D'yakov-Kontorovitch instability of shock waves in hot plasmas

Abstract

The D'yakov-Kontorovich stability criterion for spontaneous emission of acoustic waves behind shock fronts is investigated for high-temperature carbon, aluminum, silicon and niobium plasmas. The D'yakov and critical stability parameters are calculated along the principal Rankine-Hugoniot curve with an equation-of-state model in which the contribution of bound and free electrons is calculated through a relativistic quantum average-atom model, solving the Dirac equation. The pressure is determined using the stress-tensor formula in the relativistic framework. We find that the instability occurs at the end of the ionization of electronic shells, when the Hugoniot curve departs from the $\rho/\rho_0$=4 asymptote to tend to the $\rho/\rho_0$=7 limit. In such conditions, if the plasma is optically thick, the contribution of blackbody radiation to the EOS is dominant, and the system becomes always stable. Our results indicate that the conditions in which the instability takes place are different from previously published estimates, due to assumptions made in the corresponding equation-of-state models, especially as concerns the relativistic effects, and depend on the radiative opacity of the material.