Error estimations and their biases in Monte Carlo eigenvalue calculations

Journal Article · Wed Jan 01 04:00:00 EST 1997 · Nuclear Science and Engineering

DOI:https://doi.org/10.13182/NSE97-1· OSTI ID:445398

Ueki, Taro ^[1]; Mori, Takamasa; Nakagawa, Masayuki ^[2]

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1. Univ. of Michigan, Ann Arbor, MI (United States). Dept. of Nuclear Engineering and Radiological Sciences
2. Japan Atomic Energy Research Inst., Tokai, Ibaraki (Japan). Tokai Establishment

In the Monte Carlo eigenvalue calculation of neutron transport, the eigenvalue is calculated as the average of multiplication factors from cycles, which are called the cycle k{sub eff}`s. Biases in the estimators of the variance and intercycle covariances in Monte Carlo eigenvalue calculations are analyzed. The relations among the real and apparent values of variances and intercycle covariances are derived, where real refers to a true value that is calculated from independently repeated Monte Carlo runs and apparent refers to the expected value of estimates from a single Monte Carlo run. Next, iterative methods based on the foregoing relations are proposed to estimate the standard deviation of the eigenvalue. The methods work well for the cases in which the ratios of the real to apparent values of variances are between 1.4 and 3.1. Even in the case where the foregoing ratio is >5, >70% of the standard deviation estimates fall within 40% from the true value.

• Sponsoring Organization: USDOE
• OSTI ID: 445398
• Journal Information: Nuclear Science and Engineering, Journal Name: Nuclear Science and Engineering Journal Issue: 1 Vol. 125; ISSN NSENAO; ISSN 0029-5639
• Country of Publication: United States
• Language: English

Related Subjects

22 GENERAL STUDIES OF NUCLEAR REACTORS
DATA COVARIANCES
EIGENVALUES
ITERATIVE METHODS
MONTE CARLO METHOD
MULTIPLICATION FACTORS
NEUTRON TRANSPORT
PROBABILISTIC ESTIMATION
REACTOR KINETICS