Analytical criterion for shock ignition of fusion reaction in hot spot

Shock ignition of DT capsules involves two major steps. First, the fuel is assembled by means of a low velocity conventional implosion. At stagnation, the central core has a temperature lower than the one needed for ignition. Then a second, strong spherical converging shock, launched from a high intensity laser spike, arrives to the core. This shock crosses the core, rebounds at the target center and increases the central pressure to the ignition conditions. In this work we consider this latter phase by using the Guderley self-similar solution for converging flows. Our model accounts for the fusion reaction energy deposition, thermal and radiation losses thus describing the basic physics of hot spot ignition. The ignition criterion derived from the analytical model is successfully compared with full scale hydrodynamic simulations.