Expansion Solutions and Wave Propagation in Partly Ionized Gases

Abstract

Kinetic theory solutions of the Boltzmann equations for a partly ionized gas are obtained for the study of wave propagation in a three-fluid plasma. The following simplifying assumptions are made: The interactions between charged particles are divided into long-range Coulomb forces which effectively act as an external electric field, and a short-range Coulomb force which is cut off at the Debye length; the interactions between other pairs of particles are assumed to obey an inverse fifth-power law. Further, the gas is assumed to be sufficiently close to equilibrium for the usual expansions of the velocity distribution functions around the equilibrium distribution functions to be used. Under these assumptions, the general sets of coefficient equations are obtained, and a 13 and 20 coefficient approximation (which include the effects of self-collisions or viscosity and thermal conductivity) are given explicitly. For a five-coefficient approximation, corresponding to employment of the conservation equations, a dispersion relation is obtained and solved for the phase velocities and attenuation of longitudinal waves as functions of wave and collision frequencies. It is found that the solutions which correspond to waves of high phase velocity are exactly those obtained when the adiabatic law is assumed to hold. Solutions corresponding to low phase velocity waves, however, are found to be more highly attenuated than their counterparts in the adiabatic theory.