Research on the Correlations of Fission Source Distribution in the Monte Carlo Algorithm Using Mathematical Tools

Abstract

In the Monte Carlo algorithm, the power iteration method is commonly used to obtain the Fission Neutron Bank of each cycle. This method uses the offspring produced by the neutrons of the previous cycle as the next cycle’s fission neutron bank. Thus, there is physical continuity between the adjacent cycle’s fission source distributions (FSD). This physical continuity of this process will lead to the mathematical correlation of fission source distributions. We extensively investigate the correlation of fission source distributions using mathematical approaches. We analyzed the correlations of the FSD with different geometric scales and the adjacent number of cycles. The results show that the correlations between two fission source distributions decline with the adjacent cycle number increases. The miniature models would take dozes of cycles for the correlations to decline to be negligible, while the standard reactor core model would use around 500 cycles to decline. These correlations should be carefully removed if a non-bias Monte Carlo calculation is carried out. In the BEAVRS core model, the correlations would result in around 80 percent underestimating the variance for the flux tally of assemblies. These methods can be easily implemented in the standard Monte Carlo codes.