Generation of spatial weighting functions for ex-core detectors using adjointing flux

The response of ex-core detectors depends on the core power level, power distribution, and reactor configuration. To predict the response of ex-core detectors to the core power level and power distribution, it is thus necessary to know the spatial weighting functions for ex-core detectors which are functions of reactor configurations but are independent of the core power distribution. In this study, two-dimensional discrete ordinates adjoint transport method is introduced and the calculational models are presented to calculate the spatial weighting functions. Two kinds of spatial weighting functions, i. e., assembly wise weighting functions and core height wise weighting functions, are calculated for individual ex-core detectors which are mounted at different core elevations. The relationship of spatial weighting functions to the major reactor operating parameters is also analyzed and it is found that the soluble boron in the reactor coolant does not affect the spatial weighting functions but the reactor core power level affects the relative core height wise weighting functions. It is concluded that the discrete ordinates adjoint transport method is suitable for calculating the spatial weighting functions for ex-core detectors, because the method provides more detailed information and reduces the computing times. The calculated spatial weighting functions for ex-core detectors at a given reactor configurations can be used to predict the response of each ex-core detector to the core power distribution throughout the fuel cycle, but only at a specified power level. The comparison of calculated spatial weighting functions with the measured plant data on ex-core detector response rates is needed for the validation of the calculation method