Abstract
We study here the finite Larmor radius regime for the Vlasov–Poisson equations with strong external magnetic field. The derivation of the limit model follows by formal expansion in power series with respect to a small parameter. If we replace the particle distribution by the center distribution of the Larmor circles the limit of these densities satisfies a transport equation, whose velocity is given by the gyro-average of the electric field. We justify rigorously the convergence towards the above model and we investigate the well-posedness of it.