Long Time Behaviour of an Exponential Integrator for a Vlasov-Poisson System with Strong Magnetic Field (Communications in Computational Physics, 2018)
With the aim of solving in a four dimensional phase space a multi-scaleVlasov-Poisson system, we propose in a Particle-In-Cell framework a robust time-steppingmethod that works uniformly when the small parameter vanishes. As anexponential integrator, the scheme is able to use large time steps with respect to thetypical size of the solution's fast oscillations. In addition, we show numerically thatthe method has accurate long time behaviour and that it is asymptotic preserving withrespect to the limiting Guiding Center system.