Physics of ionizing shock waves in magnetic fields

Abstract

This paper presents the theory of ionizing shock waves in a magnetic field. Depending on the shock type (which is determined by the relation between the gas outflow velocity, at the shock front, and local values of the characteristic fast and slow magnetosonic speeds and Alfvén speed), the evolutionarity conditions of a shock wave either imply additional boundary conditions, apart from those which follow from the conservation laws and continuity equations, or no additional boundary conditions are implied for a shock wave of a given type. Generally, an additional relation determining the shock front structure is required in the latter case. This additional relation is a consequence of the stability condition for an ionizing shock front structure, i.e. the ionization stability condition. The ionization stability condition means that the ionization wave induced in a neutral gas by an ionizing shock waves moves, relative to the unperturbed gas, at a velocity equal to that of the shock compression front, irrespective of the mechanism of ionization transfer in the neutral gas by a transverse electric field induced by the shock wave. The explicit form of the additional relation in question can be obtained from the ionization structure of the shock front leading edge. In the simplest case where precursor ionization processes (photoionization, etc.) are negligible the additional boundary condition implies that the upstream electric field in the neutral gas should be equal to the breakdown field. For a sufficiently high intensity of the ionizing shock wave the solutions obtained are reduced to those for magnetohydrodynamic shock waves. Structures of ionizing shock fronts have been considered for different orientations of the magnetic field relative to the shock front plane: transverse, normal and switch-off shock waves. The paper presents, in particular, solutions for self-similar problems and numerical solutions for non-stationary problems on the formation of the shock front structure of transverse and normal ionizing shock waves. Solution of these problems permits a comprehensive description of flows, which arise in inverse Z-pinch type devices and coaxial electromagnetic shock tubes. The paper also presents a detailed analysis of experimental investigations of the shock structure of ionizing shock waves.