This talk concerns the numerical resolution of the Vlasov-Poisson system with a strong external magnetic field by Particle-In-Cell (PIC) methods. In this regime, classical PIC methods are subject to stability constraints on the time and space steps related to the small Larmor radius and plasma frequency. Here, we propose an asymptotic-preserving PIC scheme which is not subjected to these limitations. Our approach is based on first and higher order semi-implicit numerical schemes already validated on dissipative systems. Additionally, when the magnitude of the external magnetic field becomes large, this method provides a consistent PIC discretization of the guiding-center equation, that is, incompressible Euler equation in vorticity form. We propose several numerical experiments which provide a solid validation of the method and its underlying concepts.

Professor Francis Filbet, is a full professor in applied mathematics at Université Paul Sabatier, Toulouse III, France. He obtained his Phd degree in applied mathematics in Université Henri Poincaré, Nancy I, in 2001, and obtained his Habilitation degree in Université Paul Sabatier, Toulouse III in 2005.  He used to be a propessor of applied mathematics at Université Claude Bernard, Lyon I from 2006 to 2015. His research interests are numerical algorithms, scientific computing, partial differential equations, kinetic theory. Their applications are in rarefied gas dynamics, plasma physics, collective behavior in biology. He has published more than 60 refereed papers and is junior member of of Institut Universitaire de France.