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Maximization of nuclear fusion reactivity via optimal energy distributions

Roberto Onofrio1,*, Kamel Ourabah2,†, and Carlo Presilla3,‡

  • 1Department of Physics and Astronomy, Dartmouth College, 6127 Wilder Laboratory, Hanover, New Hampshire 03755, USA
  • 2Faculty of Physics, University of Bab-Ezzouar, USTHB, Boite Postale 32, El Alia, 16111 Algiers, Algeria
  • 3Dipartimento di Matematica, Sapienza Università di Roma, Piazzale Aldo Moro 2, 00185 Rome, Italy

  • *Contact author: onofrior@gmail.com
  • †Contact author: kam.ourabah@gmail.com
  • ‡Contact author: carlo.presilla@uniroma1.it
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Phys. Rev. E 114, 044136 – Published 23 October, 2026

DOI: https://doi.org/10.1103/xhzy-hxdw

Abstract

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.

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Information

Phys. Rev. E 114, 044136– Published 23 October, 2026
  • Received 18 June 2026
  • Accepted 2 October 2026
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