  The subject matter of the paper concerns the Vlasov-Poisson-Fokker-Planck
(VPFP) equations in the context of magnetic confinement. We study the long-time
behavior of the VPFP system with an intense external magnetic field, when
neglecting the curvature of the magnetic lines. When the intensity of the
magnetic field tends to infinity, the long-time behavior of the particle
concentration is described by a first-order nonlinear hyperbolic equation of
the Euler type for fluid mechanics. More exactly, when the magnetic field is
uniform, we find the vorticity formulation of the incompressible Euler
equations in two-dimensional space. Our proofs rely on the modulated energy
method.
