Angular Effects in Toroidal Diffusion

Analytic estimates are given for the angular dependence of the neutron (or photon) flux in toroidal geometry arising from the toroidal character of the configuration. The model used in the analysis is the one-group homogeneous diffusion model The toroidal angular effects in the local flux are shown to be first order in ϵ, the inverse aspect ratio, whereas angular effects occurring in spatial integrals of the flux are found to be of order ϵ². An analytic expression for the Green's function for diffusion equation in toroidal geometry is given correct to order ϵ², and typical numerical results are shown. A transformation of the scalar flux is presented that removes all angular dependence from the streaming term in the diffusion equation and removes the angular dependence from the absorption term correct to order ϵ. The overall conclusion reached is that angular toroidal effects are not simply characterized.