Self-similar analytical solutions for blast waves in inhomogeneous atmospheres with frozen-in-magnetic field

In the present paper, we have made an attempt to study the effects of the presence of a magnetic field on the cavity formation inside a blast wave propagating into a perfectly conducting gas with density varying as some power of distance from the plane or line of explosion. In order to obtain the closed form solutions for the flow variables inside the blast wave and to solve the problem of cavity formation analytically, a relation is taken between the ordinary pressure and the total pressure. It i s found that if the value of the inhomogeneity index \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\alpha$\end{document} is greater than a critical value \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\alpha_c$\end{document} (a function of MA - Alfven Mach Number, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\gamma$\end{document} - adiabatic index and i - wave geometry index), a contact discontinuity appears at some point inside the blast wave and the cavity formation occurs. The effect of the presence of magnetic field is found to increase the tendency of cavity formation.