Verification of 2 D × 2 D and Two-Species Vlasov-Poisson Solvers

In [2], 1 D ×1 D two-species Vlasov-Poisson simulations are performed by the semi-Lagrangian method. Thanks to a classical first order dispersion analysis, we are able to check the validity of their simulations; the extension to second order is performed and shown to be relevant for explaining further details. In order to validate multi-dimensional effects, we propose a 2 D × 2 D single species test problem that has true 2 D effects coming from the sole second order dispersion analysis. Finally, we perform, in the same code, full 2 D × 2 D non linear two-species simulations with mass ratio 0:01, and consider the mixing of semi-Lagrangian and Particle-in-Cell methods.