Approximate, semi-implicit calculation of 3D electrostatic potential in a self-consistent plasma simulation

Summary form only given. Numerical modeling of low pressure plasma reactors is subject to numerous time step constraints, and among the most restrictive of these is the dielectric relaxation time. In recent years, semi-implicit flux-correction techniques have allowed plasma modelers to loosen the dielectric relaxation time step restriction. However, since these simulations do solve a form of Poisson´s equation, they still have a restriction on time step based on a modified, albeit less restrictive, dielectric relaxation time. For some parameter spaces this is acceptable, but for very large scale simulations (for example in three dimensions) and for simulations of systems having long time scales, obtaining a longer time step is crucial. We present a method for obtaining an approximate electrostatic potential which has no dielectric relaxation time restriction. Implementation is of comparable difficulty to that of a conventional Poisson´s equation, and is no more computationally intensive.