Hydrodynamic relations for direct-drive fast-ignition and conventional inertial confinement fusion implosions

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 and for the hot-spot pressure, temperature, and areal density. A simple formula is also derived for the thermonuclear energy gain and in-flight aspect ratio. Implosions of cryogenic deuterium-tritium capsules driven by UV laser energies ranging from 25 kJ to 2 MJ are simulated with a one-dimensional hydrodynamics code to generate the implosion database used in the scaling law derivation. These scaling laws provide guidelines for optimized fuel assembly and laser pulse design for direct-drive fast ignition and conventional inertial confinement fusion.