Comments on the Solution to the Boltzmann Equation for a Weakly Ionized Plasma

Abstract

Hydrodynamic equations describing the motion of electrons in a weakly ionized plasma are derived formally from the Boltzmann equation by means of the Chapman-Enskog procedure. Two cases are considered, each with a stationary Maxwellian distribution ascribed to the atoms. In the first, electron-electron collisions are ignored, and the electron distribution function is determined by a balance between the electron-atom collisions and the electric field. There is only one conservation law, a hydrodynamic equation for the density. In the second case, electron-electron collisions are dominant, the distribution function is a local Maxwellian, and there are five conservation laws—equations for the density, drift velocity, and temperature. The equations used previously by the author to describe low-frequency oscillations are obtained in either case if the electron-atom collision frequency is independent of velocity. Otherwise, the zeroth-order equations are still exact, but first-order corrections are required, as illustrated by the example of the velocity-independent mean free path. Our results are somewhat different from those of Davidov, who made different assumptions about the dominant collision mechanisms.