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Date: Monday, March 25th
Time: 1:00 pm
Place: B343 Sterling
Speaker: Joseph Jepson, Physics Graduate Student
Abstract: Herein, a numerical method for solving a Chapman-Enskog-like (CEL) continuum kinetic model for plasmas is formulated, analyzed, and applied in the plasma fluid code NIMROD. The CEL approach is a $\delta f$ drift kinetic approach that allows rigorous closure of the plasma fluid equations in all collisionality regimes. Importantly, in this approach, the zeroth-order in $\delta$ ($\delta\equiv\rho_i/L$, with $\rho_i$ the ion gyroradius and $L$ a macroscopic length scale) distribution function is a time-evolving Maxwellian. This difference leads to an $O(\delta)$ kinetic equation that analytically enforces that the first-order kinetic distortion $f_1$ have no number density ($n$), flow ($\mathbf{u}$), and temperature ($T$) moments. The fluid variables in this method are allowed to deviate far from an initial equilibrium. The fluid equations are closed by incorporating appropriate velocity space moments of the first-order kinetic distortion.

An axisymmetric poloidal flow damping calculation is performed to benchmark the implementation. It is first shown that the kinetic aspects of the implementation give results for the steady-state poloidal flow that agree both with other codes, analytics, and a fixed-background (i.e. $f_0$ a stationary Maxwellian) $\delta f$ implementation in NIMROD. It is then shown that the flow dynamics in the full CEL approach agree well both with analytics, and with results from the fixed-background $\delta f$ implementation.

A von Neumann linear stability analysis of the full fluid-kinetic system is also performed to help elucidate methods to make the time advance of the full system numerically stable. It is shown that numerical stability is impossible to achieve without explicitly enforcing key tenets of the CEL closure approach, in particular, that the $n$, $\mathbf{u}$, and $T$ moments of the kinetic distortion remain small in time. In addition, 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. Furthermore, these linear stability results are seen to remain applicable when running NIMROD fully nonlinearly.

The methodology of applying the CEL approach to non-axisymmetric problems is also discussed. Future work will include applying this closure approach to the problem of forced magnetic reconnection in toroidal geometry, as well as to accurate simulation of neoclassical tearing modes (NTMs) in tokamaks.
Host: Chris Hegna
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