An application of the Wiener–Hopf method to the one-speed flat-flux problem in a half-space

Details of the spatial distribution of the fissile material needed to maintain a flat flux in a half-space in the region τ>0 are given. The method of Wiener and Hopf is employed to solve the resulting integral equation. In addition to the scalar flux we calculate the angular flux and show that this is not spatially constant in τ>0, even though the associated scalar flux is constant. As a measure of the anisotropy of the angular flux, we calculate the neutron current in τ>0 for a range of reflector absorptions and also the angular distribution at the boundary τ=0. For comparison purposes, the diffusion theory analogue of the problem is given in the Appendix.