Long time simulation of a beam in a periodic focusing channel via a two-scale PIC-method

Emmanuel Frénod (1, 2) , Francesco Salvarani (3) , Eric Sonnendrücker (4, 5)

1 LMAM - Laboratoire de Mathématiques et Applications des Mathématiques, EA 3885
2 LEMEL - Laboratoire d'Etude et Modélisation des Environnements littoraux
3 Dipartimento di matematica F. Casorati
4 CALVI - Scientific computation and visualization
5 IRMA - Institut de Recherche Mathématique Avancée

We study the two-scale asymptotics for a charged beam under the action of a rapidly oscillating external electric field. After proving the convergence to the correct asymptotic state, we develop a numerical method for solving the limit model involving two time scales and validate its efficiency for the simulation of long time beam evolution.

Keywords: Vlasov-Poisson system; kinetic equations; homogenization; two-scale convergence; two-scale PIC method

Domains: Numerical Analysis [math.NA]

Emmanuel Frénod, Francesco Salvarani, Eric Sonnendrücker. Long time simulation of a beam in a periodic focusing channel via a two-scale PIC-method. Mathematical Models and Methods in Applied Sciences, 2009, 19 (2), pp.175-197. ⟨10.1142/S0218202509003395⟩. ⟨hal-00180700⟩