Theory of neutron noise induced by spatially randomly distributed noise sources

Paper in proceeding, 2000

In this paper the neutron noise, induced by spatially randomly distributed noise sources is investigated. The prime example of such a case is the neutron noise induced by temperature fluctuations in a PWR core, where the temperature fluctuations in the separate channels (radial positions) are only weakly correlated and their space dependence can only be specified in a statistical sense. Solutions are given for the auto- and cross-spectra of the neutron noise, in terms of the spatial cross-spectra of the noise source (temperature fluctuations). The spatial structure of the neutron noise spectrum is investigated quantitatively as a function of the frequency and the correlation length of the perturbation. The validity of the point kinetic approximation is also investigated. It is found that in the low frequency limit, point kinetics dominates even if the noise source correlation length is zero, i.e. the noise source is completely uncorrelated in space. On the other hand, in systems of realistic sizes and at plateau frequencies, i.e. at around a few Hz, noticeable deviations occur from point kinetics if the source correlation length is much smaller than the system size. The magnitude of this deviation is only a few percents at plateau frequencies in the present 1-D model, but by extrapolation it can be expected to be much larger in realistic 2-D calculations. This latter result bears importance for the determination of the moderator temperature coefficient (MTC) with noise methods, where usually a point kinetic core response is assumed in the evaluation of measurements.