THE EFFECTIVE VLASOV-POISSON SYSTEM FOR THE FINITE LARMOR RADIUS REGIME

The subject matter of this paper concerns the finite Larmor radius regime of the Vlasov-Poisson system for strongly magnetized plasmas. We appeal to gyro-average methods and determine the explicit expressions for the velocity and acceleration fields in the limit Vlasov equation. We investigate the Hamiltonian structure of the limit model (trajectories), analyze its properties (conservations of the mass, kinetic energy, electric energy), and justify rigorously the asymptotic behavior, following the formal arguments developed in [M. Bostan, A. Finot, and M. Hauray, C. R. Math. Acad. Sci. Paris Ser. I, 354 (2016), pp. 869-964].