Analytic expressions for optimal inertial-confinement-fusion hohlraum wall density and wall loss

Solutions to the radiation diffusion equation predict the absorbed energy ("wall loss") within an inertial confinement fusion (ICF) hohlraum. Comparing supersonic versus subsonic solutions suggests that a high metallic foam as hohlraum wall material will reduce hydrodynamic losses, and hence, net absorbed energy by . We derive an analytic expression for the optimal density (for any given drive temperature and pulse-length) that will achieve this reduction factor and which agrees well with numerical simulations. This approach can increase the coupling efficiency of indirectly driven ICF capsules.