Analytical expressions for fusion spectra produced in ‘‘beam-target’’ fusion reactions

For ‘‘beam-target’’ fusion reactions, collimated measurements of the energy spectrum of one of the reaction products can provide information on the degree of anisotropy of the reacting beam ions. Analytical expressions relating the fusion spectrum to the velocity distribution of the beam ions are given. Application of the expressions to measurements of the spectrum of 15-MeV protons produced by reactions between energetic 3He ions and relatively cold deuterons during ICRF heating in the PLT tokamak indicate that the velocity distribution of fast 3He ions is peaked perpendicular to the tokamak magnetic field.