Numerical Methods for Nonlinear Fokker-Planck Collision Operator in TEMPEST

Early implementations of Fokker-Planck collision operator and moment computations in TEMPEST used low order polynomial interpolation schemes to reuse conservative operators developed for speed/pitch-angle ($v$, $\theta$) coordinates. When this approach proved to be too inaccurate we developed an alternative higher order interpolation scheme for the Rosenbluth potentials and a high order finite volume method in TEMPEST ($\epsilon, \mu$) coordinates. The collision operator is thus generated by using the expansion technique in ($v$, $\theta$) coordinates for the diffusion coefficients only, and then the fluxes for the conservative differencing are computed directly in the TEMPEST ($\epsilon, \mu$) coordinates. Combined with a cut-cell treatment at the turning-point boundary, this new approach is shown to have much better accuracy and conservation properties.