Asymptotic behavior for the Vlasov-Poisson equations with strong external curved magnetic field. Part I : well prepared initial conditions

The subject matter of this paper concerns the magnetic confinement. We focus on the asymptotic behavior of the three dimensional Vlasov-Poisson system with strong external magnetic field. We investigate second order approximations, when taking into account the curvature of the magnetic lines. The study relies on multi-scale analysis and allows us to determine a regular reformulation for the Vlasov-Poisson equations with well prepared initial conditions, when the magnetic field becomes large.