Interpretation of control rod interaction effect on the basis of modal approach

A theoretical expression of reactivity interaction between control rods is developed on the basis of the explicit higher-order perturbation method. The expression shows that the magnitude of the interaction is inversely proportional to the λ-mode eigenvalue separation and dependence on the rod patterns is governed by the higher-harmonic eigenfunctions and the adjoint ones. Application of the formula is illustrated by numerical calculations carried out for a 1-D model of a large fast reactor core. The results indicate that the first harmonics dominantly contribute to the interaction, consequently the first-harmonic eigenvalue separation can be employed as a quantitative indication of interaction effect.