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 ρ/ρ0=4 asymptote to tend to the ρ/ρ0=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-ofstate models, especially as concerns the relativistic effects, and depend on the radiative opacity of the material.

Thermochemical effects on hypersonic shock waves interacting with weak turbulence

“…For the parameters tested here, the value Γ in the upper branch of the Hugoniot curve is always larger than the critical values for the onset of (a) shock instabilities associated with multi-wave 66,67 and multi-valued 68,69 solutions, and (b) D'yakov-Kontorovich pseudo-instabilities associated with the spontaneous emission of sound 8,70 . Similar characteristics of the Hugoniot curve have been observed elsewhere for shocks subjected to endothermicity [71][72][73][74] .…”

Stability of expanding accretion shocks for an arbitrary equation of state

“…Distinguished regimes for isolated planar shocks ((a) known results) and expanding accretion shocks ((b) new findings) along the variable h. (Bates & Montgomery 2000), and magnesium (Lomonosov et al 2000;Konyukhov et al 2009); for ionizing shock waves in inert gases (Mond & Rutkevich 1994;Mond, Rutkevich & Toffin 1997); for shock waves dissociating hydrogen molecules (Bates & Montgomery 1999); for Gbar-and Tbar-pressure range shocks in solid metals, where the shell ionization affects the shapes of Hugoniot curves (Rutkevich, Zaretsky & Mond 1997;Das, Bhattacharya & Menon 2011;Wetta, Pain & Heuzé 2018); for shock fronts producing exothermic reactions, such as detonation (Huete & Vera 2019;Huete et al 2020). Other examples include EoS constructed ad-hoc specifically for analytical and numerical studies of shock instabilities: (Ni, Sugak & Fortov 1986;Konyukhov, Levashov & Likhachev 2020;Kulikovskii et al 2020).…”

Signatures of fluid and kinetic properties in the energy distributions of multicharged Ta ions from nanosecond-laser-heated plasma

“…The electron heat flux uses a Spitzer-Harm flux limiter of 0.15. The equation of state used in the simulation is relying on a quantum average-atom model calculation as described in [32]. The laser propagation, refraction and collisional absorption are treated by a ray tracing algorithm.…”