Asymptotically stable particle-in-cell methods for the Vlasov-Poisson system with a strong external magnetic field

Francis Filbet (1) , Luis Miguel Miguel Rodrigues (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 IRMAR - Institut de Recherche Mathématique de Rennes

This paper deals with the numerical resolution of the Vlasov-Poissonsystem with a strong external magnetic field by Particle-In-Cell(PIC) methods. In this regime, classical PIC methods are subject tostability constraints on the time and space steps related to the smallLarmor radius and plasma frequency. Here, we propose anasymptotic-preserving PIC scheme which is not subjected to theselimitations. Our approach is based on first and higher order semi-implicit numericalschemes already validated on dissipative systems. Additionally, when the magnitude of the external magneticfield becomes large, this method provides a consistent PICdiscretization of the guiding-center equation, that is, incompressibleEuler equation in vorticity form. We propose several numerical experiments which provide a solid validation of the method and its underlying concepts.

Mots clés: Guiding-centre model; High order time discretization; Vlasov-Poisson system; Particle methods

Domaines: Analyse numérique [math.NA]

Francis Filbet, Luis Miguel Miguel Rodrigues. Asymptotically stable particle-in-cell methods for the Vlasov-Poisson system with a strong external magnetic field. SIAM Journal on Numerical Analysis, 2016, 54 (2), pp.1120-1146. ⟨10.1137/15M104952X⟩. ⟨hal-01232404⟩