Evaluation of models for numerical simulation of the non-neutral region of sheath plasma

Abstract

Four different electron models are used to simulate the nonequilibrium plasma flow around a representative cylindrical Faraday probe geometry. Each model is implemented in a two-dimensional axisymmetric hybrid electron fluid and particle in cell method. The geometric shadowing model is derived from kinetic theory on the basis that physical obstruction of part of the velocity distribution leads to many of the expected sheath features. The Boltzmann electron fluid model relates the electron density to the plasma potential through the Boltzmann relation. The non-neutral detailed electron fluid model is derived from the electron conservation equations under the assumption of neutrality, and then modified to include non-neutral effects through the electrostatic Poisson equation. The Poisson-consistent detailed electron fluid model is also derived from the conservation equations and the electrostatic Poisson equation, but uses an alternative method that is inherently non-neutral from the outset. Simulations using the geometric shadowing and non-neutral detailed models do not yield satisfactory sheath structures, indicating that these models are not appropriate for sheath simulations. Simulations using the Boltzmann and Poisson-consistent models produce sheath structures that are in excellent agreement with the planar Bohm sheath solution near the centerline of the probe. The computational time requirement for the Poisson-consistent model is much higher than for the Boltzmann model and becomes prohibitive for larger domains.