Abstract
The aim of this work is to build an accurate numerical method for the simulation of the long time evolution of the Vlasov solution $\feps$ with an electric field $\Eeps = E_0+ \eps E_1$ for small $\eps$. To this purpose, we use the Two-Scale Convergence theory to determine a first order approximation $F+\eps F_1$ of $\feps$\!, then particle approximations to build an algorithm to obtain a numerical approximation of $F+\eps F_1$.
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