A new method for calculating the weak source startup of reactor based on Monte Carlo method

Weak source startup represents a reactor startup regime in which neutron population evolution is dominated by stochastic effects and cannot be adequately described using conventional deterministic or point-kinetics approaches. The weak source startup approach, which operates without an external neutron source, eliminates the need for costly neutron source procurement and improves the economic performance of nuclear power plants. In this study, a Monte Carlo based method is developed for simulating weak source startup processes. The proposed approach enables direct time-dependent simulation of stochastic neutron transport and allows the transition from stochastic to deterministic behavior to be identified through the evolution of the fission rate. Unlike traditional stochastic neutron kinetics methods, which are typically limited to simplified geometries, the present method is applicable to realistic three-dimensional reactor configurations. The method is demonstrated using both a KRUSTY heat-pipe-cooled reactor and a small pressurized water reactor. The results show that the transition time during weak source startup exhibits inherent statistical variability and that the spatial distribution of maximum neutron flux gradually becomes concentrated as the neutron population increases. The proposed framework provides a practical computational tool for analyzing weak source startup phenomena in engineering-scale reactor systems.