Kinetic Theory of Plasma Sheaths Surrounding Electron-Emitting Surfaces

TLDR

The paper develops a one‑dimensional kinetic theory of sheaths around planar electron‑emitting surfaces that incorporates plasma electron loss and emitted electron temperature. The theory was validated with particle‑in‑cell simulations and experimental measurements of a thermionic cathode sheath in an rf plasma afterglow. When the plasma and emitted electron temperatures are comparable, the sheath potential drops to zero, a behavior confirmed by both theory and experiment.

Abstract

A one-dimensional kinetic theory of sheaths surrounding planar, electron-emitting surfaces is presented which accounts for plasma electrons lost to the surface and the temperature of the emitted electrons. It is shown that ratio of plasma electron temperature to emitted electron temperature significantly affects the sheath potential when the plasma electron temperature is within an order of magnitude of the emitted electron temperature. The sheath potential goes to zero as the plasma electron temperature equals the emitted electron temperature, which can occur in the afterglow of an rf plasma and some low-temperature plasma sources. These results were validated by particle in cell simulations. The theory was tested by making measurements of the sheath surrounding a thermionically emitting cathode in the afterglow of an rf plasma. The measured sheath potential shrunk to zero as the plasma electron temperature cooled to the emitted electron temperature, as predicted by the theory.