Plasma fluid equations in the high collision-frequency limit

Abstract

The nature of the fluid approximation for plasmas in the high collision-frequency limit is examined in an effort to understand some of the limits of validity of the commonly used ideal magnetohydrodynamic equations. The plane wave dispersion relation for a homogeneous medium is evaluated. The dependence of the damping on the various dissipative terms is examined for each type of wave predicted by the dispersion relation. The effects of these terms are then compared, using the standard values for transport quantities with collision frequency larger than gyro-frequency. When the total dissipation is considered as a function of collision frequency, it is found that there is a minimum in the region where the collision and gyro-frequencies are about equal. This is the régime for which ideal magnetohydrodynamics is a good approximation. As collision frequency is increased, dissipation reaches a maximum when the wave is in resonance with the resistive skin depth, and then decreases into a régime where ordinary sound and light waves propagate. Lower collision frequencies, where thermal conduction and equilibration are important, are considered.