An Asymptotically Stable Semi-Lagrangian scheme in the Quasi-neutral Limit

Abstract

This paper deals with the numerical simulations of the Vlasov-Poisson equation using a phase space grid in the quasi-neutral regime. In this limit, explicit numerical schemes suffer from numerical constraints related to the small Debye length and large plasma frequency. Here, we propose a semi-Lagrangian scheme for the Vlasov-Poisson model in the quasi-neutral limit. The main ingredient relies on a reformulation of the Poisson equation derived in (Crispel et al. in C. R. Acad. Sci. Paris, Ser. I 341:341–346, 2005) which enables asymptotically stable simulations. This scheme has a comparable numerical cost per time step to that of an explicit scheme. Moreover, it is not constrained by a restriction on the size of the time and length step when the Debye length and plasma period go to zero. A stability analysis and numerical simulations confirm this statement.