Magnetohydrodynamics (MHD)

Introduction

Magnetohydrodynamics is interesting from several standpoints. It is a theory about electrically neutral, but conducting fluids. Ordinary fluids are interesting and beautiful on their own, but magnetofluids have an extra property. Magnetofluids can carry current, which means that they can both generate and be influenced by magnetic fields. This natural self-interaction between the current and the magnetic field produces some curious phenomena. Witness the behavior of the solar magnetic field, or the earth's magnetic field.

From a mathematical standpoint they are a hyperbolic (Almost. Even in the ideal case [no diffusion] there can be a problem with degenerate characteristics...) system of nonlinear coupled partial differential equations. This innocuous sounding classification hides a great deal of complexity. Hyperbolic essentially means that the system supports waves. (Also that the equations represent an initial value or time evolution problem.) Nonlinear in this context, essentially means that it is possible for the magnetofluid to support shock waves, or traveling discontinuities in the properties of the magnetofluid. Also that analytical solutions to these equations have not been found except in the simplest and most trivial cases. Consider the difficulty of turbulence as an example. MHD virtually requires numerical methods for understanding of the magnetofluids behavior in physically relevant systems.

Someday I'll finish my own description of MHD in here. I guess I'm going to have to figure out how to display equations with html. For now this is just another link to links.... Sorry if your in here because your search found all the heavy terminology I have listed below. There is no real content here yet, other than an outline.

MHD WWW resources

An (incomplete) MHD bibliography:

Polovin and Demutskii, ``Fundamentals of Magnetohydrodynamics'', Plenum, 1990

A.I.Akhiezer, I.A. Akhiezer, R.V. Polovin, A.G. Sitenko and K.N. Stepanov,``Plasma Electrodyanamics, Volume 1: Linear Theory'', Pergamon, 1975

D. Biskamp, ``Nonlinear Magnetohydrodynamics'', Cambridge, 1993

J.P. Goedbloed, ``Lecture Notes on Ideal Magnetohydrodynamics'', Rijnhuizen Report 83-145, 1983

E. R. Priest, ``Solar Magnetohydrodynamics'', D.Reidel Publishing, 1982.

Outline of Concepts in Fluids and Magnetofluids

Fluids and the fluid approximation

Kinetic theory, Liouville equation, distributions, Boltzman eq., Phase space.

Collisions, collision frequency.

Moments of the distributions.

Conservation of mass density.

Notes on the conservation form of the equations.

Compressible versus Incompressible fluids.

Conservation of momentum density.

Conservation of energy density.

Vorticity, Viscosity and diffusion.

Body forces

Bernoulli's equation. Conservation of energy for an incompressible fluid with negligible viscosity and laminar (non-turbulent) flow. (Daniel Bernoulli (1700-1782) was a Swiss mathematician and physicist who first published this in 1738 - Hydrodynamica.)

Flying and lift. ( Aren't I ambitious? Many people get this wrong...)

Waves and normal modes.

Stability.

Nonlinear terms and Shocks.

Rotation and Geophysical/Astrophysical fluids.

Magnetofluids: electrically neutral, conducting fluids

Plasmas; Atoms and Ionization

Currents, Magnetic fields, Maxwell's equations and the pre-Maxwell approximation. Time/velocity scales.

Resistivity or Conductivity and diffusive losses

Modifications to the momentum and energy density equations

Some interesting results.

MHD waves

Nonlinear effects

Connections between rotation and magnetic fields