Numerical stability of a plasma sheath**********

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 [3]. The main question addressed in this work is to know how accurately classical time-dependent Vlasov-Ampère numerical schemes preserve in long time these non-homogeneous stationary solutions with emission/absorption boundary conditions. In the context of high-order semi-Lagrangian methods, due to their large stencil, interpolation near the boundary of the domain requires also a specific treatment