Benchmarking NIMROD Continuum Kinetic Formulations through the Steady-State Poloidal Flow

In this work, continuum kinetic formulations are employed as a mechanism to include closure physics in an extended magnetohydrodynamics (MHD) model. Two continuum kinetic approaches have been implemented in the plasma fluid code NIMROD including a Chapman-Enskog-like (CEL) [1] formulation, and a more conventional $\delta f$ approach. Herein, predictions for steady-state values of poloidal flow profiles in tokamak geometry are provided, using both the $\delta f$ formulation, and two different solution methods for CEL. These results are benchmarked against analytic theory as well as results from the drift kinetic code DK4D [2]. The kinetic formulations employed here show agreement with both the analytic theory and DK4D results, and offer a novel velocity space representation involving higher-order finite elements in pitch angle. Preliminary results involving the full fluid-kinetic coupling of the CEL method are also presented. [1] J. J. Ramos, “Fluid and drift-kinetic description of a magnetized plasma with low collisionality and slow dynamics orderings. i. electron theory,” Physics of Plasmas \textbf{17}, 082502 (2010). [2] B. C. Lyons, “Steady-state benchmarks of DK4D: A time-dependent, axisymmetric drift-kinetic equation solver,” Physics of Plasmas \textbf{22}, 056103 (2015).