Two-step Monte Carlo sensitivity analysis of alpha- and gamma-eigenvalues with the differential operator sampling method

Abstract

A new Monte Carlo method is developed to calculate the sensitivity coefficients of the α-eigenvalue (the time decay constant) and the γ-eigenvalue (the spatial decay constant in an exponential experiment) with respect to nuclear data. A method that was previously developed for the sensitivity analyses of the α-eigenvalue, which is not based on the normal k-α algorithm, is not applicable to the γ-eigenvalue due to its inability to obtain a converged source distribution. Then, a two-step method in which two sensitivity coefficients are separately calculated using the k-α or k-γ algorithm and the differential operator sampling method is newly developed. The sensitivity coefficient of the α- or γ-eigenvalue is represented by the ratio of the two sensitivity coefficients. Some numerical tests for three-energy group problems are performed using the new method. The sensitivity coefficients that are obtained by the new method are verified by comparing them to the solutions of deterministic transport calculations or to the approximate results that are obtained from the direct perturbations of the cross-sections.