The Vlasov-Poisson system with strong magnetic field

This paper establishes various asymptotic limits of the Vlasov-Poisson equa tion 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 variou s situations (noncollisional or weakly collisional). The 3D case is studied on the time scale of the motion along the lines of the magnetic field, muc h shorter than that of the guiding center motion. We discuss in particular the effect of nonconstant external magnetic fields. (C) Elsevier, Paris.