Tradeoffs of efficiency and symmetry control for z-pinch driven ICF hohlraums

Time-dependent symmetry control for a double z-pinch driven hohlraum using only structures within the hohlraum has allowed the symmetric implosion and ignition of a 500 MJ inertial fusion capsule in detailed two-dimensional simulations [1]. The secondary hohlraum surrounding the capsule has a case-to-capsule radius ratio of 3.8, which provides geometric averaging of modes P$_{6}$ and higher, while mode-selective burnthrough shields provide time-dependent control of modes P$_{2}$ and P$_{4}$. The clearest path to improving the hohlraum efficiency and increasing the system energy gain is to decrease the amount of x-ray energy deposited in the hohlraums that surround the imploding z-pinches, which may be achieved by reducing the wall area. This computational study quantifies the tradeoffs between system efficiency and symmetry control for the 500 MJ capsule in reduced case-to-capsule ratio hohlraums and in single-ended (1-pinch) and double-ended (2-pinch) hohlraums. [1] R. A. Vesey \textit{et al}., Phys. Plasmas \textbf{14}, 056302 (2007).