Anisotropic Neutron Diffusion in Lattices of the Zero-Power Plutonium Reactor Experiments

Diffusion coefficients are computed for a typical lattice cell of the zero-power plutonium reactor experiments using the methods of Benoist and Bonalumi. It is noted that the diffusion coefficients, D_x, for leakage normal to the plates, as defined by Benoist and by Bonalumi, are both double valued. The spread between Benoist’s x-diffusion coefficient is, in the lattice cell, over half as large as the difference between D_x and D_y. Bonalumi’s x-diffusion coefficients are much farther apart, the interval between them being considerably larger than the difference between D_x and D_y. Neither the Benoist nor the Bonalumi method yields homogenized diffusion coefficients that preserve fluxes, reaction rates, or eigenvalues. Using an approach similar to that of Deniz, the diffusion coefficient is redefined and constructed in such a way as to guarantee that eigenvalues will be preserved in the homogenization process. The relation between the new diffusion coefficients and the Benoist coefficients is discussed.