
Contents
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15 Dynamics with thermal pressures—II. Magnetized plasma: —Appendix: Time and space dispersive media
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Preamble Preamble
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30.1 Introduction 30.1 Introduction
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30.2 Relaxation rates and Fokker–Planck equations 30.2 Relaxation rates and Fokker–Planck equations
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30.2.1 Energy and momentum changes in binary collisions 30.2.1 Energy and momentum changes in binary collisions
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(a) Test particles scattered by field particles (a) Test particles scattered by field particles
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(b) Collisions with a distribution of field particles—relaxation rates (b) Collisions with a distribution of field particles—relaxation rates
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30.2.2 Fokker–Planck equation 30.2.2 Fokker–Planck equation
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(a) Fokker–Planck operator for binary collisions (a) Fokker–Planck operator for binary collisions
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(b) Diffusion relaxation rates (b) Diffusion relaxation rates
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(c) Properties of collision operators (c) Properties of collision operators
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(d) Relativistic effects (d) Relativistic effects
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30.3 Transport in a fully-ionized plasma 30.3 Transport in a fully-ionized plasma
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30.3.1 Introduction 30.3.1 Introduction
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30.3.2 Electrical conductivity 30.3.2 Electrical conductivity
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(a) Lorentz conductivity (a) Lorentz conductivity
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(b) Spitzer–Härm conductivity (b) Spitzer–Härm conductivity
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30.4 Particle motions and transport in plasma confinement -fields 30.4 Particle motions and transport in plasma confinement -fields
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30.4.1 Uniform -fields 30.4.1 Uniform -fields
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30.4.2 Closed -field geometry—Toroidal (see Chapter 8) 30.4.2 Closed -field geometry—Toroidal (see Chapter 8)
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(a) Tokamak -fields and particle motions [] (a) Tokamak -fields and particle motions []
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(b) Estimated time and space scales of particle orbits (b) Estimated time and space scales of particle orbits
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30.5 Problems 30.5 Problems
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P30-1 Landau collision operator from Rosenbluth form P30-1 Landau collision operator from Rosenbluth form
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P30-2 Proofs of the collision operator properties P30-2 Proofs of the collision operator properties
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P30-3 Approximate, relativistic Fokker–Planck collision operator [, , ] P30-3 Approximate, relativistic Fokker–Planck collision operator [, , ]
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P30-4 Solution of the coupled relativistic relaxation equations [] P30-4 Solution of the coupled relativistic relaxation equations []
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P30-5 Positive-definite nature of in pitch-angle scattering P30-5 Positive-definite nature of in pitch-angle scattering
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Bibliography Bibliography
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30 Kinetic theory of collisions and transport—I. Fully-ionized plasmas
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Published:August 2016
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Abstract
This chapter explores the kinetic theory of collisions and transport for fully-ionized plasmas. It first derives the Fokker–Planck collision equation analyzed in previous chapters by presenting them in two commonly used forms—the Landau form, and the form in terms of Rosenbluth potentials—and examines electrical conductivity through the Spitzer–Härm problem. The chapter then discusses the collisional transport theory, which entails slowly-varying (low-frequency and long-wavelength) hydrodynamics in a short mean-free-path limit. It shows that responses to drives such as the thermodynamics equilibrium entail the collisional transport coefficients of electrical conductivity, particle and heat diffusivities, and viscosity that enter into, and that specify the hydrodynamic transport equations. The kinetic theory analysis of arriving at the electrical conductivity of a fully-ionized plasma is carried out and used to appreciate some general aspects in the analysis and computation required for finding any transport coefficient.
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