Calculation of the Scale Factor for Inference of Pressurized Water Reactor Core Barrel Motion from Neutron Noise Spectral Density

To quantify the core barrel motion in a typical pressurized water reactor, a scale factor was calculated for both one- and two-dimensional geometries, using forward, variational, and perturbation methods of discrete-ordinates transport. The calculational results show that, although perturbation theory is adequate for estimating the scale factor, two-dimensional geometric effects are important enough to rule out the use of a one-dimensional approximation for all but the crudest calculations. Also, contributions of gamma rays can be ignored, and the results are relatively insensitive to the nuclear cross-section set employed. A method was then developed for inferring, with the aid of this scale factor, the magnitude of the core barrel motion from the following statistical descriptors: cross-power spectral density, auto-power spectral density, and amplitude probability density.