An analysis of the propagation of concentric shock wave fronts in a nonhomogeneous polytropic gas

The propagation of concentric shock wave fronts, of any initial intensity, in a nonhomogeneous polytropic gas is studied using the Chester-Chisnell-Whitham method. The problem is reduced to that of solving an ordinary differential equation of the first order, and a closed-form solution is given for strong shock waves. It is shown that, if the initial density decreases toward the center of the system, the temperature at the shock wave front increases at a higher rate than in the case of a homogeneous gas. This fact can be used to improve the efficiency of shock heating of plasma in implosion experiments.