Stability of shock waves in high temperature plasmas

Abstract

The Dyakov-Kontorovich criteria for spontaneous emission of acoustic waves behind shock fronts are investigated for high temperature aluminum and beryllium plasmas. To this end, the Dyakov and critical stability parameters are calculated from Rankine-Hugoniot curves using a more realistic equation of state (EOS). The cold and ionic contributions to the EOS are obtained via scaled binding energy and mean field theory, respectively. A screened hydrogenic model, including l-splitting, is used to calculate the bound electron contribution to the electronic EOS. The free electron EOS is obtained from Fermi-Dirac statistics. Predictions of the model for ionization curves and shock Hugoniot are found to be in excellent agreement with available experimental and theoretical data. It is observed that the electronic EOS has significant effect on the stability of the planar shock front. While the shock is stable for low temperatures and pressures, instability sets in as temperature rises. The basic reason is ionization of electronic shells and consequent increase in electronic specific heat. The temperatures and densities of the unstable region correspond to those where electronic shells get ionized. With the correct modeling of bound electrons, we find that shock instability for Al occurs at a compression ratio ~5.4, contrary to the value ~3 reported in the literature. Free electrons generated in the ionization process carry energy from the shock front, thereby giving rise to spontaneously emitted waves, which decay the shock front.