Fast, Kinetically self-consistent simulation of RF modulated plasma boundary sheaths

A mathematical model is presented which enables the efficent, kinetically self-consistent simulation of RF modulated plasma boundary sheaths in all technically relevant discharge regimes. The model consists of a set of kinetic equations for the ions, Boltzmann's relation for the electrons and Poisson's equation for the electrical field. Boundary conditions specify the ion flux at a point deep in the bulk and a periodically modulated sheath voltage or sheath charge. The equations are solved in a statistical sense. However, it is not the well-known particle-in-cell (PIC) scheme that is employed, but an alternative iterative algorithm termed ensemble-in-spacetime (EST). Three modules are called in a sequence: a Monte Carlo module, a harmonic analysis module, and a field module. The iteration is started with the potential values of a self-consistent fluid model and terminates when the updates become sufficiently small, i.e. when self-consistency is achieved. A drastic reduction of the computational effort compared with PIC calculations is achieved. As a first application of the new model, the influence of ion inertia on the dynamics of a collisionless sheath is studied and a comparison of the simulated ion energy distribution with published analytical solutions is performed.