Theory of Neutron Noise in a Temporally Fluctuating Multiplying Medium

Neutron fluctuations in a constant multiplying medium (zero power noise) and those in a fluctuating medium (power reactor noise) have been traditionally considered as two separate disciplines that exist in two opposing limiting areas of operation (low and high power, respectively). They have also been treated by different mathematical methods, i.e., master equations and Langevin equation, respectively. In this paper we develop a theory of neutron fluctuations in a medium randomly varying in time, based on a forward-type master equation approach. This method accounts for both the zero power and the power reactor noise simultaneously. Factorial moments and related quantities (variance, power spectrum, etc.) of the number of the neutrons are calculated in subcritical systems with a stationary external source. It is shown that the pure zero power and power reactor noise results can be reconstructed in the cases of vanishing system fluctuations and high power, respectively, the latter being a nontrivial result. Further, it is shown that the effect of system fluctuations on the zero power noise is retained even in the limit of vanishing neutron number (reactor power). The results have thus even practical significance for low-power systems with fluctuating properties. The results also have a bearing on other types of branching processes such as evolution of biological systems, germ colonies, epidemics, etc., which take place in a time-varying environment.