Conservative Recovery Discontinuous Galerkin Scheme for the Fokker-Planck Collision Operator

Continuum kinetic plasma models are used to study plasmas by directly evolving ion and electron distribution functions using the Vlasov equation along with Maxwell's equations. In this work, a novel implementation of the Fokker-Planck operator for collisions is presented. It is based on the Rosenbluth formulation where the increments $\langle\Delta v_{\mu}\rangle$ and $\langle\Delta v_{\mu} \Delta v_{\nu}\rangle$ are calculated as the derivatives of the Rosenbluth potentials. Recovery of higher-order representation and computer algebra systems are highly utilized to calculate the derivatives and integrals in the discontinuous Galerkin algorithm. These two key elements allow for a high-order, efficient, and conserving scheme.