Plasma Theory: An Advanced Guide for Graduate Students

Introduction
Contents
Chapter 1: Plasma Kinetics
	1.1 Boltzmann Equation
	1.2 Collision Operator for Coulomb Collisions
		1.2.1 General Expression for a Flow in the Velocity Space Caused by Collisions
		1.2.2 Deceleration and Diffusion of Test Particles Cloud in the Velocity Space
		1.2.3 Momentum and Energy Loss of the Test Particles
		1.2.4 Landau Collision Operator
	1.3 Relativistic Collision Operator
	1.4 Fokker-Planck Equation
	1.5 Runaway Electrons in Fully Ionized Plasma
	1.6 Distribution Function of Electrons in Slightly Ionized Plasma
		1.6.1 Approximation
		1.6.2 Distribution Function in the Electric Field
		1.6.3 Impact of Electron-Electron Collisions
		1.6.4 General Expression for
	1.7 Transport Coefficients for Electrons in Slightly Ionized Plasma
	1.8 Drift Kinetic Equation in a Stationary Electric and Magnetic Field
	1.9 Gyrokinetic Equation
	1.10 Pellet Ablation in a Tokamak
Chapter 2: Transport Equations
	2.1 Momentum Equations
	2.2 Transport Coefficients in Fully Ionized Plasma. Method of Chapman and Enskog
	2.3 Summary of the Results for the Fully Ionized Plasma
	2.4 Transport Coefficients in Fully Ionized Plasma. Qualitative Considerations
		2.4.1 Friction Caused by the Relative Mean Velocity and Thermal Force
		2.4.2 Spitzer Conductivity
		2.4.3 Heat Flux: Conductive and Convective Parts
		2.4.4 Collisional Heat Production
		2.4.5 Viscosity
	2.5 Equation for Entropy
	2.6 Viscosity in the BGK Approximation
	2.7 Thermal Force for Impurities
	2.8 First Ionization Potential Effect and Impurity Retention in a Tokamak Edge
Chapter 3: Quasineutral Plasma and Sheath Structure
	3.1 Quasineutrality Maintenance
	3.2 Collisionless Sheath at the Material Surfaces
		3.2.1 Electrons in a Capacitor with a Reflecting Electric Field
		3.2.2 Particle and Energy Fluxes to the Material Surfaces
		3.2.3 Current-Voltage Characteristics of the Sheath. Floating Potential
		3.2.4 Sheath Structure. Bohm Criterion
	3.3 Impact of Electron Emission. Double Sheath
	3.4 Sheath in Magnetic Field
	3.5 Thermoelectric Current Between Two Electrodes
Chapter 4: Diffusion in Partially Ionized Unmagnetized Plasma
	4.1 Ambipolar Diffusion
	4.2 Examples of Solutions of the Ambipolar Diffusion Equation
		4.2.1 Decay of Initial Perturbation in Infinite Plasma
		4.2.2 Positive Column of Glow Discharge
		4.2.3 Diffusive Decay
		4.2.4 Diffusive Probe
	4.3 Diffusion of Slightly Ionized Multispecies Plasma
	4.4 Diffusion in the Ionosphere
Chapter 5: Diffusion of Partially Ionized Magnetized Plasma
	5.1 Diffusion and Mobility in a Magnetic Field
	5.2 One-Dimensional Diffusion in Magnetized Plasma
		5.2.1 Diffusion Across a Magnetic Field
		5.2.2 1D Diffusion at an Arbitrary Angle with a Magnetic Field
	5.3 Diffusion of Perturbation in Unbounded Plasma
	5.4 Diffusion in Plasma Restricted by Dielectric Walls
	5.5 Diffusion in a Cylinder with Conducting Walls
	5.6 Diffusive Probe in Magnetic Field
	5.7 Experiments in Laboratory Plasma
Chapter 6: Partially Ionized Plasma with Current
	6.1 Plasma with Net Current in the Absence of a Magnetic Field
		6.1.1 Small Perturbations
		6.1.2 Nonlinear Evolution
	6.2 Magnetized Plasma with Current
		6.2.1 One-Dimensional Evolution
		6.2.2 Multidimensional Evolution of Small Perturbation in Unbounded Plasma
		6.2.3 Effect of Conductivity Recovery in a Weak Magnetic Field
	6.3 Plasma Clouds in the Ionosphere
		6.3.1 Redistribution of Metal Ions in the Polar Ionosphere. Sporadic Layers
		6.3.2 Active Experiments with Barium Clouds
Chapter 7: Transport in Strongly Ionized Plasma Across a Magnetic Field
	7.1 Classical Diffusion of Fully Ionized Plasma Across a Magnetic Field
	7.2 Transport of Impurities in Fully Ionized Plasma Across a Magnetic Field
	7.3 Partially Ionized Magnetized Plasma with an Inhomogeneous Neutral Component
	7.4 Penetration of Neutral Particles into Hot Tokamak Plasma
Chapter 8: Drift Waves and Turbulent Transport
	8.1 Drift Waves in Inhomogeneous Plasma
	8.2 Drift-Dissipative Instability
	8.3 Universal Instability
		8.3.1 Fluid Ions
		8.3.2 Kinetic Ions
	8.4 Instabilities Caused by the Temperature Gradient
	8.5 Turbulent Transport Caused by Random Electric Fields
	8.6 Effect of Magnetic Shear on Plasma Instabilities
Chapter 9: Dynamics of Fully Ionized Plasma in the Absence of a Magnetic Field
	9.1 Ion Acoustic Waves
	9.2 Nonlinear Dynamics. Self-Similar Solutions
	9.3 Simple Nonlinear Waves. Overturn
	9.4 Nonlinear Ion Acoustic Waves with Dispersion
	9.5 Plasma Expansion During Pellet Injection
Chapter 10: Magnetohydrodynamics (MHD)
	10.1 Magnetohydrodynamic Equations
	10.2 Magnetic Field Frozen in and Skin Effect
	10.3 MHD Waves
	10.4 Nonlinear MHD Waves
	10.5 Magnetosonic Waves with Dispersion
	10.6 Alfven Masers
Chapter 11: Dynamics of Plasma Blobs and Jets in a Magnetic Field
	11.1 Plasma Motion Across Magnetic Field in Vacuum
	11.2 Deceleration of the Plasma Jet by Ambient Plasma
	11.3 Edge Localized Modes and Filaments
Chapter 12: Plasma Equilibrium
	12.1 On the Possibility of Equilibrium in the Absence of a Vacuum Magnetic Field
	12.2 Equilibrium of a Pinch
	12.3 Magnetic Flux Surface Functions
	12.4 Grad-Shafranov Equation
	12.5 Integral Equilibrium in a Tokamak
	12.6 Plasma Equilibrium in a Tokamak with Circular Cross-Sections
	12.7 Coordinates for Arbitrary Flux Surfaces
	12.8 Force-Free Equilibrium and Pinch with Canonical Profiles
	12.9 2D Modeling of the Tokamak Edge
Chapter 13: Transport Phenomena in Tokamaks
	13.1 Fluid Regime (Pfirsch-Schlueter Regime)
		13.1.1 Qualitative Estimates
		13.1.2 Heat Conductivity
		13.1.3 Plasma Flows on the Flux Surface, Density, Temperature and Potential Perturbations
		13.1.4 Particle Fluxes
	13.2 Radial Electric Field, Poloidal and Toroidal Rotation
	13.3 Neoclassical Transport in Collisionless Regimes
		13.3.1 Particle Trajectories
		13.3.2 Ware Drift
		13.3.3 Estimation of Transport Coefficients in the Plateau Regime
		13.3.4 Estimation of Transport Coefficients in the Banana Regime
	13.4 Distribution Function in the Collisionless Regimes
		13.4.1 Plateau Regime
		13.4.2 Banana Regime
	13.5 Particle and Heat Balance Equations
	13.6 Transport Codes
Chapter 14: Instabilities in Magnetized Plasma
	14.1 Rayleigh-Taylor Instability in Fluids
	14.2 Flute Instability
	14.3 Dissipative Modifications of Flute Instability
		14.3.1 RT Instability in Partially Ionized Plasma
		14.3.2 Flute Instability in Plasma Contacting Metal Surfaces
		14.3.3 Gravitational-Dissipative Flute Instability
	14.4 Energy Principle
	14.5 Kink Instability
	14.6 Tearing Instability
	14.7 Geodesic Acoustic Mode and Zonal Flows
	14.8 Equatorial Plasma Bubbles
Chapter 15: Magnetic Islands and Stochastic Magnetic Field
	15.1 Magnetic Islands
	15.2 Stochastic Instability and Magnetic Field Line Diffusion
	15.3 Transport in Stochastic Magnetic Field
	15.4 Resonant Magnetic Perturbations in Tokamak
	15.5 Simulation of Resonant Magnetic Perturbations Effects with Codes and Examples of Experimental Results
Chapter 16: Improved Confinement Regime (H-Mode)
	16.1  Drift Shear and Transport Barriers
	16.2 Transition from Low to High Confinement Regime (L-H Transition)
	16.3 L-H Transition Power Threshold
Bibiliography
Index