Perturbation theory for nuclear fuel depletion calculations with predictor-corrector method

The perturbation theory for nuclear fuel depletion calculations with the predictor-corrector method is derived. This theory is implemented to a reactor physics code system CBZ, and the theory itself and its implementation are numerically verified. Sensitivities of nuclide number densities after fuel depletion with respect to nuclear data calculated with this theory are compared with reference sensitivities calculated by numerical differentiation, and good agreements are obtained. Importance of accurate angle integration on product of neutron flux and generalized adjoint neutron flux is also pointed out. Sensitivities in a 3x3 multi-cell system including a gadolinium-bearing fuel pin are calculated, and it is demonstrated that the derived theory yields accurate sensitivities even if coarse depletion time step division is adopted. The present work drastically increases the applicability of the depletion perturbation theory to actual problems