Effects of Hohlraum Plasma Filling on Implosion Symmetry

We describe a study with the design code \textsc{hydra} to understand how hohlraum plasma filling impacts symmetry control. The 2010 National Ignition Facility (NIF) symmetry campaign demonstrated symmetry tuning via cross-beam transfer in ignition-scale hohlraums driven by 1.3 MJ of laser energy. Following the subsequent NIF shock-tuning campaign, the implosion symmetry changed from prolate to oblate ($a_2/a_0 \approx -50 \%$). Optical and x-ray data suggested higher hohlraum plasma density than in previous experiments, impairing the inner laser beam propagation. Design calculations with \textsc{hydra} were consistent with this finding; however, they also predicted an increase in cross-beam transfer that would counteract the impaired propagation, resulting in round implosions. We can empirically restore symmetry control by changing the hohlraum geometry, fielding conditions, or laser pulse.