Neutron Fluctuations in a Reactor of Finite Size

Fluctuations of the neutron populations in various phase-space regions in a reactor have been examined by development of a three-step analysis. First, the usual transport equation, or an approximation to it, is used to compute the probability that a neutron injected at a certain location in the reactor gives rise to a chain-related descendant neutron in each of a number of differential volume elements in phase space. Second, these conditional probabilities are used to compute product densities, probabilities that nuclear reactions of a certain class are induced in various time intervals by neutrons in each of a number of differential volume elements. Finally, the product densities are used to compute local population moments, parameters arising in the Rossi alpha experiment, auto- and cross-correlation functions, and other quantities of interest in fluctuation studies. The analysis, as applied to various reactor geometries, shows that the usual point-reactor analysis of reactor neutron fluctuations can lead to substantial error in predicting fluctuation magnitudes in startup studies and in determination of some reactor parameters from fluctuation experiments.