| Contents |
| We aim at studying the dynamics of long and thin beams of charged particles focused by external electric fields. Under the axisymmetric assumption on the beam, we use the paraxial approximation of the full Vlasov-Maxwell system.
We therefore have to solve some small parameter dependent Vlasov-Poisson system in a two dimensional phase space.
In a Particle-In-Cell framework, we propose a time-stepping method which works uniformly when the parameter vanishes. 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. Both short and long time simulations will be presented. |
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