Hydrodynamic Scaling Analysis of Nuclear Fusion in Hot Plasma

Proton beams generated by ultraintense laser pulse irradiations have potential applications in industry and in medicine. However, the laser pulse parameters are currently not optimized for practical applications. We discuss scaling laws of fusion yields generated by laser-plasma interactions. The yields are found to scale as a function of the laser power. The origin of the scaling law in the laser driven fusion yield is derived in terms of hydrodynamical scaling and it is attributed to the laser power dependence of three terms: the reaction rate, the density of the plasma and the projected range of the plasma particle in the medium. The resulting scaling relations have a powerful predictive power that enables estimating the fusion yield for a nuclear reaction which has not been investigated by means of the laser accelerated ion beams.