The Definition of Neutron Diffusion Parameters for a Uniform Reactor Lattice

Two equally valid systems of definitions are given for the neutron diffusion parameters of a reactor lattice: cell-average and cell-surface. In defining the cell-average parameters, we imagine a macroscopic flux distribution to be fixed in space while the lattice is translated with respect to it. In defining the cell-surface parameters, we work in terms of fluxes and currents on the surface of a cell having the fissile material at its center. Parameters from both systems have been used before; but until recently we have lacked complete clarity of definition and the realization that there are two valid systems of parameters that should not be mixed in the one calculation. The early formula, L² is equal to the summation over all values of i of f_iL_i², is for a cell-average thermal diffusion area; L² = (outleakage)/B² (absorption), applied to a cell with the fissile material at the center, is a cell-surface diffusion area and is less than the summation over all values of i of f_iL_i² by ≈(lattice spacing)²/24.