Delayed neutron effect in time-domain fluctuation analyses of neutron detector current signals

In the previous study, the theoretical formulae of two time-domain reactor noise techniques, i.e., the auto-covariance and the variance-to-mean function techniques, were derived (Kitamura et al., 2018). These two techniques analyse the temporal fluctuation in continuous neutron detector current signals arising from ionization chambers such as the fission chamber. They are hence inherently insensitive to the count-loss effect that sometimes brings serious difficulties to the conventional time-domain techniques that analyse the number of detector pulse signals. With regard to these two techniques, the experimental conditions under which they successfully measure the subcriticality through determination of the prompt neutron decay constant were clarified. However, for mathematical simplicity and the sake of insight, the previous study was performed on the basis of a theoretical model neglecting delayed neutrons. The formulae of these two techniques are hence re-derived by taking delayed neutrons into consideration. Using the formulae thus derived, the delayed neutron effect in these two techniques is discussed.