Analytic criteria for shock ignition of fusion reactions in a central hot spot

Shock ignition is an inertial confinement fusion scheme where the ignition conditions are achieved in two steps. First, the DT shell is compressed at a low implosion velocity creating a central core at a low temperature and a high density. Then, a strong spherical converging shock is launched before the fuel stagnation time. It increases the central pressure and ignites the core. It is shown in this paper that this latter phase can be described analytically by using a self-similar solution to the equations of ideal hydrodynamics. A high and uniformly distributed pressure in the hot spot can be created thus providing favorable conditions for ignition. Analytic ignition criteria are obtained that relate the areal density of the compressed core with the shock velocity. The conclusions of the analytical model are confirmed in full hydrodynamic simulations.