Analysis of compression of a small sphere of matter by means of n successive strong imploding shocks

The imploding shock is induced by the process of ablation, i.e., an energy pulse is delivered at the rim of the sphere, it ionizes and causes a rapidly outwardly expanding plasma. The domain of interaction between matter and energy pulse is idealized by means of the spherical deflagration front which acts thereby as a spherical piston. The fluid between the deflagration front and the shock front follows a self-similar solution of the conservation equations. Expressions for the pressure, density, gas velocity, and temperature are derived. It is shown that the density saturates at about seven times the initial density. A succession of n strong imploding shocks is considered and the state of the sphere is derived. Analysis shows that the small amount of matter is able to be compressed to the superhigh density, 10 to the 26 power particles/cu cm, and heated to the high temperature 5 KeV.