important Plasma Parameters F. Approximate Magnitudes in Some Typical Plasmas