Non-ideal convergence of the fission matrix fundamental eigenpair in monte-carlo calculations

Continuous energy Monte Carlo methods can simulate the transport of neutrons in nuclear reactors with the best available data and the most accurate geometrical representation. However, when systems with high-dominance ratios are simulated, the computational cost can become prohibitive. A method that could assure a faster convergence relies on the computation of the fission matrix (FM) and the extraction of its fundamental eigenpair. In this paper, the convergence of the fission matrix fundamental eigenpair is investigated. In particular, it will be demonstrated that, even though the FM-based calculation can converge faster, the quality of the results is strictly dependent on the use of an optimal mesh-size for the FM definition. This optimum, in general, is different for the fundamental eigenvalue and eigenvector. More importantly, when using a finite number of particles, the accuracy of the FM estimation through the Monte Carlo method is limited by the high statistics needed to estimate the peripheral matrix elements. It will be shown that the impossibility to estimate these elements leads to neutron clustering in the high importance zones.