Statistics of Zero Power Nuclear Reactors

In a zero power nuclear reactor operating in steady state fluctuations in the neutron population about the average neutron population are observable. These fluctuations are related to the dynamic parameters of the reactor and may be of interest in measurements of dynamic parameters or in the analysis of sensitive experiments in which the characteristics of this population fluctuation are important. In this paper equations are developed for the autocorrelation function and the power spectral density function for zero power, point reactor fluctuations. An equation is also derived for the ratio of the variance to the mean of the integrated value of the noise as a function of time interval. The derivation of these equations uses the concepts of noise analysis common to optimum design theory. The effects of delayed neutrons and of source neutrons are included. A typical experimental curve for the variance to mean ratio taken on the Ford Nuclear Reactor at the University of Michigan is shown which displays the form of this function.