Symmetric Set of Transport Coefficients for Collisional Magnetized Plasma
James Sadler, C. A. Walsh, Hui Li
Abstract
Braginskii extended magnetohydrodynamics is used to model transport in collisional astrophysical and high energy density plasmas. We show that commonly used approximations to the ${\ensuremath{\alpha}}_{\ensuremath{\perp}}$ and ${\ensuremath{\beta}}_{\ensuremath{\perp}}$ transport coefficients [e.g., Epperlein and Haines, Phys. Fluids 29, 1029 (1986)] have a subtle inaccuracy that causes significant artificial magnetic dissipation and discontinuities. This is because magnetic transport actually relies on ${\ensuremath{\beta}}_{\ensuremath{\parallel}}\ensuremath{-}{\ensuremath{\beta}}_{\ensuremath{\perp}}$ and ${\ensuremath{\alpha}}_{\ensuremath{\perp}}\ensuremath{-}{\ensuremath{\alpha}}_{\ensuremath{\parallel}}$, rather than ${\ensuremath{\alpha}}_{\ensuremath{\perp}}$ and ${\ensuremath{\beta}}_{\ensuremath{\perp}}$ themselves. We provide fit functions that rectify this problem and thus resolve the discrepancies with kinetic simulations in the literature. When implemented in the gorgon code, they reduce the predicted density asymmetry amplitude at laser ablation fronts. Recognizing the importance of ${\ensuremath{\alpha}}_{\ensuremath{\perp}}\ensuremath{-}{\ensuremath{\alpha}}_{\ensuremath{\parallel}}$ and ${\ensuremath{\beta}}_{\ensuremath{\parallel}}\ensuremath{-}{\ensuremath{\beta}}_{\ensuremath{\perp}}$, we recast the set of coefficients. This makes explicit the symmetry of the magnetic and thermal transport, as well as the symmetry of the coefficients themselves.