Part III: Fluid Theory
Magnetohydrodynamics (MHD) treats plasma as an electrically conducting fluid, valid when collisions are frequent enough to maintain local thermodynamic equilibrium.
Part Overview
MHD combines fluid dynamics with Maxwell's equations, providing an efficient description for large-scale plasma phenomena in fusion, astrophysics, and space physics.
Key Concepts
- • Moment equations and fluid closures
- • Ideal and resistive MHD equations
- • Grad-Shafranov equation for tokamak equilibrium
- • Alfvén and magnetosonic waves
- • MHD instabilities (kink, sausage, ballooning)
- • Two-fluid theory and Hall MHD
- • Closure problem
7 chapters | Foundation of fusion and astrophysical MHD
Chapters
Chapter 1: Moment Equations
Deriving fluid equations from kinetic theory by taking velocity moments of the distribution function.
Chapter 2: MHD Equations
Ideal and resistive MHD, Ohm's law, frozen-in flux theorem, and magnetic Reynolds number.
Chapter 3: MHD Equilibrium
Force balance, Grad-Shafranov equation, tokamak equilibrium, and beta limits.
Chapter 4: MHD Waves
Alfvén waves, fast and slow magnetosonic waves, CFL diagrams, and wave heating.
Chapter 5: MHD Instabilities
Kink modes, sausage instability, ballooning modes, and stability criteria.
Chapter 6: Two-Fluid Theory
Separate electron and ion fluids, Hall MHD, whistler waves, and electron inertia.
Chapter 7: Closure Problem
CGL equations, double-adiabatic theory, and when fluid models break down.