Status and example cases of Fokker Planck calculations with ASGaRD

The need for a higher-dimensional Fokker Planck code arises in non-axisymmetric configurations such as mirrors and stellarators. We are using the AsGard [1] framework to do the higher order Fokker Planck solution which employs a sparse grid discontinuous Galerkin method. This has favorable scaling to error ratio for high dimensions. For verification we present the 1D parallel velocity and 2D (parallel, perpendicular) velocity calculations and compare with calculations done in [2, 3]. 1D case demonstates the ability to simulate parallel velocity space diffusion from a model lower hybrid operator. 2D case introduces pitch angle scattering which captures an important effect in lower hybrid current drive. We will discuss next steps which will lead to development of a 4D (two velocity, two space) simulation capability applicable to mirror and stellarator geometries.

[1] S. E. Hahn et al., J. Open Source Software 9(100), 6766, (2024).

[2] N. J. Fisch, Phys. Rev. Lett. 41, 873 (1978).

[3] C. F. F. Karney and N. J. Fisch, Phys. Fluids 22, 1817 (1979).