Investigations on the migration mode method (MMM) for reactor calculations

Abstract

Current calculation codes for reactor analysis are based on the multi-group method to evaluate energy distribution of neutron flux. Usually a two energy group diffusion equation is adopted. This choice is adequate for PWRs associated to cross sections libraries tabulated versus fuel exposure and other state parameters as moderator density, fuel temperature, boron concentration. An improvement of this approach is represented by the migration mode method (MMM) by which the neutron spectrum is expanded in terms of base functions corresponding to the different modes of migration of the neutrons in the energy dimension. For a thermal reactor, three such functions may be easily identified: the Maxwellian distribution of the neutrons at thermal equilibrium with the moderator, the 1/ E slowing down distribution (corrected to take into account resonance absorption effects) and the fission neutron spectrum. The (space-dependent) coefficients of the expansion are calculated by solving a differential equation which results having a structure similar to the one relevant to multi-group theory. The method can therefore be easily implemented adopting existing diffusion theory codes. With the present work, some investigations on the MMM are described relevant to UO 2 fuelled PWR systems. Demonstrative results are given to validate the potentiality of the method.