An analysis and successful benchmarking of the Chapman-Enskog-like (CEL) continuum kinetic closure approach algorithm in NIMROD

Herein, we formulate, analyze, and apply a numerical method for solving a Chapman-Enskog-like (CEL) continuum kinetic model for plasmas. It is shown that centering the heat flux at the beginning of the time step and the ion temperature at the end of the time step in the kinetic equation allows for a numerically-stable time advance of the coupled fluid-kinetic system. In addition, it is shown that numerical stability is impossible to achieve without explicitly enforcing key tenets of the CEL closure approach, in particular, that the number density (n), flow (u), and temperature (T) moments of the kinetic distortion remain small in time. We show that with a method to constrain these moments, it is possible to remove both the numerical growth and numerical damping from the linear modes. We apply the results from the linear stability analysis to allow for a numerically-stable fully nonlinear axisymmetric evolution of profiles in NIMROD, wherein we observe the asymptotic evolution of the flow in a DIII-D tokamak equilibrium (based on DIII-D ITER Baseline Scenario (IBS) discharge 174446 at 3390 ms). We compare the self-consistently computed results to analytics and to results from a previously benchmarked fixed-background δf implementation in NIMROD. Agreement with prediction is found for both the dynamics and asymptotics of the flow. This work demonstrates the first successful published benchmarking of the full CEL approach in a plasma fluid code.