The Marshak wave model extended to converging geometry and hydrodynamic response as a guide to radiation trapping experiment design

An opaque internal pusher layer is a standard component of the “volume-burn” approach to inertial confinement fusion ignition as a “radiation trap” to reduce hot-spot cooling prior to ignition. We quantify the effectiveness of radiation trapping by means of a reduced model where the radiation escapes via a diverging Marshak wave. The well-known Marshak wave model is extended to include geometrical divergence effects and the hydrodynamic response of the pusher layer to the radiation-driven heat wave. This defines a comprehensive design-parameter space for anticipating radiation trapping effectiveness in experiments on existing and planned platforms and for selecting interesting cases for more realistic integrated simulations. To generalize the Marshak wave model to diverging geometry, the temperature boundary condition of the source surface has been replaced by a fluence boundary condition which we have verified numerically. Marshak waves carry substantial flux, and in some cases, they are not effective radiation traps. This material is based upon work supported by the Department of Energy National Nuclear Security Administration under Award Number DE-NA0003856.