SPONTANEOUS ACOUSTIC-EMISSION FROM STRONG IONIZING SHOCKS

Dyakov (1954) and Kontorovich (1957) formulated the conditions for cor rugation instability of shock waves as well as for spontaneous emissio n of sound and entropy-vortex waves from them. For the first time sinc e then, it is shown here that physical circumstances do exist under wh ich shocks in gases spontaneously emit sound waves. Such circumstances are provided by strong ionizing shocks. In order to see that, the coe fficient of reflection of an acoustic wave from a shock is derived as a function of the wave's frequency and the ionization degree. Spontane ous emission of sound occurs when the reflection coefficient becomes i nfinitely large. It is shown that the relevant frequency range for the occurrence of spontaneous emission is that for which the electrons ar e not in local thermodynamic equilibrium with the heavy particles. The special properties of acoustic perturbations behind the ionizing shoc k are considered for this frequency range and the sound velocity in a partially ionized gas is derived. In addition, the condition for spont aneous emission of sound is modified in order to take into account the difference between the electrons and heavy-particle perturbed tempera tures. It is shown, by numerical calculations, that the criterion for spontaneous emission is satisfied behind ionizing shocks in argon. In particular, for an initial pressure of 5 Torr, the threshold for the o ccurrence of the spontaneous emission is found to be M(1) = 15. This c ritical value of the shock Mach number, as well as other calculated ph ysical features, agree very well with those obtained experimentally by Glass and Liu (1978) who observed the occurrence of instability behin d shocks in argon.