Long Time Behavior of the Two-Dimensional Vlasov Equation with a Strong External Magnetic Field
Résumé
When charged particles are submitted to a large external magnetic field, their movement in first approximation occurs along the magnetic field lines and obeys a one dimensional Vlasov equation along these field lines. However, when observing the particles on a sufficiently long time time scale, a drift phenomenon perpendicular to the magnetic field lines superposes to this first movement. In this report, we present a rigorous asymptotic analysis of the two-dimensional Vlasov equation when the magnetic field tends to infinity, the observation time scale growing accordingly. Techniques based on the two-scale convergence and the introduction of a second problem enable us to find an equation verified by the weak limit of the distribution function.