An extension of the Generalized Perturbation Theory for spatial and energy collapsing

In this paper an extension of the Classical and Generalized Perturbation Theory is proposed which enables evaluating, at the 1st order, the contribution of any single spatial mesh to the variation of reactivity and reaction-rate ratios when an energy, spatial or energy/spatial collapsing is performed. An important achievement of the method is that it allows evaluating the individual asymptotic contribution of each spatial mesh to the variation, which enables investigating its spatial origin, very easily. Together with 1st order formulation, a simplified version is provided, which allows saving computation time while keeping an acceptable quality of the results. Some simple examples are provided, aimed at highlighting that the results obtained adopting the proposed formulation have a physical meaning and could be used to analyze the usual spatial/energy collapsing process in a convenient way.This formulation enlarges to the energy and spatial meshing the Classical and Generalized Perturbation Theory approaches to evaluate reactivity and reaction-rate ratio sensitivity to parameter variations.