Development of Generalized Perturbation Theory Algorithms for Monte Carlo Eigenvalue Calculations

A generalized perturbation theory (GPT) formulation suited for the Monte Carlo (MC) eigenvalue calculations is newly developed to estimate sensitivities of a general MC tally to input data. In the new GPT formulation, the tally perturbation due to an input parameter change is expressed as a sum of the perturbed operator effect and the perturbed source effect requiring the generalized adjoint function weighting. It is shown that the new GPT formulation is equivalent to the conventional first-order differential operator sampling method augmented by the fission source perturbation method. Because the GPT formulation makes it necessary to compute the generalized adjoint function, MC sensitivity estimation algorithms can consume a huge computer memory space to save historywise estimates of tallies. As a way to alleviate the memory space problem, the MC Wielandt iteration method is incorporated into the MC GPT algorithm. For the purpose of comparison, MC GPT algorithms by both the standard power iteration and the Wielandt iteration methods are implemented in the Seoul National University MC code, McCARD. Their performances are examined in two-group homogeneous problems, Godiva and the TMI-1 pin cell problem. From the nuclear data sensitivity and uncertainty analyses of these problems, it is demonstrated that the new GPT methods can predict the sensitivities of reaction rate tallies to cross-section data very well. It is also demonstrated that the incorporation of the MC Wielandt iteration method into the new GPT calculations consumes a negligibly small amount of memory required for—and thus resolves—the computer memory issue associated with the adjoint function calculations.