Derivation of multigroup diffusion coefficients to preserve moments of neutron migration

Although nodal diffusion codes are in major use for reactor analysis, the methods used to generate the required multigroup diffusion coefficients are often proprietary. The generation of these coefficients is still an active area of research in the open literature. Recently, the Cumulative Migration Method (CMM) was introduced to define diffusion coefficients using Monte Carlo codes, and has shown good results. However, the mathematical framework of CMM in previous publications is relatively light. In this paper, we provide a detailed mathematical framework for CMM, together with methods to obtain equivalent results to CMM that can be implemented in existing deterministic lattice codes. The mathematical framework presented in this paper sheds light on the exact physical quantity that is preserved by the CMM’s diffusion coefficient definition. However, both CMM itself and the framework given in this work only apply to single assembly lattice problems. Additional work is necessary to generalize this framework, as well as its implementations, to colorset problems.