Effect of the polarization drift in a strongly magnetized plasma

We consider a strongly magnetized plasma described by a Vlasov-Poisson system with a large external magnetic field. The finite Larmor radius scaling allows to describe its behaviour at very fine scales. We give a new interpretation of the asymptotic equations obtained by Frénod and Sonnendrücker [SIAM J. Math. Anal. 32 (2001) 1227-1247] when the intensity of the magnetic field goes to infinity. We introduce the so-called polarization drift and show that its contribution is not negligible in the limit, contrary to what is usually said. This is due to the non linear coupling between the Vlasov and Poisson equations.