New Variational Formulation of Maxwell-Vlasov and Guiding Center Theories Local Charge and Energy Conservation Laws

Abstract

A new variational formulation of Maxwell-Vlasov and related theories is given in terms of a common Lagrangian density for both the "Vlasov particles" and the Maxwell fields. This formulation is used to derive in a consistent way, on the one hand, correct charge and current densities and, on the other, corresponding energy and energy flux densities. All of these densities generally show in addition to particle like contributions electric polarization and magnetization terms. By some limiting procedure collisionless guiding center theories with polarization drifts included are also treated. In this way local energy conservation laws are formulated for such theories, which has not been possible up to now