The Gaussian radial basis function method for plasma kinetic theory

• A radically new method to address the velocity space discretization of the non-linear kinetic equation of plasmas.
• Elegant and physically intuitive, flexible and mesh-free.
• Demonstration of numerical solution of both 2-D and 3-D non-linear Fokker–Planck relaxation problem.

Description of a magnetized plasma involves the Vlasov equation supplemented with the non-linear Fokker–Planck collision operator. For non-Maxwellian distributions, the collision operator, however, is difficult to compute. In this Letter, we introduce Gaussian Radial Basis Functions (RBFs) to discretize the velocity space of the entire kinetic system, and give the corresponding analytical expressions for the Vlasov and collision operator. Outlining the general theory, we also highlight the connection to plasma fluid theories, and give 2D and 3D numerical solutions of the non-linear Fokker–Planck equation. Applications are anticipated in both astrophysical and laboratory plasmas.