Possible simplifications of the equations of a two-temperature partially ionized plasma

Abstract

In investigating the behavior of an ionized gas in electromagnetic fields use is often made of the equations of conservation of mass, momentum and energy, the equation of state, Maxwell's equations and Ohm's law relating the electric field to the current flowing in the plasma. In a homogeneous Isotropic medium this relation is a simple proportionality between the current density and the electric field strength [1, 2]. In the general case it is more complex in nature. Possible forms of Ohm's law for a fully ionized one-temperature plasma were investigated in [3], and for a two-temperature plasma in [4]. Moreover, it was shown in [4] that, in general, we must take into account terms proportional to the temperature gradients in Ohm's law, and that in this case it also becomes necessary to take viscous terms into account when the electron temperature exceeds the ion temperature by a significant amount. In [5] in order to facilitate the description of a three-component one-temperature plasma the equations of motion for each component, arrived at as a result of a series of simplifying assumptions, are replaced by an equation of motion for the mixture and two diffusion equations (Ohm's laws). One Ohm's law (the relation of current density to electric field) was investigated for the case of a partially ionized gas in [6, 7], where it was assumed that the medium was inviscid and had one temperature, and, moreover, that anisotropy was not allowed for in writing down the frictional forces between components.

The present paper proposes a simplification of the equations given in [8–10] for a two-temperature plasma containing electrons, singlyionized ions, and neutral atoms. The effect of the viscosity of the components and of thermal forces is allowed for. Particle collisions are taken to be elastic, and it is assumed that T_e ≥ T, where T = =t_i=T_a. In the investigation we pass from the equations of motion for each component to an equation of motion for the mixture and two diffusion equations (Ohm's laws). An investigation is made of how the possible forms of diffusion equations depend on the concentration of the medium, the parameters describing the anisotropy of the transport coefficients, etc., while the necessity of allowing for viscous terms and thermal forces is also investigated. Dimensionless criteria are given for which Ohm's laws simplify considerably (viscous terms, pressure gradients, etc. may be discarded).