Comparison of tungsten versus molybdenum for double shell capsules using machine learning design optimization

Double shell targets are an alternative ignition platform for inertial confinement fusion. One design consideration for double shell targets is the choice of inner shell material to help trap radiation emitted by the hot fuel to aid ignition. Materials such as molybdenum and tungsten are of interest for the inner shell layer of the targets. While molybdenum has a lower density that could inhibit instability growth and allow for radiography and code benchmarking, tungsten has a higher density that could provide more compression and confinement. These tradeoffs have been explored using optimized designs for each material. Our previous work [Vazirani et al., “Coupling 1D xRAGE simulations with machine learning for graded inner shell design optimization in double shell capsules,” Phys. Plasmas 28, 122709 (2021); Vazirani et al., “Coupling multi-fidelity xRAGE with machine learning for graded inner shell design optimization in double shell capsules,” Phys. Plasmas 30, 062704 (2023); and Vazirani et al., “Bayesian batch optimization for molybdenum versus tungsten inertial confinement fusion double shell target design,” Stat. Anal. Data Min. 17, e11698 (2024)] resulted in a multi-fidelity Bayesian optimization framework to find yield-optimized double shell target geometries. By leveraging simulations of varying fidelities (one-dimensional and two-dimensional) to inform one another, the multi-fidelity optimization was able to optimize a design in the highest fidelity with significantly fewer simulations than would be used in a systematic parameter scan. In this work, we apply the multi-fidelity Bayesian optimization to explore the optimized designs of double shell targets with molybdenum and tungsten inner shells as well as the physics producing the high performing implosions. A physics exploration of all the simulations used in this study shows trends in designs that contribute to high yields, ion temperatures, and fuel areal densities. Comparison of molybdenum and tungsten simulations shows that they can produce similar implosion conditions with different geometries, which would be important to study in experiments. Graded density layers produce varying performances with the two materials but continue to be of interest for future studies along with studies of doped inner shell materials and applied surface roughness.