Numerical stability of plasma sheath
For computational plasma physicists, this work addresses a numerical stability issue in simulating plasma-wall interactions, but the results are incremental as they extend existing methods to a specific problem.
The paper investigates whether classical numerical schemes can preserve stationary plasma sheath solutions in a Vlasov-Ampère model, finding that they cannot without specific boundary treatments, and proposes a high-order semi-Lagrangian method with adapted boundary interpolation.
We are interested in developing a numerical method for capturing stationary sheaths, that a plasma forms in contact with a metallic wall. This work is based on a bi-species (ion/electron) Vlasov-Amp{è}re model proposed in [3]. The main question addressed in this work is to know if classical numerical schemes can preserve stationary solutions with boundary conditions, since these solutions are not a priori conserved at the discrete level. In the context of high-order semi-Lagrangian method, due to their large stencil, interpolation near the boundary of the domain requires also a specific treatment.