Calculations of spatial harmonics in two-dimensional multiplicative systems

The improved power method in the higher-harmonic eigenvalue calculation of nuclear plant thermal-hydraulic dynamics was applied to the λ- and ω_p-eigenvalue problems of thermal and fast reactor systems to obtain the two-dimensional, few-energy-group higher-harmonic eigenvalues and eigenfunctions. As a result, the efficiency of the method was confirmed in the large-scale neutron diffusion problems consisting of the variables amounting to tens of thousands, and the interesting spatial patterns of the eigenfunction were obtained. Even though a harmonic order may be lower, the discrepancy between λ- and ω_p-eigenfunctions, which are usually assumed to be approximately identical, is significant in a thermal system with low-absorbing region (e.g. reflector). In the higher ω_p-harmonics of the system, zero loci of the eigenfunctions depend on neutron energy group. Therefore, the particular attention should be paid to placements and energy-response of detectors in the kinetic experiments. (author)