A geometric Particle-In-Cell discretization of the drift-kinetic and fully kinetic Vlasov-Maxwell equations

Abstract

In this paper, we extend the geometric Particle in Cell framework on dual grids to a gauge-free drift-kinetic Vlasov--Maxwell model and its coupling with the fully kinetic model. We derive a discrete action principle on dual grids for our drift-kinetic model, such that the dynamical system involves only the electric and magnetic fields and not the potentials as most drift-kinetic and gyrokinetic models do. This yields a macroscopic Maxwell equation including polarization and magnetization terms that can be coupled straightforwardly with a fully kinetic model.