Study on X-ray Energy Deposition in Slab and Droplet Cases Using FLASH

We present a new implementation of the Beer-Lambert law within the FLASH radiation-hydrodynamics framework to model X-ray energy deposition in fusion chamber materials for inertial fusion energy systems. Using a three-dimensional–in–two-dimensional ray-tracing approach, we simulate multi-energy X-ray absorption (0.5 to 5 keV) in molten flibe across three target configurations: a 340-µm-thick cylindrical slab, a 100-µm spherical droplet, and a 5-mm spherical droplet. The Beer-Lambert model employs opacity data from the Henke database validated against transmission measurements through flibe slabs. Energy balance calculations confirm that the X-ray energy reaching the target is almost entirely absorbed, verifying the Beer-Lambert predictions. Our three-temperature radiation-hydrodynamics simulations reveal a striking scale-dependent transition in ablation dynamics: the 100-µm droplet undergoes complete rarefaction within 80 ns, while the 5-mm droplet exhibits surface ablation and shock during the X-ray pulse but subsequently expands and would rarefy on larger timescales.