A criterion for a two temperature plasma nuclear fusion ignition is derived by using a common model. In particular, deuterium-tritium (DT) and proton–boron11 (pB11) are considered for pre-compressed plasma. The ignition criterion is described by a surface in the three-dimensional space defined by the electron and ion temperatures Te, Ti, and the plasma density times the hot spot dimension, ρ·R. The appropriate fusion ion temperatures Ti are larger than 10 keV for DT and 150 keV for pB11. The required value of ρ·R for pB11 ignition is larger by a factor of 50 or more than for DT, depending on the electron temperature. Furthermore, our ignition criterion obtained here for pB11 fusion is practically impossible for equal electron and ion temperatures. In this paper it is suggested to use a two temperature laser induced shock wave in the intermediate domain between relativistic and non-relativistic shock waves. The laser parameters required for fast ignition are calculated. In particular, we find that for DT case one needs a 3 kJ/1 ps laser to ignite a pre-compressed target at about 600 g/cm3. For pB11 ignition it is necessary to use more than three orders of magnitude of laser energy for the same laser pulse duration.

This paper analyzes the one dimensional shock wave created in a planar target by the ponderomotive force induced by very high laser irradiance. The laser-induced relativistic shock wave parameters, such as compression, pressure, shock wave and particle flow velocities, sound velocity and temperature are calculated here for the first time in the context of relativistic hydrodynamics. For solid targets and laser irradiance of about 2 × 1024 W/cm2, the shock wave velocity is larger than 50% of the speed of light, the shock wave compression is larger than 4 (usually of the order of 10) and the targets have a pressure of the order of 1015 atmospheres. The estimated temperature can be larger than 1 MeV in energy units and therefore very excited physics (like electron positron formation) is expected in the shocked area. Although the next generation of lasers might allow obtaining relativistic shock waves in the laboratory this possibility is suggested in this paper for the first time.