Higher order perturbation calculation with higher mode eigenfunctions in homogeneous system

By introducing two perturbed systems from a homogeneous core the higher order perturbation calculation of a heterogeneous core was performed to obtain the neutron flux and reactivity change with the higher mode eigenfunctions in the homogeneous core system which is considered to be an unperturbed system. The main feature of this perturbation calculation is to express analytically the perturbed flux with the trigonometric functions for the purpose of saving a computational time to obtain numerically the higher mode eigenfunctions in the unperturbed system beforehand the perturbation calculation. Then the two higher order perturbation calculations were executed by the Modified Explicit Higher Order Perturbation (MHP) method with two energy groups in a two-dimensional x-y geometry for the two perturbed systems. The objective reactivity was obtained from the difference between the two calculated results of perturbation. For the heterogeneous bare system it was demonstrated that the neutron flux and reactivity change can be accurately evaluated by this perturbation calculation with large numbers of expansion modes and perturbation orders and that the computational time can be reduced economically. However for the perturbation causing the big difference in group constants from the unperturbed system including the change from a bare core with the reflector it was found that the higher order perturbation calculation encounters the difficulty which is closely related to that pointed out so far for the application of explicit higher order perturbation theory itself.