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Volumetric neutron sources (VNS) are being developed to produce 14 MeV DT neutrons for fusion materials testing. To limit the size and cost of such VNS, beam-driven systems utilising beam-target fusion reactions are widely studied [1]. Accurate prediction of the beam-target fusion rate is therefore essential for VNS design. Beam-target fusion rates are typically evaluated by first calculating the beam ionisation distribution, then following the ions as they slow down, and finally combining the resulting fast-ion density with the background plasma to obtain the fusion rate. This workflow neglects the depletion of fast ions by fusion reactions during slowing down, causing the steady-state fast-ion distribution—and consequently the fusion rate—to be systematically overestimated.
We implement a self-consistent treatment in ASCOT5 [2] by reducing marker weights at each time step according to the local fusion probability. This accounts for the loss of ions due to fusion during the slowing-down simulation. For a representative VNS spherical tokamak case with 150 keV NBI tritium, neglecting fusion depletion overestimates the fusion power by 0.2% and the steady-state fast-ion density by 0.3%. The latter error propagates into various moments that can be evaluated from the distribution, for instance, the power deposition.
The discrepancy increases with slowing-down time because ions have more opportunity to undergo fusion. In a homogeneous 20 keV plasma with 1 MeV deuterium ions, neglecting fusion depletion overestimates the fusion rate by 1.8%, while the total steady-state fast-ion probability mass differs by 1.5%. These results not only facilitate accounting for the fusion depletion in numerical calculations but also demonstrate the parameter space where such effects could potentially make a significant difference.
[1] C. Bachmann et al., ‘Progress in the concept development of the VNS—a beam-driven tokamak for component testing’, Nucl. Fusion, vol. 66, no. 4, p. 046015, Mar. 2026, doi: 10.1088/1741-4326/ae4e46.
[2] K. Särkimäki, ‘ASCOT5 5.6.3 documentation’. Accessed: May 27, 2026. [Online]. Available: https://ascot4fusion.github.io/ascot5/index.html