Development of Collision Models for Applications in Plasmas

Plasma applications require modeling techniques that elucidate the relationship between microscopic and macroscopic processes. One example of this is how particle-based and Monte Carlo (MC) simulation codes require an input model describing angular scattering of electrons following elastic scattering events. High energy electron elastic scattering is relatively trivial to accurately describe in plasma simulations. However, there is not a consensus within the plasma modeling community on how to best model the angular scattering trends in lower energy collisions that produce near isotropic or backwards peaked differential cross sections. In this study, we propose a systematic method to approximate the non-trivial angular scattering behavior with a formula that can be readily implemented in particle-in-cell and/or MC plasma simulation codes. The initial goal was to find one functional for all atomic and molecular species. Here we present methods that did not work well, as well as a Legendre polynomial approach that seems promising. We take atomic nitrogen cross sections that were calculated using a B-spline atomic R-matrix (BSR) code and fit them to a Legendre polynomial series to find an analytic form. We then do the same fitting procedure for experimentally measured molecular cross sections for N₂ and O₂.