Radiation temperature is a key quantity in indirect drive inertial confinement fusion. Based on Marshak-wave scaling, Callahan et al. established a scaling relation between hohlraum radiation temperature and wall absorbed energy, from which a simple model was developed for rapid evaluation in low-gas-fill hohlraums^[1]. However, the formulation is referenced to a baseline cylindrical hohlraum and neglects the explicit loading-time dependence in the Marshak-wave scaling. As a result, the radiation-temperature behavior must be described by empirical piecewise slopes, whose fitted values show noticeable design dependence.

In this work, we extend the scaling from the perspective of wall energetics. The scaling is expressed in terms of wall-absorbed laser energy per unit wall area, and the Marshak-wave wall-loss relation for a constant-temperature source is extended to a time-dependent radiation-temperature history by a perturbative treatment. This yields a unified full-pulse linear relation that remains robust across substantially different hohlraum geometries and pulse designs, including complex configurations beyond the baseline cylindrical hohlraum. Based on this relation, a simplified model is constructed for rapid evaluation of radiation-temperature histories. By further introducing a backscatter fraction scaling law constrained by experimentally measured backscatter light, the model can be extended to higher-gas-fill hohlraums. The resulting framework provides an efficient tool for design evaluations, parameter scans, and shot comparisons.
[1] D. A. Callahan, O. A. Hurricane, A. L. Kritcher et al., “A simple model to scope out parameter space for indirect drive designs on NIF,” Phys. Plasmas 27, 072704 (2020).
 

inertial confinement fusion,hohlraum,radiation temperature