3-D anisotropic neutron diffusion in optically thin channels

Neutron diffusion theory is an approximation that accurately describes the neutron transport process for optically thick, scattering-dominated systems in which the angular neutron flux is a weak function of angle. These conditions imply that standard fine-mesh diffusion theory cannot be used for the design and analysis of Very High Temperature Reactors (VHTRs), in which narrow but nearly voided channels occurring in the reactor core can lead to boundary layer effects and angular fluxes that are strong functions of angle. Here we show that a new, more accurate diffusion equation can be derived for such problems. This new diffusion approximation is the same as the standard equation away from optically thin regions, but has different anisotropic diffusion coefficients near optically thin regions. The new diffusion approximation significantly improves the accuracy of diffusion simulations without significantly increasing the computational cost.