Unified one-dimensional model of bounded plasma with nonzero ion temperature in a broad pressure range

Abstract

A one-dimensional model for steady state plasmas bounded either between large parallel walls, or by a cylinder or a sphere, valid in a wide range of gas pressures, is considered. The model includes nonzero ion temperature, inertial terms in the ion momentum equations, and allows one to calculate the plasma electron temperature and ion current density reaching the wall, as well as the spatial distributions of the ion fluid velocity, plasma density, and plasma potential in the plasma bulk. In addition, the effect of electron inertia is analyzed. The model includes as particular cases several earlier models that were based on a similar set of differential equations, but that are restricted to a specific pressure regime (low, intermediate, or high). Analytical solution is found in planar geometry, and numerical solution is given in cylindrical and spherical geometry. The results obtained are compared with those of earlier models and the differences are analyzed.