Section: New Results

Numerical scheme for sheath equilibria

Participants : Mehdi Badsi, Michel Mehrenberger, Laurent Navoret.

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-Ampère model proposed in [19]. 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 also requires a specific treatment. Moreover, for preventing instabilities from developing in large time, the proposed method guaranties that the discrete Gauss equation is satisfied in time.