Vlasov Equation

Plasma Physics · Part 2

298 KB10 sections4 key equationsLaTeX typeset
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Table of Contents

  1. 1.1.1 Introduction
  2. 2.1.2 Derivation from Liouville's Theorem
  3. 3.1.3 Self-Consistent Fields: Vlasov-Maxwell System
  4. 4.1.4 Linearization: Electrostatic Perturbations
  5. 5.1.5 Conservation Laws
  6. 6.1.6 Physical Interpretation
  7. 7.1.7 Validity and Limitations
  8. 8.1.8 Applications
  9. 9.🌌 Space Plasmas & Vlasov Kinetics
  10. 10.🔥 Fusion Plasmas & Kinetic Effects

Key Equations

$$f_s(\mathbf{r}, \mathbf{v}, t) \, d^3r \, d^3v = \text{number of particles of species } s$$
$$\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t}$$
$$\frac{\partial}{\partial t}\left(\sum_s \int \frac{1}{2}m_s v^2 f_s \, d^3v\right) + \nabla \cdot \mathbf{S} = -\mathbf{J} \cdot \mathbf{E}$$
$$J_{CD} = -e \int v_\parallel f_1 \, d^3v \propto \frac{\partial f_0}{\partial v_\parallel}\bigg|_{v_\parallel = \omega/k_\parallel}$$

Equations are rendered with MathJax in the PDF with professional LaTeX typesetting.

Course Context

This PDF is part of the Plasma Physics course on CoursesHub.World. Comprehensive study of the fourth state of matter. Covers single-particle motion, kinetic theory, MHD, waves and instabilities, collisional processes, magnetic and inertial confinement fusion, space a...

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