Stability of perpendicular MHD shocks in materials with ideal and non-ideal EoS

Magnetically assisted indirect-drive laser fusion, as well as MagLIF and Staged Z Pinch pulsed-power approaches to the ICF, involve strong shock waves propagating in a magnetized plasma. Shock waves, which play a dominant role in thermalizing the kinetic energy generated in the implosion stage, are typically perturbed by the drive's non-uniformity and wrinkle responding to upstream disturbances. We report a theoretical analysis of the stability of planar perpendicular MHD shocks propagating in a medium with an arbitrary equation of state (EoS) to interchange perturbation modes. Then the effect of a transverse magnetic field is translated into a modification of the EoS, making it possible to reduce our MHD problem to the classical D'yakov-Kontorovich (DK) shock-front stability analysis. In contrast with gasdynamic shocks, which are stable in ideal gases independently of shock strength and specific heat ratio (gamma), strong perpendicular MHD shocks exhibit the DK instability in plasmas with gamma>1+sqrt(2). The shock fronts in van der Waals fluids that are DK-unstable without a magnetic field are stabilized by its presence if the magnetic pressure is high enough. Shock fronts in simple metals at pressures not exceeding several Mbar are stable with or without the magnetic field.