Vlasov simulations of beams with a moving grid

Eric Sonnendrücker (1) , Francis Filbet (1) , Alex Friedman , Edouard Oudet (2) , Jean-Luc Vay

1 IRMA - Institut de Recherche Mathématique Avancée
2 LAMA - Laboratoire de Mathématiques

Numerical simulation of intense particle beams can be performed by solvingthe Vlasov equation on a grid of phase-space using a semi-Lagrangian method. This is fairly efficient in the case of a uniform focusing field. However in configurations using a periodic focusing field or alternating-gradient focusing a lot of computing effort using a uniform grid is wasted on empty space as the motion in phase space is important.This paper introduces the concept of a moving grid whichis mapped at each time step from a logical uniform grid to thebeam, so that it contains the whole beam without needing too manypoints with vanishing values of the distribution function.In order to implement this new method, we introducea new time stepping algorithm which does not rely on the time splittingprocedure traditionally used in Vlasov solvers.

Mots clés: Vlasov; semi-Lagrangian; "Vlasov; moving grid; semi-Lagrangian"

Domaines: Analyse numérique [math.NA]

Eric Sonnendrücker, Francis Filbet, Alex Friedman, Edouard Oudet, Jean-Luc Vay. Vlasov simulations of beams with a moving grid. 2003. ⟨hal-00129695⟩