A Simple Model for the Calculation of the Sodium-Voiding Effect on Neutron Leakages in a Fast Reactor Lattice I. Formalism

A simple formalism, which can be introduced into routine analyses, is presented for the calculation of the effect of sodium voiding on neutron leakages in a fast reactor lattice. The diffusion coefficients in plane or in two-dimensional lattices are calculated following a method that is very analogous to the method proposed earlier by the author for the treatment of thermal reactors. The two situations, sodium present and sodium voided, are calculated with the same approximations. It is known that it is impossible in the situation where the sodium is voided to calculate buckling-independent diffusion coefficients, for they diverge. These coefficients are hence calculated in both situations at the lowest order of the expansion in terms of the buckling, which introduces a logarithmic term. The calculation is performed in the actual geometry of the lattice without cylindricalizing the cell.