Estimation of Sample Reactivity Worth with Differential Operator Sampling Method

Applicability of the Taylor series approach with the arbitrary-order differential operator sampling (DOS) method is examined for the calculation of sample reactivity worth. The DOS method is extended to obtain the differential coefficients of the effective multiplication factor and the perturbed source effect up to the arbitrary order. The methodology is implemented into a continuous-energy Monte Carlo code MVP to perform benchmark calculations. It is found that the second-order Taylor series approach gives an enough accurate result for simple fast systems of Godiva and Jezebel. A discrepancy of ∼10% is, on the other hand, observed for the Np-237 sample worth calculation for the tank-type critical assembly TCA even with the fifth-order Taylor series approach. The perturbed source effect has a significant contribution for the calculation of sample reactivity worth; it must be estimated for all the cases. Alternative approaches such as the Padé approximation, the midpoint and interpoint methods are also examined for the TCA sample worth problem. They give similar results as the ordinary higher-order Taylor series approach.