Thermonuclear Yield Degradation Due to Low Mode Capsule Shape Asymmetries on NIF Inertial Fusion Implosions

The effects of Legendre polynomial $P_4$ capsule shapes on NIF inertial fusion implosions have been modelled using the radiation-hydrodynamics code Hydra. Large $P_4$ mode shapes cause regions of the hotspot/DT ice interface to become unstable during capsule deceleration, preventing stagnation; up to 50\% of the peak capsule kinetic energy remains unconverted to hotspot pressure, causing hotspot pressures to fall by up to $3.5\times$ and neutron yields to be reduced by up to $20\times$. Synthetic x-ray images show that positive $P_4$ amplitudes $>5\mu$ m are undetectable experimentally when using cryogenic DT capsules. Analysis of DHe$^3$ filled CH capsules and comparison with NIF experimental data indicate that the yield reduction for DT capsules with the same x-ray drive would be $\sim10-20\times$. The presence of undetectable $P_4$ modes would explain many characteristics of current NIF implosions including; large negative $P_2$ modes, the $\sim30\mu$ m hotspot size, the low inferred pressures and hotspot masses, and most importantly the $\sim10\times$ discrepancy between the measured capsule kinetic energy and the observed neutron yield. Experimental methods are proposed to infer the $P_4$ mode amplitude of DT capsules and then reduce this to ignition specification.