On the upper bound of non-thermal fusion reactivity with fixed total energy

Fusion reactivity represents the integration of fusion cross-sections and the velocity distributions of two reactants. In this study, we investigate the upper bound of fusion reactivity for a non-thermal reactant coexisting with a thermal Maxwellian background reactant while maintaining a constant total energy. Our optimization approach involves fine-tuning the velocity distribution of the non-thermal reactant. We employ both Lagrange multiplier and Monte Carlo methods to analyze Deuterium–Tritium (D–T) and proton-Boron11 (p-B11) fusion scenarios. Our findings demonstrate that, within the relevant range of fusion energy, the maximum fusion reactivity can often surpass that of the conventional Maxwellian–Maxwellian reactants case by a substantial margin, ranging from 50% to 300%. These enhancements are accompanied by distinctive distribution functions for the non-thermal reactant, characterized by one or multiple beams. These results not only establish an upper limit for fusion reactivity but also provide valuable insights into augmenting fusion reactivity through non-thermal fusion, which holds particular significance in the realm of fusion energy research.