Analytical physical models for cryogenic double-shell capsule design driven by Z-pinch dynamic Hohlraum

The Z-pinch dynamic Hohlraum (ZPDH) is a promising indirect-drive approach for inertial confinement fusion. The volume ignition capsule is more robust than the hot-spot ignition capsule for ZPDH due to the fact that the ZPDH radiation drive source has a high energy but low symmetry. Focusing on the ignition design of cryogenic double-shell volume ignition capsules using ZPDH radiation sources, three analytical physical models, including the ablation and implosion model, the shell collision model, and the burn fraction model, are established to quantitatively characterize the relation of capsule parameters. Robust capsule designs are then determined based on these analytical models together with 1D radiation hydrodynamics simulations. The results show that under the 10 ns, 308 eV radiation drive source produced by ZPDH with 50 MA load current, capsules with a large range of parameters can ignite. The fusion yield of the recommended capsule is 16.0 MJ, and the absorbed energy is 1.28 MJ.