Static generalized perturbation theory with feedback effects and criticality reset

The primary emphasis in the application of generalized perturbation theory (GPT) methods to date has been in the computation of cross-section sensitivities. These data sensitivity coefficients have been used extensively to evaluate the uncertainty of fast reactor performance parameters and to quantify the need for further nuclear data measurements. However, some recent work associated with the development of a GPT-based fuel management optimization algorithm has shown that perturbation methods can also play an important role in the engineering design of light water reactor (LWR) reload cores. These GPT methods, however, must be adapted to reflect current LWR design practices. In particular, the reactor must be kept critical and the effects of thermal-hydraulic feedback must be considered. Although criticality reset techniques (or k-reset) have been addressed previously, there does not appear to be any comprehensive GPT development that accounts for the indirect coupling (through feedback mechanisms) of the macroscopic cross sections to the neutron flux or reactor power distribution. The purpose of this paper is to present such a development - a static GPT formulation that includes feedback effects and k-reset. The approach taken here is to define a variational principle that includes these phenomena as constraint equations appended to the response functional using Lagrange multipliers