Saturation Currents to Langmuir Probes in a Collision-Dominated Plasma with Uniform Magnetic Field

Abstract

Electrostatic probe theory for a slightly ionized, collision-dominated plasma is extended, in the sense of problem formulation, to allow for the presence of a uniform magnetic field. Provided that the Debye length is very much smaller than a probe dimension, ion and electron currents to the probe saturate, respectively, at large negative and positive probe bias with respect to the plasma potential. It is shown that it is not necessary to go through a lengthy asymptotic analysis to compute the saturation currents. Ion and electron saturation currents to ellipsoids of revolution inclined at an arbitrary angle to the magnetic field are given in compact form in terms of common elliptic functions.