Self-Similar Solutions With Electro-Thermal Processes for Plasmas of Arbitrary Beta*

Self-similar, magnetohydrodynamic (MHD) solutions are developed for a cold planar wall next to a hot plasma with an embedded magnetic field parallel to the wall, including electro-thermal terms. Velikovich et al. [1] studied the Nernst electro-thermal effect for such a problem under the assumption that the ratio of thermal to magnetic pressure (plasma beta) was large. Other electro-thermal processes, such as the Ettingshausen and plasma Thomson effects, vary inversely with beta, as does Joule heating, and may impact the plasma evolution at low beta. To study all these processes we have extended the self-similar formulation to allow for an arbitrary beta. Self-similar solutions are presented with conditions characteristic of the plasma immediately following laser pre-heat in the MagLIF experiment. Solutions for the density, temperature, and velocity are largely insensitive to the electro-thermal effects. However, the profile of the magnetic field changes significantly with electro-thermal effects. One interesting case is simulated with a 1D MHD code. The solutions are proposed as verification tests for advanced, multi-physics, MHD codes.

[1] A.L. Velikovich, J.L. Giuliani, and S.T. Zalesak, Phys. Plasmas, vol. 22, 042702, 2015.