Modeling of dynamic bipolar plasma sheaths

Abstract

The behavior of a one-dimensional plasma sheath is described in regimes where the sheath is not in equilibrium because it carries current densities that are either time dependent, or larger than the bipolar Child–Langmuir level determined from the injected ion flux. Earlier models of dynamic bipolar sheaths assumed that ions and electrons evolve in a series of quasiequilibria. In addition, sheath growth was described by the equation Zen0ẋs=‖ ji‖−Zen0u0, where ẋs is the velocity of the sheath edge, ji is the ion current density, n0u0 is the injected ion flux density, and Ze is the ion charge. In this paper, a generalization of the bipolar electron-to-ion current density ratio formula is derived to study regimes where ions are not in equilibrium. A generalization of the above sheath growth equation is also developed, which is consistent with the ion continuity equation and which reveals new physics of sheath behavior associated with the emitted electrons and their evolution. Based on these findings, two new models of dynamic bipolar sheaths are developed. Larger sheath sizes and potentials than those of earlier models are found. In certain regimes, explosive sheath growth is predicted.