Eulerian variational formulations and momentum balance equations for kinetic plasma systems

Eulerian variational formulations are presented to derive governing equations for kinetic plasma systems. As examples, the Vlasov-Poisson-Amp`ere system and the drift kinetic systems are investigated. For the drift kinetic system, the additional case is also considered in which the quasineutrality condition and Amp`ere’s law are included as supplementary governing equations to describe the self-consistent fields. For all cases treated here, general spatial coordinates are used to represent the action integrals and the derived governing equations which take the forms being invariant under an arbitrary transformation of spatial coordinates. Furthermore, the invariance of the action integral under the spatial coordinate transformation is made use of to derive the momentum conservation laws and/or the momentum balance in which the functional derivatives of the Lagrangians with respect to the metric tensor components yield the proper symmetric pressure tensors more directly than conventional techniques using translational and rotational symmetries or taking the moments of the kinetic equations.