On the vlasov–maxwell system with a strong magnetic field^*

This paper establishes the long time asymptotic limit of the 2d×3d Vlasov–Maxwell system with a strong external magnetic field. Hence, a guiding-center approximation is obtained in the two-dimensional case with a self-consistent electromagnetic field given by Poisson type equations. Then, we perform several numerical experiments with high order approximation of the asymptotic model, which provide a solid validation of the method and illustrate the effect of the self-consistent magnetic field on the current density.