Theoretical investigation of the MTC noise estimate in 1-D homogeneous systems

In this paper, the accuracy of the noise-based determination of the moderator temperature coefficient (MTC) is investigated theoretically and quantitatively. It is known from earlier work that the noise method systematically underestimates the MTC. In this paper, it is found that the main reason for the underestimation lies with the radial incoherence of the temperature fluctuations. The deviation of the reactor response from point-kinetics is another possible reason, but it was found to play a quite insignificant role. The theory of neutron noise, induced by spatially random perturbations is elaborated and by its help the inaccuracy (bias) of the noise based MTC estimation was quantitatively investigated. It was found that a relatively short correlation length of the temperature fluctuations, which is in agreement with experimental evidence, can explain the observed underestimation of the MTC by the noise method.