Nonlinear Fokker-Planck collision operator in Rosenbluth form for gyrokinetic simulations using discontinuous Galerkin method

Abstract

A gyroaveraged nonlinear collision operator is formulated based on the Fokker-Planck operator in the Rosenbluth-MacDonald-Judd (RMJ) potential form and implemented for the gyrokinetic simulations with the discontinuous Galerkin scheme. The divergence structure of the original RMJ form is carefully preserved throughout the formulation to guarantee the density conservation while neglecting the finite Larmor radius effect. The B-spline finite element method is used to calculate the Rosenbluth potentials for the nonlinear collision operator. In addition to the nonlinear collision operator, linear and Dougherty collision models are also implemented to assess the benefits and drawbacks of each model. For the conservation of the parallel momentum and energy, we adopt a simple advection-diffusion model which numerically enforces the conservation of physical quantities. From bump-on-tail relaxation tests, the monotonically increasing entropy in time and conservation properties are demonstrated for the developed collision operator. Also, a few theoretical predictions for the neoclassical physics such as the neoclassical heat flux, poloidal flow and collisional damping of zonal flow are successfully reproduced by numerical simulations.