Hybrid kinetic-MHD simulations in general geometry

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 n(h) much less than n(0) beta(h) similar to beta(0) 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 n(h) --> 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. (C) 2004 Elsevier B.V. All rights reserved.