Effect of inner DT gas-density on energy gain accounting for a simple modeling of the instabilities growth at the hot-spot surface

In a classical Inertial Confinement Fusion capsule a shell of solid Deuterium-Tritium fuel encloses an inner sphere of gas at vapor pressure. The temperature of the cryogenic fuel determines the vapor pressure and thus the density of the DT gas which decreases proportionally to the temperature. Typically, temperatures of the cryogenic DT shell and densities of the inner gas are around ≈ 18 K and 0.3 mg/cm 3 , respectively. A parametric study was conducted to analyze the effect of gas density on the final energy gain, assuming a simplified model for the evolution of the Rayleigh-Taylor instability at the hot spot surface. It is found that small gas densities (< 0.1 mg/cm 3 ) avoid the formation of a sufficiently large hot-spot mass, preventing high-energy gains. On the other hand, high-densities (> 1.0 mg/cm 3 ) are associated to larger deceleration times that allow for thicker mixing-layers surrounding the hot spot that quench the propagation of the fusion reactions reducing the final gain. This implies that there is an optimal gas density window between 0.1 to 1 mg/cm 3 that maximizes the capsule performance.