A minimum mechanistic model for hohlraum radiation temperature

A minimum model that maps the time-dependent laser power to the corresponding radiation temperature (Tr) pulse in the inertial confinement fusion hohlraum is presented. Instead of using phenomenological scaling laws for the wall albedo, the underlying Marshak wave is explicitly solved. The model consists of only two ordinary differential equations: one describes the propagation of the Marshak wave into the wall material, and the other describes the overall balance of energy. By assuming a self-similar spatial temperature profile of the Marshak wave, material properties such as heat capacity and opacity are effectively packed into a single dimensionless parameter, which is then calibrated against a single reference data of re-emission factor. The model has minimum complexity, but achieves remarkable agreement with experiments and simulations for a diverse set of time-dependent laser-Tr mapping cases collected from the literature. This model allows for both forward and inverse mappings between laser and Tr pulses, which is useful for preliminary hohlraum designs. It also enables rapid sampling of “realistic” Tr pulses on large scales, which can be used in machine-learning exploration of the design space of Tr pulses.