Fission source convergence diagnosis in Monte Carlo eigenvalue calculations by skewness and kurtosis estimation methods

Abstract

In this study, a skewness estimation method (SEM) and kurtosis estimation method (KEM) are introduced to determine the number of inactive cycles in Monte Carlo eigenvalue calculations. The SEM and KEM can determine the number of inactive cycles on the basis that fully converged fission source distributions may follow normal distributions without asymmetry or outliers. Two convergence criteria values and a minimum cycle length for the SEM and KEM were determined from skewness and kurtosis analyses of the AGN-201K benchmark and 1D slab problems. The SEM and KEM were then applied to two OECD/NEA slow convergence benchmark problems to evaluate the performance and reliability of the developed methods. Results confirmed that the SEM and KEM provide appropriate and effective convergence cycles when compared to other methods and fission source density fraction trends. Also, the determined criterion value of 0.5 for both ε1 and ε2 was concluded to be reasonable. The SEM and KEM can be utilized as a new approach for determining the number of inactive cycles and judging whether Monte Carlo tally values are fully converged. In the near future, the methods will be applied to various practical problems to further examine their performance and reliability, and optimization will be performed for the convergence criteria and other parameters as well as for improvement of the methodology for practical usage.

Keywords

• Monte Carlo
• Eigenvalue
• Convergence
• Fission source distribution
• Skewness
• Kurtosis