Enhancement of fusion reactivities using non-Maxwellian energy distributions

We discuss conditions for the enhancement of fusion reactivities arising from different choices of energy distribution functions for the reactants. The key element for potential gains in fusion reactivity is identified in the functional dependence of the tunneling coefficient on the energy, ensuring the existence of a finite range of temperatures for which reactivity of fusion processes is boosted with respect to the Maxwellian case. This is shown using a convenient parametrization of the tunneling coefficient dependence on the energy, analytically in the simplified case of a bimodal Maxwell-Boltzmann distribution, and numerically for kappa distributions. We then consider tunneling potentials progressively better approximating fusion processes and evaluate in each case the average reactivity in the case of kappa distributions.