Semi-Analytic Solutions for Diffusive Transport in Plasmas of Arbitrary Beta

Abstract

Magneto-inertial fusion (MIF) approaches offer a promising route to ignition and a platform to study high energy density physics. Understanding the transport of magnetic field and how it affects the transport of energy is of crucial importance for modelling of MIF schemes. To aid this, we develop semi-analytic self-similar solutions for subsonic magnetised transport. These solutions can be used as test problems to validate magnetohydrodynamic (MHD) codes. The MHD equations in 1D planar geometry are numerically solved for arbitrary plasma beta and boundary conditions, using a shooting method boundary value problem code. We validate this model against the MHD code Gorgon, demonstrating the use of these semi-analytic solutions as a flexible test problem for extended MHD algorithms. We show another use as a parameter scan over plasma beta, highlighting the change in relevance of different transport terms in different parameter regimes. We also discuss the breakdown of these self-similar solutions in the regime of strong Ohmic heating which leads to electron-ion temperature separation. It is shown that the Ettingshausen effect mitigates this separation, causing overestimates of the electron temperature if this term is ignored. These results are relevant to MHD models of pulsed power, for example at the edge of a z-pinch.