Symmetric theory of heat and magnetic transport in a collisional magnetized plasma *

Braginskii extended-magnetohydrodynamics (XMHD) is used to model the effect of magnetic fields on the hydrodynamics of high energy density plasmas. This theory is a central modelling capability for hohlraums, Z-pinches, laser ablation fronts, magnetized inertial confinement fusion concepts, fast ignition, and certain astrophysical settings. Even if the magnetic field has a pressure far less than the plasma pressure, it can still indirectly affect hydrodynamics by insulating and deflecting the heat flux. This is described by the transport coefficients, found from kinetic theory. In XMHD codes, these are calculated at each timestep using a fit to the results of kinetic simulations. We present a re-worked formulation of Braginskii's original equations, explicitly demonstrating the symmetry between heat flux and magnetic field advection in the plasma. We show that, although superficially accurate, commonly used fit functions [e.g. Epperlein and Haines, Phys. Fluids (1986)] cannot correctly reproduce this theoretical symmetry. This means that XMHD simulations in the literature, using codes such as Gorgon and Hydra, have produced incorrect and discontinuous magnetic field profiles. We have implemented corrected fit functions into the Gorgon code. This resolves discrepancies with the results of two-dimensional fully kinetic simulations. We explore the interpretation of each XMHD term in relation to high energy density experiments and instabilities such as Kelvin-Helmholtz induced mixing.