The Vlasov-Poisson system with strong magnetic field

This paper establishes various asymptotic limits of the Vlasov-Poisson equation with strong external magnetic field, some of which were announced in [14]. The so-called "guiding center approximation" is proved in the 2D case with a constant magnetic field orthogonal to the plane of motion, in various situations (noncollisional or weakly collisional). The 3D case is studied on the time scale of the motion along the lines of the magnetic field, much shorter than that of the guiding center motion. We discuss in particular the effect of nonconstant external magnetic fields.