Density Estimation Techniques for Multiscale Coupling of Kinetic Models of the Plasma Material Interface

We analyze two classes of Density-Estimation techniques which can be used to consistently couple kinetic models of the plasma-material interface, intended as the region of plasma immediately interacting with the first surface layers of a material wall. In particular, we handle the general problem of interfacing a continuum multi-species Vlasov-Poisson-BGK plasma model to discrete surface erosion models. The continuum model solves for the energy-angle distributions of the particles striking the surface, which are then driving surface response. A modification to the classical Binary-Collision Approximation method is utilized as a prototype discrete model of the surface, to provide boundary conditions and impurity distributions representative of the material behavior during plasma irradiation. The numerical tests revealed superior convergence properties of Kernel Density Estimation methods over Gaussian Mixture Models, with Epanechnikov-KDEs being up to two orders of magnitude faster than Gaussian-KDEs. The methodology presented allows a self-consistent treatment of the dynamic response of the surface including effects such as sputtering, back-scattering, and ion implantation.