Kinetic Theory of a Spherical Electrostatic Probe in a Stationary Plasma

Abstract

The spherical electrostatic probe in a weakly-ionized gas is analyzed on the basis of kinetic theory using a Krook-type model for the collision integral. The charged particle motions are analyzed in energy-angular momentum phase space, and formal integral solutions for the distribution functions are obtained. Moment equations based on the Less method are derived, taking into account curvature of the particle paths, and sample solutions of these equations are presented. The results obtained agree well with the numerical analysis of Laframboise, in the collisionless limit. It is found that the effect of charged-neutral particle collisions is to extend the probe sheath farther into the plasma and reduce the electron and ion currents, as well as the departures from neutrality within the sheath. Fair agreement is obtained with a moment method based on straight-line trajectories for the charged particles. The continuum limit is not included in the computations.