Moment Equations

Plasma Physics · Part 3

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Table of Contents

  1. 1.1.1 From Kinetic to Fluid Description
  2. 2.1.2 Macroscopic Quantities
  3. 3.1.3 The Fluid Equations
  4. 4.1.4 Closure Approximations
  5. 5.Continuity Equation
  6. 6.Momentum Equation
  7. 7.Energy Equation
  8. 8.Key Takeaways

Key Equations

$$\int (\text{Boltzmann equation}) \times \{1, \mathbf{v}, \tfrac{1}{2}m v^2\} \, d^3v$$
$$P_{ij} = m \int (v_i - u_i)(v_j - u_j) f \, d^3v$$
$$mn\left(\frac{\partial \mathbf{u}}{\partial t} + \mathbf{u} \cdot \nabla \mathbf{u}\right) = qn(\mathbf{E} + \mathbf{u} \times \mathbf{B}) - \nabla \cdot \mathbf{P} + \mathbf{R}$$
$$p = nk_BT, \quad T = \text{const}$$

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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