On the Upper Bound of Non-Thermal Fusion Reactivity with Fixed Total Energy

TL;DR

This paper investigates the theoretical upper limit of fusion reactivity when a non-thermal reactant coexists with a thermal background, revealing potential reactivity enhancements up to 300% through optimized velocity distributions.

Contribution

It introduces an optimization framework to determine the maximum fusion reactivity with a non-thermal reactant, providing new upper bounds and insights for fusion energy research.

Findings

Maximum reactivity exceeds Maxwellian cases by 50-300%.

Non-thermal reactants often form beam-like velocity distributions.

Results offer upper bounds and strategies for reactivity enhancement.

Abstract

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.