A high-order finite-volume algorithm for Fokker–Planck collisions in magnetized plasmas

A high-order finite-volume algorithm is developed for the Fokker–Planck Operator (FPO) describing Coulomb collisions in strongly magnetized plasmas. The algorithm uses a generic fourth-order reconstruction scheme on an unstructured grid in the velocity space spanned by parallel velocity and magnetic moment. By analytically mapping between different coordinates, it produces an accurate and density-conserving numerical FPO for an arbitrary choice of velocity space coordinates. A linearized FPO in constants-of-motion coordinates is implemented as an example of the present algorithm combined with a cut-cell merging procedure. Numerical tests include the thermalization of a test distribution with a background Maxwellian at a different temperature, and the return to isotropy for a distribution initialized with a velocity space loss-cone. Utilization of the method for a nonlinear FPO is straightforward but requires evaluation of the Trubnikov–Rosenbluth potentials.