Modeling Electrode Plasma Effects in Particle-in-Cell Simulation of High Power Devices

A new method for including electrode plasma effects in particle-in-cell simulation of high power devices is presented. It is not possible to resolve the plasma Debye length, $\lambda _{D} \quad \sim $ 1 $\mu $m, but using an explicit, second-order, energy-conserving particle pusher avoids numerical heating at large $\Delta $x/$\lambda _{D} \quad >>$ 1. Non-physical plasma oscillations are mitigated with Coulomb collisions and a damped particle pusher. A series of 1-D simulations show how plasma expansion varies with cell size. This reveals another important scale length,$\lambda _E =T/(eE)$, where E is the normal electric field in the first vacuum cell in front of the plasma, and T is the plasma temperature. For $\Delta $x/$\lambda _{E}$ $< \quad \sim $1, smooth, physical plasma expansion is observed. However, if $\Delta $x/$\lambda _{E} \quad >>$ 1, the plasma ``expands'' in abrupt steps, driven by a numerical instability. For parameters of interest, $\lambda _{E} \quad <<$ 100 $\mu $m. It is not feasible to use cell sizes small enough to avoid this instability in large 3-D simulations.