The Vlasov-Poisson system with strong magnetic field in quasineutral regime

Consider the motion of a gas of electrons with a background of ions, subject to the self-consistent electric field and to a constant external magnetic field. As the Debye length and the Larmor radius vanish at the same rate, the asymptotic current density is governed by the 2D1/2 incompressible Euler equation. Establishing limit requires to overcome various difficulties: compactness with respect to the space variable, control of large velocities, oscillations in the time variable. Yet, for particular initial data, the simultaneous gyrokinetic and quasineutral approximation is completely justified.