Hybrid kinetic-MHD simulations in general geometry Original Research Article

We present a hybrid kinetic-MHD model consisting of 3 species, the bulk fluid ions and electrons, and a kinetic minority hot particle species. The 3 species equations are derived from moments of the Vlasov Equation and then reduced using the usual hot particle assumption of nh⪡n0, βh∼β0 to formulate the hybrid kinetic MHD model. The 3 species equations reproduce the usual MHD equations with the addition of a hot particle pressure in the momentum equation. In the limit nh→0, the MHD equations are recovered. These model equations are implemented and examined in the NIMROD code [C.R. Sovinec, et al., Nonline magnetohydrodynamic simulations using higher-order finite elements, JCP submitted for publication] which solves three dimensional magnetohydrodynamic initial-value problems using the finite element method (FEM). The finite elements allow the representation of highly shaped geometries, but the particle-in-cell (PIC) method is complicated by the irregular grid. The associated complications are a nontrivial shape function, a more complex search algorithm, parallelization. We present our implementation of PIC in a FEM simulation and some preliminary results and performance measurements.