With the aim of solving in a four dimensional phase space a multi-scale VlasovPoisson system, we propose in a Particle-In-Cell framework a robust time-stepping method that works uniformly when the small parameter vanishes. As an exponential integrator, the scheme is able to use large time steps with respect to the typical size of the solution's fast oscillations. In addition, we show numerically that the method has accurate long time behaviour and that it is asymptotic preserving with respect to the limiting Guiding Center system.

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Abstract. We study the dynamics of charged particles under the influence of a strong magnetic field by numerically solving the Vlasov-Poisson and guiding center models. By using appropriate data structures, we implement an efficient (from the memory access point of view) particle-in-cell method which enables simulations with a large number of particles. We present numerical results for classical one-dimensional Landau damping and two-dimensional Kelvin-Helmholtz test cases. The implementation also relies on a standard hybrid MPI/OpenMP parallelization. Code performance is assessed by the observed speedup and attained memory bandwidth.