A relation of the coupling coefficient to the eigenvalue separation in the coupled reactors theory

Abstract-A relation of the coupling coefficient with eigenvalues for coupled reactors is given by making use of the rigorous expression for the coupling coefficient derived by using the region-wise importance function to produce fission neutrons. From this relation, an approximate relation of the coupling coefficient to the eigenvalue separation of the fundamental and first higher mode is obtained, in which the coupling coefficient is expressed simply in terms of the difference of the two eigenvalues. It is shown numerically for simple coupled reactors of one dimensional slab geometry by comparing with exact values that the accuracy of this relation becomes better as the strength of the coupling between cores becomes weaker