Symmetric set of transport coefficients for collisional magnetized plasma

In Braginskii extended magneto-hydrodynamics (ExMHD), applicable to collisional astrophysical and high energy density plasmas, the electric field and heat flow are described by the $\alpha$, $\beta$ and $\kappa$ transport coefficients. We show that magnetic transport relies primarily on $\beta_\parallel-\beta_\perp$ and $\alpha_\perp-\alpha_\parallel$, rather than $\alpha_\perp$ and $\beta_\perp$ themselves. However, commonly used coefficient fit functions [Epperlein and Haines, Phys. Fluids 29, 1029 (1986)] cannot accurately calculate these quantities. This means that many ExMHD simulations have significantly over-estimated the cross-gradient Nernst advection, resulting in artificial magnetic dissipation and discontinuities. We repeat the kinetic analysis to provide fits that rectify this problem. Use of these in the Gorgon ExMHD code resolves the known discrepancies with kinetic simulations in the literature. Recognizing the fundamental importance of $\alpha_\perp-\alpha_\parallel$ and $\beta_\parallel-\beta_\perp$, we re-cast the set of coefficients to find that each of them now shares the same underlying properties. This makes explicit the symmetry of the magnetic and thermal transport equations, as well as the symmetry of the coefficients themselves.