Dynamic evolutions of Bohm sheaths and pre-sheaths

Abstract

The time evolutions of the Bohm sheath and the related pre-sheath are analyzed as an initial value problem. The standard classical fluid model of a collisionless plasma is used with cold ions and Boltzmann distributed electrons. Numerical solutions of the basic equations show that a stationary plasma sheath itself is established within a few ion plasma periods. It is demonstrated analytically that for infinitely extended homogeneous plasmas in one spatial dimension, the only possible pre-sheath solution is dynamic, giving a steady expansion: no stationary solution exists for this one-dimensional case. The potential and density drops along the dynamic pre-sheath differ notably from the values found for stationary models suggested in the literature. Collisions give only formal changes to the collisionless results, and their substance remains the same in one spatial dimension. Cylindrical and spherical geometries, on the other hand, allow for physically acceptable, fully nonlinear, stationary solutions with analytical results given. These are supported by numerical solutions.