Comparison of velocity space coordinates for stellarator neoclassical calculations

Solution of the drift kinetic equation (DKE) is a required step in analyzing and optimizing neoclassical transport in stellarators. Because of the complex geometry and wide range of collisionality regimes present in stellarators, this often requires the use of numerical solvers, a number of which have been developed. Among all of these codes, the dominant choice for velocity space coordinates is the speed v and pitch angle v_|| /v, equivalent to spherical coordinates in velocity space. While this choice can be convenient for representing the effects of pitch angle scattering and using the so called ”mono-energetic approximation” (where coupling in speed is neglected), these coordinates can make the important trapped-passing boundary in phase space difficult to resolve, often requiring very high

resolution in both pitch angle and real space coordinates. In this work, we survey a wide range of other possible choices for coordinates in velocity space and analyze both their physical and numerical properties, with particular attention paid to coordinates that admit an efficient discretization of the DKE allowing for fast and accurate calculations of neoclassical transport in stellarators.