Aneutronic H + B11nuclear fusion driven by Coulomb explosion of hydrogen nanodroplets

Abstract

We consider a reaction design for table-top nuclear fusion between two distinct nuclei, with high-energy nuclei being produced by a Coulomb explosion (CE) of homonuclear nanodroplets of one reagent reacting with a solid target of a second reagent. This scheme was applied for a theoretical-computational study of the table-top aneutronic $p+{}^{11}\mathrm{B}\ensuremath{\rightarrow}3\ensuremath{\alpha}+8.7$ MeV reaction generated by a source of high-energy (0.3--6 MeV) protons produced by a CE of hydrogen nanodroplets driven by ultra-intense, femtosecond, near-infrared laser pulses and which penetrate into a solid $^{11}\mathrm{B}$ target. The averaged reaction probability and the yield for ${}^{11}\mathrm{B}(p,\ensuremath{\alpha})2\ensuremath{\alpha}$ fusion were calculated from the energy-dependent reaction probability, which was obtained from the ratio of the large fusion cross sections and the stopping power of the protons, and by the proton kinetic energy distribution function, which was obtained from scaled electron and ion dynamics simulations. The fusion yields were determined in the nanodroplet size range and in the laser intensity domain, satisfying the conditions of weak laser intensity attenuation within a single nanodroplet and within an assembly of exploding nanodroplets in the macroscopic plasma filament. The highest values of the fusion yield of 10${}^{8}$ per laser pulse were attained for the largest nanodroplets with initial radii of 200 nm at the laser peak intensity of 10${}^{19}$ W cm${}^{\ensuremath{-}2}$. The ${}^{11}\mathrm{B}(p,\ensuremath{\alpha})2\ensuremath{\alpha}$ fusion yields for the exploding hydrogen nanodroplet source-solid $^{11}\mathrm{B}$ cylindrical target are higher by three to four orders of magnitude than the yields of ${10}^{4}\ensuremath{-}{10}^{5}$ per laser pulse from a laser-irradiated mixed boron-hydrocarbon solid and from a CE of boron-hydrogen heteronuclear nanodroplets. The high efficiency for fusion within the exploding nanodroplets source-cylindrical solid target design provides guidelines for the optimization of yields for table-top nuclear fusion.