Stochastic differential equations for non-analog Monte Carlo model of point kinetics equations

Abstract

The stochastic form of one-point and two-point reactor kinetics models have been extensively investigated in the literature. We have noticed that, in some studies, the probabilistic nature of neutron interaction mechanisms was not incorporated truly. For instance, in the case of negative reactivity insertions, one of the presented probability functions becomes negative, making the Monte Carlo (MC) simulation impossible. In this manuscript, the non-analog stochastic point reactor kinetics models are developed to simulate the stochastic behavior of nuclear systems. To reduce the imposed variance from the leakage and capture of neurons, both capture and leakage events are sampled implicitly. Precursors are also forced to decay in each simulation step. The true variances of the neutron’s and delayed neutron precursor’s populations are determined from the solution of the developed non-analog stochastic models. Also, they are compared with those of both analog and non-analog Monte Carlo methods. The results show that the analog Monte Carlo (MC) has a larger variance than the non-analog MC.