Monte Carlo Calculation Method for Reactor Period Utilizing the Differential Operator Sampling Technique

The inverse reactor period alpha is a fundamental mode eigenvalue of the alpha-mode nonlinear Boltzmann eigenvalue equation that considers delayed neutron contributions. Thus far, several Monte Carlo methods, including the alpha-k, weight balancing, and transition rate matrix methods, have been developed to calculate alpha. This study presents a new Monte Carlo method for predicting alpha by using the derivatives of the k-eigenvalue with respect to alpha. Formulae are derived to calculate the first and second derivatives using the differential operator sampling method. The key feature of the new proposed method is its ability to estimate the uncertainty of the predicted alpha by considering the uncertainty of the k-eigenvalue and its derivatives with respect to alpha.