Landau Damping

Plasma Physics · Part 2

243 KB10 sections4 key equationsLaTeX typeset
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Table of Contents

  1. 1.2.1 Introduction
  2. 2.2.2 Physical Picture
  3. 3.2.3 Mathematical Derivation
  4. 4.2.4 Landau Damping Rate
  5. 5.2.5 Energy Transfer Mechanism
  6. 6.2.6 Experimental Verification
  7. 7.2.7 Related Phenomena
  8. 8.2.8 Applications
  9. 9.Resonant Particles
  10. 10.The Distribution Function Slope

Key Equations

$$1 + \frac{\omega_{pe}^2}{k^2} \int_{-\infty}^{\infty} \frac{k \, \partial f_0/\partial v}{\omega - kv} \, dv = 0$$
$$Z(\zeta) = \frac{1}{\sqrt{\pi}} \int_{-\infty}^{\infty} \frac{e^{-x^2}}{x - \zeta} \, dx$$
$$1 + \frac{1}{k^2 \lambda_D^2} \left(1 + \zeta Z(\zeta)\right) = 0$$
$$\omega = \omega_{pe}\left(1 + \frac{3}{2}k^2\lambda_D^2\right) - i \sqrt{\frac{\pi}{8}} \frac{\omega_{pe}}{k^3\lambda_D^3} e^{-1/(2k^2\lambda_D^2)}$$

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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