BEGIN:VCALENDAR VERSION:2.0 CALSCALE:GREGORIAN PRODID:UW-Madison-Physics-Events BEGIN:VEVENT SEQUENCE:0 UID:UW-Physics-Event-8641 DTSTART:20240325T180000Z DURATION:PT1H0M0S DTSTAMP:20260413T205402Z LAST-MODIFIED:20240226T152155Z LOCATION:B343 Sterling SUMMARY:A CHAPMAN-ENSKOG-LIKE (CEL) CONTINUUM KINETIC CLOSURE APPROACH IN NIMROD\, Thesis Defense\, Joseph Jepson\, Physics Graduate Student DESCRIPTION:Herein\, a numerical method for solving a Chapman-Enskog-l ike (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\, i n 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 diffe rence leads to an $O(\\delta)$ kinetic equation that analytically enfo rces that the first-order kinetic distortion $f_1$ have no number dens ity ($n$)\, flow ($\\mathbf{u}$)\, and temperature ($T$) moments. The fluid variables in this method are allowed to deviate far from an init ial equilibrium. The fluid equations are closed by incorporating appro priate velocity space moments of the first-order kinetic distortion.\n
\nAn axisymmetric poloidal flow damping calculation is perform ed to benchmark the implementation. It is first shown that the kinetic aspects of the implementation give results for the steady-state poloi dal flow that agree both with other codes\, analytics\, and a fixed-ba ckground (i.e. $f_0$ a stationary Maxwellian) $\\delta f$ implementati on 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 fi xed-background $\\delta f$ implementation.
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\nA von Neumann li near stability analysis of the full fluid-kinetic system is also perfo rmed to help elucidate methods to make the time advance of the full sy stem numerically stable. It is shown that numerical stability is impos sible to achieve without explicitly enforcing key tenets of the CEL cl osure 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 tim e step and the ion temperature at the end of the time step in the kine tic equation allows for a numerically-stable time advance of the coupl ed fluid-kinetic system. Furthermore\, these linear stability results are seen to remain applicable when running NIMROD fully nonlinearly.\n
\nThe methodology of applying the CEL approach to non-axisymme tric problems is also discussed. Future work will include applying thi s closure approach to the problem of forced magnetic reconnection in t oroidal geometry\, as well as to accurate simulation of neoclassical t earing modes (NTMs) in tokamaks. URL:https://www.physics.wisc.edu/events/?id=8641 END:VEVENT END:VCALENDAR