Propagation of ionizing shock wave in a dusty gas medium under the influence of gravitational and azimuthal magnetic fields

Abstract

In this paper, a closed-form solution for an ionizing spherical shock/blast wave in a dusty gas (a mixture of an ideal gas and solid particles of micrometer size) under the influence of gravitational and azimuthal magnetic fields is derived. In the dusty gas mixture, the solid particles are continuously distributed, and the equilibrium flow condition holds in the entire flow field region. Analytical solutions in the closed form for the first-order approximation are derived for adiabatic and isothermal flows. Furthermore, for the second approximation, the set of ordinary differential equations is derived. The influence of problem parameters, such as the ratio of the density of the solid particles to the initial density of the ideal gas, the gravitational parameter, the solid particles mass concentration in the mixture, adiabatic index, and Alfvén-Mach number on the peak pressure on the blast wave, on physical variables and the damage radius of the blast wave is studied for the first-order approximation. Our closed-form solution for the first-order approximation in the case of adiabatic flow is analogous to Taylor's solution in the case of a strong explosion-generated blast wave. It is shown that the damage radius of the blast wave and the peak pressure on the blast wave both decrease with the addition of dust particles, and hence, the shock/blast wave strength decreases. It is observed that in the whole flow field region, the quantity J0 increases with an increase in the Alfvén-Mach number value, and hence, the shock decay with an increase in the Alfvén-Mach number.