Calculation of Spatial Weighting Functions for Ex-Core Neutron Detectors

A mathematical model for ex-core detector response in pressurized water reactor (PWR) configurations is presented, based on the use of a spatial weighting function that is independent of core power distribution. The spatial weighting function is derived equivalently using a point kernel model and from numerical solutions of the adjoint neutron transport equation. These methods are verified through the use of experimental thermal flux data for deep penetration in water and metal media. An adjoint ANISN weighting function calculation for a one-dimensional cylindrical PWR model also shows good agreement with an equivalent point kernel calculation. Weighting function calculations using the point kernel method for a detailed three-dimensional model based on the Indian Point Unit 2 Reactor indicate that 91% of ex-core detector response is due to the five fuel assemblies nearest the detector. We believe that the weighting functions obtained with the point kernel method represent reliable information that can be used in the analysis of ex-core detector response during reactor operations.