Section: New Results

Simulations of highly oscillatory Vlasov-Poisson system

Participants : E. Frénod, S. Hirstoaga, M. Lutz, E. Sonnendrücker.

In paper [45] a Lie Transform method is applied for a charged beam under the action of a radial external electric field. The aim of the Lie transform method that is used here is to construct a change of variable which transforms the 2D kinetic problem into a 1D problem. This reduces the dimensionality of the problem and make it easier to solve numerically.

In paper [41] , in the framework of a Particle-In-Cell scheme for some 1D Vlasov-Poisson system depending on a small parameter, we propose a time-stepping method which is numerically uniformly accurate when the parameter goes to zero. Based on an exponential time differencing approach, the scheme is able to use large time steps with respect to the typical size of the fast oscillations of the solution.