The low-frequency limit of Maxwell equations is considered in the Maxwell-Vlasov system. This limit produces a neutral Vlasov system that captures essential features of plasma dynamics, while neglecting radiation effects. Euler-Poincar\'e reduction theory is used to show that the neutral Vlasov kinetic theory possesses a variational formulation in both Lagrangian and Eulerian coordinates. By construction, the model recovers all collisionless neutral models employed in plasma simulations. Then, comparisons between the neutral Vlasov system and hybrid kinetic-fluid models are presented in the linear regime.
Physics of Plasmas
Multiscale Dynamics

Tronci, C., & Camporeale, E. (2015). Neutral Vlasov kinetic theory of magnetized plasmas. Physics of Plasmas, 22(020704 ). doi:10.1063/1.4907665