Multigroup Diffusion Coefficients from Transport Theory

Operations are performed on the neutron transport equation in general form to obtain an exact multigroup Fick’s Law formalism consistent with the standard multigroup conservation equation. The inherent accuracy of the transport equation is maintained in the derived form of the spatially dependent “diffusion coefficient,” which is shown to be highly dependent on the angular flux spectra. Numerical investigations on fast reactor configurations substantiate the feasibility of incorporating a transport calculated diffusion coefficient in existing diffusion theory codes for reactor design and analysis with dual utility: (a) the errors in diffusion calculations due to incorrect diffusion coefficients can be separated from boundary-condition errors, and (b) the diffusion calculations of certain parametric design studies can be improved to accuracy approaching that of transport theory using spatially averaged diffusion coefficients obtained from a single transport calculation.