An Adjoint-Weighting in Neutron Fluctuation Analysis with Emphasis on an Effective Detector Efficiency

A set of fundamental equations for fluctuations about the mean neutron density is studied for a reactor-detector system in which the detector is treated as an integral part of the system. The reactor-detector system is described, mathematically, as a general Markov process, and expressions for various descriptive parameters are derived in a consistent manner within the context of the basic equations. The role of the general adjoint neutron density is discussed with special emphasis on the mean and second-moment functions, and a relationship between the second-moment equations similar to the relationship between first-moments (mean and its adjoint) is observed. The extension to higher moments is also noted. A reduction of the second-moment equations is carried out, without approximation, using a variational principle. This consistent reduction allows a definition of the parameters involved, especially a definition of the detector efficiency, through a comparison of this reduced form with the usual point-reactor equations. The parameters defined contain weighting functions dependent upon the number of detectors used in the experiment.