Plasma Physics

4.

Kinetic Theory of Plasmas

4.1.

Phase Space and Distribution Functions

4.1.1.

Six-Dimensional Phase Space

4.1.2.

Single-Particle Distribution Function

4.1.3.

Physical Interpretation

4.1.4.

Normalization and Moments

4.2.

Liouville's Theorem

4.2.1.

Conservation of Phase Space Density

4.2.2.

Application to Plasma Physics

4.3.

The Vlasov Equation

4.3.1.

Derivation from Liouville's Theorem

4.3.2.

Collisionless Plasma Assumption

4.3.3.

Self-Consistent Field Approach

4.3.4.

Vlasov-Maxwell System

4.4.

The Boltzmann Equation

4.4.1.

Collision Integral

4.4.2.

H-Theorem and Entropy

4.4.3.

Relaxation Time Approximation

4.4.4.

BGK Collision Model

4.5.

Moments of the Distribution Function

4.5.1.

Zeroth Moment: Particle Density

4.5.2.

First Moment: Mean Velocity

4.5.3.

Second Moment: Pressure Tensor

4.5.4.

Third Moment: Heat Flux

4.5.5.

Higher Order Moments

4.6.

Equilibrium Distributions

4.6.1.

Maxwell-Boltzmann Distribution

4.6.1.1.

Derivation and Properties

4.6.1.2.

Temperature and Thermal Velocity

4.6.2.

Relativistic Maxwell-Jüttner Distribution

4.6.3.

Degenerate Plasmas

4.6.3.1.

Fermi-Dirac Distribution

4.6.3.2.

Quantum Effects

4.7.

Non-Equilibrium Distributions

4.7.1.

Anisotropic Distributions

4.7.2.

Bi-Maxwellian Distributions

4.7.3.

Loss-Cone Distributions

4.7.4.

Beam Distributions

4.7.5.

Kappa Distributions

4.8.

Kinetic Equations for Multiple Species

4.8.1.

Multi-Species Vlasov Equations

4.8.2.

Species Coupling

4.8.3.

Charge and Current Densities

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5. Fluid Description of Plasmas