Fast ignition hot spot break-even scaling

A series of numerical simulations have been performed to determine scaling laws for fast ignition break even of a hot spot formed by energetic particles created by a short pulse laser. Hot spot break even is defined to be when the fusion yield is equal to the total energy deposited in the hot spot through both the initial compression and the subsequent heating. In these simulations, only a small portion of a previously compressed mass of deuterium-tritium fuel is heated on a short time scale, i.e., the hot spot is tamped by the cold dense fuel which surrounds it. The hot spot tamping reduces the miminum energy required to obtain break even as compared to the situation where the entire fuel mass is heated, as was assumed in a previous study [S. A. Slutz, R. A. Vesey, I. Shoemaker, T. A. Mehlhorn, and K. Cochrane, Phys. Plasmas 7, 3483 (2004)]. The minimum energy required to obtain hot spot break even is given approximately by the scaling law ET=7.5(ρ/100)-1.87 kJ for tamped hot spots, as compared to the previously reported scaling of EUT=15.3(ρ/100)-1.5 kJ for untamped hotspots. The size of the compressed fuel mass and the focusability of the particles generated by the short pulse laser determines which scaling law to use for an experiment designed to achieve hot spot break even