Relationship between flux tilt in two-energy-group and eigenvalue separation

A new formula of flux tilt in two-energy-group is defined and a higher-mode and higher-order formulation of flux tilt in two-energy-group is successfully derived on the basis of the modified explicit higher order perturbation (MHP) method, and a relationship between the flux tilt in two-energy-group and the first-mode eigenvalue separation is obtained. Then, it was found that the flux tilt in two-energy-group is proportional to the perturbed reactivity and inversely proportional to the first-mode eigenvalue separation. To show the validity of the relationship, numerical simulations are performed with two-energy-group for a decoupling core at the Kyoto University Critical Assembly (KUCA). Through the numerical simulations for inferring the eigenvalue separation from the perturbed reactivity and the degree of flux tilt induced by a perturbation, it was shown that the validity of the relationship is confirmed and that the flux tilt is independent of the neutron energy. Moreover, by considering the higher-mode and the higher-order terms in the new formula, it was found that the effects of the higher-mode and the higher-order components can be clearly observed in the decoupling core.