Analytic formula for the interface temperature when a Marshak wave propagates from one medium to the next

There is current interest in designing and experimentally testing a thin “window” in the gold wall of a laser-heated hohlraum that has produced an igniting capsule. This window can ultimately shine on an external physics package to extend the field of high energy density, taking advantage of the enhanced temperature of the hohlraum following ignition. The window must still have some amount of gold to ensure good drive symmetry for the implosion of the ignition capsule. This thin gold must be backed by a lower-Z material for structural integrity. Simulations of such a two-medium structure show the usual non-linear, x-radiation-driven, conduction-heating Marshak wave (MW) propagating through the thin gold. They also show the MW propagating further through the low-Z backing. The radiation-hydrodynamic simulations show a particular transition temperature at the boundary of the two media. We present here an analytic theory for this value, as a function of the low-Z material, which matches the simulations well. This work may also be of interest to the general problem of transport transitions between two media.