Hybrid collisional-radiative modeling for high-fidelity atomic kinetics

TL;DR

This work addresses the computational cost of high-fidelity collisional-radiative modeling by developing hybrid schemes that retain fine-structure detail for lower-lying states while statistically averaging higher-lying states into superconfigurations. Implemented within the Fusion Collisional-Radiative (FCR) code and using FAC-generated atomic data, two variants—Hybrid-($n_ ext{valence}+4$) and Hybrid-($n_ ext{valence}$)—balance accuracy and efficiency across He, Li, and Be. Benchmark comparisons against fully FS CR calculations show that Hybrid-($n_ ext{valence}+4$) reproduces radiative power loss, average charge, and effective charge to within a few percent for most conditions, while the reduced hybrid exhibits larger deviations at low temperatures where metastable populations are important; efficiency gains are substantial (up to $\sim$25× for Be and $\sim$6–18× for the other elements). The approach enables scalable, predictive plasma modeling for fusion, astrophysical, and laboratory plasmas, and can be extended to higher-$Z$ ions and non-Maxwellian electron distributions in future work.

Abstract

The fidelity of collisional-radiative (CR) models is critical for advancing our understanding of radiative properties and ionization balance in fusion plasmas. In this work, we present and evaluate hybrid CR schemes that combine fine-structure resolution with superconfiguration averaging, offering a practical compromise between accuracy and computational efficiency. Two hybrid CR models are developed for helium, lithium, and beryllium, retaining detailed fine-structure states up to selected principal quantum numbers, while higher-lying states are statistically averaged to form superconfigurations. These models are applied to compute radiative power loss, as well as average and effective charge states, across a wide range of electron temperatures and densities. The results are benchmarked against a fully fine-structure-resolved CR model to assess the accuracy of the hybrid approach. The findings demonstrate the versatility of hybrid CR schemes and their suitability for detailed plasma simulations where predictive fidelity must be balanced with computational cost.

Figures (8)

• Figure 1: Hydrogen: Comparison of radiative power loss calculated using the superconfiguration ($-\cdot$), configuration-average ($\cdots$), and fine-structure (--) CR models for $n_e = 10^{12}$ cm$^{-3}$. It is noteworthy that the superconfiguration and configuration-average CR models shown here are constructed through statistical averaging of the underlying fine-structure states and the atomic processes connecting them.
• Figure 2: Schematic of the hybrid scheme for helium (or helium-like ions), showing transitions among fine-structure states, superconfiguration states, and the "handshake" coupling that connects these two regimes. The lower-lying levels are treated with full fine-structure resolution, while higher-lying and continuum-like states are grouped into superconfigurations.
• Figure 3: Helium: Comparison of (a) radiative power loss, (b) average charge state, and (c) effective charge state obtained from the fine-structure CR model and two hybrid models, Hybrid-($n_\text{valence}$) and Hybrid-($n_\text{valence}+4$), at $n_e = 10^{14}$ cm$^{-3}$. The right-hand axes show the percentage deviation of each hybrid model from the fine-structure results. Here, "val." = valence and "Hyb." = Hybrid.
• Figure 4: Helium: Parity plots comparing (a) radiative power loss, $P_\mathrm{rad}$, (b) average charge state, $Z_\mathrm{avg}$, and (c) effective charge state, $Z_\mathrm{eff}$, predicted by the Hybrid-($n_\text{valence}$) and Hybrid-($n_\text{valence}+4$) models against the fine-structure CR model across electron densities from $10^{12}$ to $10^{17}$ cm$^{-3}$. The dashed diagonal represents perfect agreement ($y = x$); points closer to the line indicate better agreement with the fine-structure benchmark.
• Figure 5: Lithium: Comparison of (a) radiative power loss, (b) average charge state, and (c) effective charge state obtained from the fine-structure CR model and two hybrid models, Hybrid-($n_\text{valence}$) and Hybrid-($n_\text{valence}+4$), at $n_e = 10^{14}$ cm$^{-3}$. Right-hand axes show the percentage deviation of each hybrid model from the fine-structure results. Here, "val." = valence and "Hyb." = Hybrid.