A limiting factor in long duration space missions is the electrode lifetime for devices such as Hall thrusters. In order to improve thruster performance, an understanding of plasma-material interactions is critical. Plasma sheaths form at the interface of a plasma and a surface and high energy particles may increase the rate of surface erosion. The focus of this paper is on numerical studies of sheaths relevant to Hall thrusters. A novel version of Discontinuous Galerkin (DG) scheme allows for a continuum-kinetic solution of the Vlasov-Poisson system of equations. This method conserves energy (in the continuous-time limit) and provides noise-free simulations. The dynamic electric field is obtained using the Poisson equation and static electric and magnetic fields for the Hall thruster configuration are then naturally added to the Vlasov equation solver. The code includes an impact ionization source and inter-species collisions. Surface effects are neglected. Benchmarks of the solver are presented for the Weibel instability that occurs when magnetic field in counter-streaming populations of electrons is perturbed. Initial results of plasma sheaths using the continuum-kinetic and multi-fluid models are presented.
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