Mhd Instabilities

Plasma Physics · Part 3

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Table of Contents

  1. 1.5.1 Energy Principle
  2. 2.5.2 Interchange Instability
  3. 3.5.3 Sausage and Kink Instabilities
  4. 4.5.4 Tearing Mode
  5. 5.5.5 Ballooning Modes
  6. 6.5.6 Rayleigh-Taylor Analog
  7. 7.Sausage Instability (m = 0)
  8. 8.Kink Instability (m = 1)
  9. 9.Key Takeaways

Key Equations

$$\delta W = \frac{1}{2}\int \left[\frac{|\mathbf{Q}|^2}{\mu_0} + \gamma p|\nabla \cdot \boldsymbol{\xi}|^2 + (\boldsymbol{\xi} \cdot \nabla p)(\nabla \cdot \boldsymbol{\xi}) + \mathbf{J} \cdot (\boldsymbol{\xi} \times \mathbf{Q})\right] d^3r$$
$$\nabla p \cdot \boldsymbol{\kappa} > 0 \quad \Rightarrow \quad \text{Unstable}$$
$$\gamma^2 = \frac{k^2 v_A^2}{1 + k^2 a^2}\left(\frac{B_z^2}{B_\theta^2} - 1 - k^2 a^2\right)$$
$$\text{Kruskal-Shafranov: } q(a) = \frac{2\pi a B_z}{\mu_0 I} > 1$$

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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