  This paper is devoted to numerical simulation of a charged particle beam
submitted to a strong oscillating electric field. For that, we consider a
two-scale numerical approach as follows: we first recall the two-scale model
which is obtained by using two-scale convergence techniques; then, we
numerically solve this limit model by using a backward semi-lagrangian method
and we propose a new mesh of the phase space which allows us to simplify the
solution of the Poisson's equation. Finally, we present some numerical results
which have been obtained by the new method, and we validate its efficiency
through long time simulations.
