A model for analytical calculations of synthetic neutron energy spectra from beam-target reactions

We present a fully analytical model for calculating energy spectra of neutrons generated by fusion reactions involving a fast ion, or beam, and a stationary ion, or target, in magnetic fusion plasmas. For neutrons moving along the line-of-sight of a detector, the neutron spectrum is given by an analytical expression and the usual differential cross section. This makes the model several orders of magnitude faster than ordinary Monte Carlo simulations and free of any related statistical noise. Additionally, the analytical description of the reaction physics provides much more insight into the formation of the spectrum. An example of this is the bias of beam-target spectra towards high-energy neutron counts, which corresponds to forward-emission events. On the other hand, the fast-ion uniform gyro-angle distribution has an opposite effect, but is ultimately weaker than the preferential forward emission of neutrons. The model is validated against numerical calculations from the forward model code GENESIS to verify its validity and it is furthermore derived from a probabilistic viewpoint, adding further insight.