The solution of the plasma equation in plane parallel geometry with a Maxwellian source

TLDR

The plasma equation for a warm collisionless plasma with a Maxwellian source is solved in plane parallel geometry. The generalized Bohm criterion identifies the plasma–sheath boundary. The kinetic treatment predicts an infinite electric field at the sheath edge, unlike Emmert et al.’s finite‑field model, and yields a higher presheath potential that aligns better with fluid results. Citation: Phys.

Abstract

The plasma equation for a warm collisionless plasma with a Maxwellian particle source is solved in plane parallel geometry. The generalized Bohm criterion is used to identify the plasma–sheath boundary. This kinetic treatment, in common with fluid and cold-ion kinetic models, results in an infinite electric field at the sheath edge. This is in sharp contrast to results from a previous warm-ion kinetic model, by Emmert et al. [Phys. Fluids 23, 803 (1980)], which gave a finite electric field at the sheath edge. Also, the presheath potential given by the present model is greater than that given by Emmert and is in better agreement with fluid results.