Simulation of quasilinear theory with high-order discontinuous Galerkin method

Quasilinear theory is one of the simplest reduced models for collisionless plasma turbulence. Its similarity to Reynolds averaging suggests using the coupled quasilinear kinetic and wave kinetic equations as a model for subgrid-scale physics in reduced kinetic simulations. This work investigates such a reduced model numerically. After splitting between resonant and nonresonant interactions, diffusion coefficients from the classic Bohm-Gross dispersion relation are derived analytically and utilized. Results are compared to Vlasov-Poisson simulations. These numerical experiments are conducted using a high-order parallelized nodal explicit Runge-Kutta discontinuous Galerkin method, with benchmark results given for the linear advection-diffusion equation on a finite-interval.