HIGH-ORDER FINITE ELEMENT METHOD FOR PLASMA MODELING* U. Shumlak, R. Lilly, S. Miller, N. Reddell, E. Sousa Aerospace and Energetics Research Program University of Washington, Seattle, USA, 98195-2250 Email:
[email protected] Abstract—High-order accurate finite element methods provide description. Plasmas may be most accurately modeled using unique benefits for problems that have strong anisotropies and kinetic theory, where distribution functions, fs(x; v; t), are complicated geometries and for stiff equation systems that are governed by a Boltzmann equation coupled through large source terms, e.g. Lorentz force, collisions, @f @f q @f @f or atomic reactions. Magnetized plasma simulations of realistic s + v · s + s (E + v × B) · s = s (1) devices using the kinetic or the multi-fluid plasma models are @t @x ms @v @t collisions examples that benefit from high-order accuracy. The multi-fluid plasma model only assumes local thermodynamic equilibrium for each species s, e.g. ions, electrons, neutrals. Combined within each fluid, e.g. ion and electron fluids for the two- with Maxwell’s equations, the system leads to the continuum fluid plasma model. The algorithm implements a discontinu- kinetic plasma model, as well as the particle kinetic plasma ous Galerkin method with an approximate Riemann solver to model. Kinetic models, in their most general form, are six- compute the fluxes of the fluids and electromagnetic fields at dimensional, but reduced models with limited dimensionality the computational cell interfaces. The multi-fluid plasma model can also be meaningful, e.g. gyrokinetic. Further reduced has time scales on the order of the electron and ion cyclotron plasma models result by taking moments over velocity space frequencies, the electron and ion plasma frequencies, the electron of Eq.