Electrostatic Sheath in a Weakly Ionized Gas

Abstract

The behavior of a thin electrostatic sheath adjacent to a body immersed in a flowing weakly ionized gas is analyzed on the basis of kinetic theory using a moment method. The study is confined to the regime of mean free path and Debye length small compared to body size but for arbitrary ratios between them. When the mean free path is the smallest parameter, the solution reduces to the continuum solution with a thin ``Knudsen layer'' at the body. In the opposite limit of smallest Debye length, a departure in the potential drop from that in the continuum regime occurs within the quasi-neutral solution. The point at which this solution terminates can be interpreted as a sonic point for the attracted particles. There is then a thin transitional layer, followed by a free-fall sheath. The case of negative potential is analyzed in detail, and the current-voltage characteristics are obtained in an explicit form.