Discontinuous Galerkin simulations of the nonlinear Rosenbluth/Fokker-Planck collision operator

When using a kinetic model to investigate regimes in which collisional physics are relevant, the choice of collision operator naturally determines what physical collisional mechanisms are included in the model. While approximate models like the Bhatnagar-Gross-Krook or Dougherty operators are typically adequate when considering the larger-scale impact of collisions on the plasma velocity distribution, a more accurate model is required for proper treatment of the high-energy tails of the distribution. The nonlinear Rosenbluth/Fokker-Planck collision operator (FPO) is a highly accurate treatment of the effect of small-angle Coulomb collisions on a plasma population, including a velocity-dependent effective collision frequency for accurate modeling of the high-energy tails, but this operator is highly nontrivial to efficiently implement numerically. We present results from a discontinuous Galerkin implementation of the FPO in the plasma simulation framework Gkeyll that properly handles the cross-derivatives and conserves density, momentum, and energy. Comparisons are drawn between the FPO and Dougherty models for relaxation to Maxwellian from various initial conditions, and the FPO applied to a study of the reduction of thermal conductivity due to superthermal electrons.