A Boltzmann Model for Trapped Particles in a Surface Potential

In this article, we propose a model describing the transport of trapped particles in a surface potential. The potential confines particles close to the surface, increasing the number of surface collisions. First, we consider the case of noncharged particles. From a kinetic description, we rigorously derive a two dimensional Boltzmann equation. In the case of charged particles we introduce the coupling with the Poisson equation. We perform a formal asymptotic analysis which leads to a two dimensional Boltzmann equation coupled with a three dimensional Poisson equation. We illustrate the charged particle model with some numerical simulations of a gas discharge on a satellite solar array. We use a particle in cell (P.I.C.) scheme that is a particle discretization for the Boltzmann equation and a Fourier approximation for the Poisson equation.