Perturbation Theory Based on the Method of Cyclic Characteristics

Generalized perturbation theory (GPT) is a technique used for the estimation of small changes in performance functionals, such as linear reaction rate ratios, eigenvalues, power density, etc., affected by small variations in reactor core compositions. Here, a GPT algorithm is developed for the multigroup integral neutron transport problems in two-dimensional fuel assemblies with isotropic scattering. We then use the relationship between the generalized flux importance and generalized source importance functions to transform the generalized flux importance transport equations into the integrodifferential equations for the generalized adjoints. The resulting adjoint and generalized adjoint transport equations are then solved using the method of cyclic characteristics (MOCC). Because of the presence of negative adjoint sources, a coupled flux biasing/decontamination scheme is applied to make the generalized adjoint functions positive in such a way that it can be used for the multigroup rebalance technique. After convergence is reached, the decontamination procedure extracts from the generalized adjoints the component parallel to the adjoint function. Three types of biasing/decontamination schemes are investigated in the study. To demonstrate the efficiency of our solution algorithms, calculations are performed on 17 × 17 pressurized water reactor and 37-pin Canada deuterium uranium reactor (CANDU) lattices. Numerical comparisons of the generalized adjoint functions and GPT estimates using the MOCC and collision probability method are presented as well as sensitivity coefficients of nuclide densities.