Nernst thermomagnetic waves in magnetized high energy density plasmas

The Nernst effect plays the dominant role in the subsonic transport of magnetic flux in magnetized high-energy-density (HED) plasmas, where the plasma beta is high and the temperature diffusivity is much greater than the magnetic diffusivity. This parameter range is characteristic of the Magnetized Liner Inertial Fusion and other magnetoinertial fusion approaches near stagnation. It is demonstrated that the transport of magnetic flux in HED plasmas proceeds via the Nernst thermomagnetic waves propagating at the local Nernst velocity with respect to the plasma particles down the temperature gradient. The plasma resistivity strongly damps their propagation in the opposite direction. The Nernst waves, which had been theoretically predicted in the 1960s and observed in metals at cryogenic temperatures, have never been discussed for strongly driven, highly inhomogeneous, magnetized HED plasmas at kilo-electron-volt temperatures. Semianalytical, self-similar solutions are developed for the plasma transport equations at constant pressure involving the Nernst waves. The effect of the Nernst waves on the losses of heat and magnetic flux from magnetically insulated hot plasmas is discussed. The results from finite difference MHD simulations with particular numerical techniques are compared with the self-similar solutions. Finally, the constraint of constant pressure is removed and the simulations show that the self-similar profiles are asymptotically reproduced in a region between outgoing pressure disturbances. The self-similar solutions and finite difference simulations provide a challenging verification test for MHD codes that include the Nernst effect.