Stability of ionizing shock waves in monatomic gases

Abstract

The stability properties of strong shocks propagating in monatomic gases are investigated. The need for modification of the classical Dyakov-Kontorovich criteria for stability of shocks rose as the straightforward application of the latter failed to explain the accumulating observations of irregular behavior behind strong shocks. In the current work, it is shown that the thermal nonequilibrium between the electrons that are produced by the electron-atom ionization process and the remaining atoms and ions plays a decisive role in the onset of a particular type of instability, namely, spontaneous emission. For that purpose, a two-fluid model is constructed in order to describe those perturbations whose frequencies are high enough so that a difference between the temperatures of the electrons, atoms, and ions may be maintained over a single period of the perturbations. Within the framework of this model, the energy losses due to the excitations of the electronic levels of the atoms as well as the ionization processes are taken into account. The two-fluid model allows the reformulation of the stability criterion in order to take into account the electronic temperature, as follows from the dominance of the electron-atom collisions in the ionization processes. In addition, the sound velocity, which plays an important role in calculating the stability criteria, is derived for the two-fluid system. It is shown that the modified criterion for spontaneous emission from the shock's front is satisfied for Mach numbers beyond a certain threshold. Furthermore, it is shown that the main mechanism for that instability is provided by the single ionization process, whereas the excitations of the electronic energy levels result in a slight modification of the instability threshold. A parametric study is carried out in order to find the domains in parameter space in which spontaneous emission occurs. It is shown that the parameters of available experiments that exhibit irregular behavior behind strong shocks do indeed fall within the theoretical domains of spontaneous emission.