Revisiting p-$^{11}$B Fusion: Updated Cross-sections, Reactivity, and Energy Balance

TL;DR

This work reassesses p-$^{11}$B fusion viability by delivering a high-precision parameterization of the cross-section over $0$--$10$ MeV using recent measurements, including a newly observed resonance near $4.7$ MeV. Thermonuclear reactivity is computed via Maxwellian averaging, with particular attention to the resonances at $0.6$ MeV and $4.7$ MeV. The energy balance is analyzed with a self-consistent electron temperature, showing a finite temperature window where fusion power can exceed bremsstrahlung losses, even under conservative cross-section variations. The results indicate that bremsstrahlung constraints are not inherently prohibitive for p-$^{11}$B fusion under contemporary data and modeling, though exploiting this potential requires stringent plasma conditions and further experimental and theoretical refinement.

Abstract

Recent experimental progress has substantially improved the available cross-section data for the p-$^{11}$B fusion reaction, particularly in energy regions that previously lacked direct measurements. In this study, we develop a high-precision analytical parameterization of the p-$^{11}$B reaction cross-section over the 0--10 MeV energy range, incorporating the new experimental data into a continuous and numerically efficient representation. Using this parameterization, we evaluate the thermonuclear reactivity of the p-$^{11}$B reaction and examine the effects of the dominant resonance at 0.6 MeV and a newly observed resonance around 4.7 MeV. Furthermore, we assess the energy balance by analyzing the fusion power density and the electron bremsstrahlung power density. Our results indicate that p-$^{11}$B fusion is not precluded by bremsstrahlung constraints when contemporary cross-section data and self-consistent thermal modeling are employed.

Figures (9)

• Figure 1: Astrophysical $S$-factor of the p-$^{11}$B fusion reaction as a function of the center-of-mass energy. Experimental data are taken from Becker et al.Becker1987 and Mazzucconi et al.Mazzucconi2025 for $E \leq 5$ MeV, and from Buck et al.Buck1983 for $E \geq 5$ MeV. The analytic parameterization frame used herein, which is defined by Eqs. (\ref{['s123']})-(\ref{['s3']}), is shown together with previous parameterizations by Nevins and Swain Nevins2000 and Tentori et al.Tentori2023 for comparison.
• Figure 2: p-$^{11}$B fusion reaction cross-section $\sigma(E)$ as a function of the center-of-mass energy, obtained by transforming the fitted astrophysical $S$-factor using Eq. (\ref{['SE']}). The cross-section corresponds to the same parameter set shown in Fig. \ref{['fig:Sfactors']}.
• Figure 3: Thermonuclear reactivity of the p-$^{11}$B reaction as a function of ion temperature. The red solid curve shows the result obtained with inclusion of the resonance structure near 4.7 MeV, while the blue dashed curve corresponds to the calculation with this resonance removed.
• Figure 4: Ratio of the thermonuclear reactivity calculated without the 4.7 MeV resonance to that obtained with the full cross-section parameterization, shown as a function of ion temperature.
• Figure 5: Illustrative variations of the p-$^{11}$B reaction cross-section associated with the dominant resonance near 0.6 MeV and the newly observed resonance around 4.7 MeV. These variations are used to assess the sensitivity of the thermonuclear reactivity to uncertainties in the resonance structures.