Asymptotic theory of spherical electrostatic probes in large Debye length plasmas containing negative ions

Abstract

The problem of a spherical electrostatic probe in negative ion containing oxygen plasmas is treated by the matching asymptotic expansions technique [A. H. Nayfeh, Perturbation Methods (Wiley, New York, 1973)]. Assuming that the energy relaxation length is much smaller than the local characteristic length, explicit results are obtained in the asymptotic limits, (rp/rD)2≪1,(rp/rS)2≪1, where rD is the Debye radius, rS is the recombination length and rp is the probe radius. The perturbation region divides naturally into a thin space charged sheath, a transitional sheath, and a quasineutral chemically equilibrium plasma. The potential and charged particle density distributions are obtained. The calculated probe characteristic is presented in an analytical form.