Increased shell entropy as an explanation for observed decreased shell areal densities in OMEGA implosions

A reduced ion-kinetic (RIK) model used in hydrodynamic simulations has had some success in explaining time- and space-averaged observables characterizing the fusion fuel in hot low-density ICF capsule implosions driven by 1-ns 60-beam laser pulses at OMEGA [Rosenberg \textit{et al}., Phys. Rev. Lett. \textbf{112}, 185001 (2014); Rinderknecht \textit{et al}., Phys. Plasmas \textbf{21}, 056311 (2014); Hoffman \textit{et al}., in preparation]. But observables characterizing the capsule shell, e.g., the areal density of $^{12}$C in a plastic shell, have proved harder to explain. Recently we have found that assuming the shell has higher entropy than expected in a 1D laser-driven RIK simulation allows an explanation of the observed values of $^{12}$C areal density, and its dependence on initial shell thickness in a set of DT-filled plastic capsules. If, for example, a 15-$\mu $m CH shell implodes on an adiabat two to three times higher than predicted in a typical unmodified RIK simulation, the calculated burn-averaged shell areal density decreases from $\sim$ 80 mg/cm$^{2}$ in the unmodified simulation to the observed value of $\sim$ 25 mg/cm$^{2}$. We discuss possible mechanisms that could lead to increased entropy in such implosions.