The production spectrum in fusion plasmas

Significant broadening of the energy spectrum of the products of nuclear reactions occurs in fusion plasmas. We provide a method for calculating the shape of this production spectrum for arbitrary plasma distribution functions. The method is exact and can be used for both isotropic and anisotropic distributions. We derive expressions for Maxwellian (both stationary and moving with a bulk fluid velocity), bi-Maxwellian and beam-target plasmas. The neutron spectrum produced by the D + D → He3 + n reaction is studied as an example. It is shown that the neutron spectrum produced from a Maxwellian plasma becomes asymmetric at high plasma temperatures with a long high-energy tail. The effect of bulk fluid velocity on the neutron spectrum is shown to be significant in some cases. In particular, the spectrum produced by an imploding shell has a much greater FWHM than the spectrum obtained from a stationary plasma. The spectrum produced by a beam-target interaction shows significant anisotropy in the high-energy tail as the viewing angle varies from perpendicular to parallel to the beam direction.