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

TL;DR

This paper compares density estimation techniques for coupling kinetic plasma models with surface erosion models, demonstrating that Kernel Density Estimation methods, especially Epanechnikov-KDEs, offer superior convergence and speed, enabling self-consistent plasma-material interface simulations.

Contribution

It introduces and evaluates density estimation methods for coupling plasma and surface models, highlighting the advantages of KDEs over Gaussian Mixture Models in this context.

Findings

KDEs outperform GMMs in convergence speed.

Epanechnikov-KDEs are up to 100 times faster than Gaussian-KDEs.

The methodology enables self-consistent plasma-surface interaction modeling.

Abstract

In this work we analyze two classes of Density-Estimation techniques which can be used to consistently couple different 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 the surface response. A modification to the classical Binary-Collision Approximation (BCA) method is here 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 the 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 here presented allows a self-consistent treatment of the plasma-material interface in magnetic fusion devices, including both the near-surface plasma (plasma sheath and presheath) in magnetized conditions, and surface effects such as sputtering, back-scattering, and ion implantation. The same coupling techniques can also be utilized for other discrete material models such as Molecular Dynamics.