Geometric Particle-in-Cell Simulations of the Vlasov--Maxwell System in Curvilinear Coordinates

Abstract

Numerical schemes that preserve the structure of the kinetic equations can provide stable simulation results over a long time. An electromagnetic particle-in-cell solver for the Vlasov--Maxwell equations that preserves at the discrete level the noncanonical Hamiltonian structure of the Vlasov--Maxwell equations has been presented in [Kraus et al., J. Plasma Phys., 83 (2017)]. While the original formulation has been obtained for Cartesian coordinates, we extend the formulation to curvilinear coordinates in this paper. For the discretization in time, we discuss several (semi-)implicit methods either based on a Hamiltonian splitting or a discrete gradient method combined with an antisymmetric splitting of the Poisson matrix and discuss their conservation properties and computational efficiency.