A New Accumulation Scheme for the Monte Carlo Implementation of the Modified Power Method

Abstract

The Modified Power Method (MPM) has been implemented and applied to three-dimensional (3D) criticality eigenvalue problems. Monte Carlo (MC) implementation of the MPM has been difficult due to the inherent statistical noises introduced during the MC simulations. The one-cycle tally should be avoided because it contains too much noises and cause big fluctuation in the MPM simulation. Therefore, accumulation should be adopted. In addition, previous studies have shown that to obtain the first several eigenmodes for the multi-dimensional problems, more number of sub-regions than the number of desired eigenmodes should be adopted for the calculation of the transfer matrix, which makes the linear system of equations become over-determined and the accumulation become problematic. In this paper, a proper accumulation scheme was developed, which was based on the preprocessing of the neutron weight integrals. The performance of the proposed method has been successfully demonstrated with the 3D numerical tests.