Biases in the estimation of k sub(eff) and its error by Monte Carlo methods

Biases occur in the estimation of K sub(eff) and its variance by conventional Monte Carlo programs simulating neutron transport theory. The simple method embodied in the U.K. code MONK is analysed and formulae for the biases are worked out. The K sub(eff) bias is found to be of order M super(-1) whi...

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Bibliographic Details
Published in:Annals of nuclear energy 1986-01, Vol.13 (2), p.63-83
Main Authors: Brissenden, R J, Garlick, A R
Format: Article
Language:English
Online Access:Get full text
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Summary:Biases occur in the estimation of K sub(eff) and its variance by conventional Monte Carlo programs simulating neutron transport theory. The simple method embodied in the U.K. code MONK is analysed and formulae for the biases are worked out. The K sub(eff) bias is found to be of order M super(-1) whilst that of the variance is of order (NM) super(-1), where M is the number of neutrons in a stage and N is the number of stages. The K sub(eff) bias is shown to be the same as that derived by Gelbard and Prael (1974) and Zolotukhin and Maiorov (1983). A physical explanation of it is given and used to construct a weighting method for its elimination. A new algorithm for the Monte Carlo simulation is devised which effectively gets rid of both biases and, as a bonus, reduces the true variance of the sampling for K sub(eff). The result is a method which can cope with systems beyond the range of conventional powering, and which has better fail-safe characteristics for criticality applications.
ISSN:0306-4549