  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.
