Fuel Assembly for Conventional, Fast and Shock Ignition Direct-Drive Inertial Confinement Fusion

Relations between stagnation and in-flight phases are derived both analytically and numerically, for hydrodynamic variables relevant to direct-drive inertial confinement fusion implosions. Scaling laws are derived for the stagnation values of the shell density and areal density; also the hot spot pressure, temperature and areal density. Simple formulas are derived for the thermonuclear energy gain and the in-flight aspect ratio. The ignition condition (Lawson criterion) for conventional hot-spot inertial confinement fusion is cast in a form dependent on the only two measurable parameters of the compressed fuel assembly: the hot-spot ion temperature (T h i ) and the total areal density (ρRtot) that includes the cold shell contribution. A marginal ignition curve is derived in the ρRtot, T h i plane and current implosion experiments are compared with the ignition curve. On this plane, hydrodynamic equivalent curves show how a given implosion would perform with respect to the ignition condition when scaled up in the laser-driver energy. The hydrodynamic scaling laws and the ignition criterion provide guidelines for the optimized fuel assembly design in direct-drive fast ignition and conventional inertial confinement fusion implosions. It is found that massive cryogenic shells can be imploded with a low implosion velocity on a low adiabat using the relaxation-pulse technique, to assemble thermonuclear fuel at high densities, high ρR, and with a small-size hot spot,