Maximization of nuclear fusion reactivity via optimal energy distributions

We investigate the optimization of nuclear fusion reactivity relative to the choice of energy probability distribution. A single Maxwell-Boltzmann (MB) distribution is found to be optimal in the region where reactivity is a concave function of the average available kinetic energy, specifically near the reactivity peak. Conversely, in regions where the reactivity curve is convex, optimization is achieved through a bimodal MB distribution. We then discuss our results in the context of three classes of generalized energy distributions (superstatistics), which are modeled as a continuum of MB distributions. As expected, in all cases examined, the reactivity gains provided by superstatistics are bounded by the proposed optimal distribution. Finally, we apply these findings to deuterium-deuterium and deuterium-tritium fusion processes using empirical parametrizations of their respective cross sections. For both reactions, employing optimal bimodal MB distributions at low average energies-of particular interest for magnetically confined plasmas-yields a reactivity enhancement of approximately a factor of 2.