Normality of Monte Carlo criticality eigenfunction decomposition coefficients

Conference · Mon Jul 01 04:00:00 EDT 2013

OSTI ID:22212922

Toth, B. E.; Martin, W. R. ^[1]; Griesheimer, D. P. ^[2]

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1. Department of Nuclear Engineering and Radiological Sciences, University of Michigan, 2355 Bonisteel Boulevard, Ann Arbor, MI 48109 (United States)
2. Bechtel Bettis, Inc., P.O. Box 79, West Mifflin, PA 15122 (United States)

A proof is presented, which shows that after a single Monte Carlo (MC) neutron transport power method iteration without normalization, the coefficients of an eigenfunction decomposition of the fission source density are normally distributed when using analog or implicit capture MC. Using a Pearson correlation coefficient test, the proof is corroborated by results from a uniform slab reactor problem, and those results also suggest that the coefficients are normally distributed with normalization. The proof and numerical test results support the application of earlier work on the convergence of eigenfunctions under stochastic operators. Knowledge of the Gaussian shape of decomposition coefficients allows researchers to determine an appropriate level of confidence in the distribution of fission sites taken from a MC simulation. This knowledge of the shape of the probability distributions of decomposition coefficients encourages the creation of new predictive convergence diagnostics. (authors)

• Research Organization: American Nuclear Society, 555 North Kensington Avenue, La Grange Park, IL 60526 (United States)
• OSTI ID: 22212922
• Country of Publication: United States
• Language: English

Related Subjects

22 GENERAL STUDIES OF NUCLEAR REACTORS
97 MATHEMATICS AND COMPUTING
CAPTURE
CONVERGENCE
CORRELATIONS
CRITICALITY
EIGENFUNCTIONS
FISSION
ITERATIVE METHODS
MONTE CARLO METHOD
NEUTRON TRANSPORT
PROBABILITY
SIMULATION