Prediction of statistical error underestimation of Monte Carlo method in a two-dimensional heterogeneous system

Monte Carlo method as one of the core characteristics calculation methods is a method for probabilistically reproducing the behavior of neutrons and tracking this behavior to evaluate the physical quantities. However, this method inevitably accompanies statistical error in calculation results due to the use of a random table, and in the case of a system having a strong intergenerational correlation, the output statistical error may be underestimated. This study theoretically derived the true statistical error by approximating the generational transition of the expansion coefficient, when the neutron flux has been subjected to eigenvalue expansion, to the autoregressive model. By comparing the predicted value obtained by the theoretical formula of the statistical error underestimation ratio and the reference value calculated by statistically processing the results of the multigroup Monte Carlo code GMVP that was implemented 100 times by changing the initial random number, the appropriateness of the proposed method was verified. Although the predicted value of the underestimation rate was able to reproduce the relative spatial distribution of the reference value, there was a difference of about 0.1 to 0.25 at the edge of the system, so this cause will be examined in the future. (A.O.)