# American Institute of Mathematical Sciences

June  2009, 2(2): 251-274. doi: 10.3934/krm.2009.2.251

## Two-scale semi-Lagrangian simulation of a charged particle beam in a periodic focusing channel

 1 Institut de Recherche Mathématique Avancée (IRMA) - Université de Strasbourg, 7, rue René Descartes, 67084 Strasbourg, France

Received  July 2008 Revised  January 2009 Published  May 2009

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 Poisson's equation. Finally, we present some numerical results which have been obtained by the new method, and we verify its efficiency through long time simulations.
Citation: Alexandre Mouton. Two-scale semi-Lagrangian simulation of a charged particle beam in a periodic focusing channel. Kinetic & Related Models, 2009, 2 (2) : 251-274. doi: 10.3934/krm.2009.2.251
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