Some properties of zero power neutron noise in a time-varying medium with delayed neutrons

The temporal evolution of the distribution of the number of neutrons in a time-varying multiplying system, producing only prompt neutrons, was treated recently with the master equation technique by some of the present authors. Such a treatment gives account of both the so-called zero power reactor noise and the power reactor noise simultaneously. In particular, the first two moments of the neutron number, as well as the concept of criticality for time-varying systems, were investigated and discussed. The present paper extends these investigations to the case when delayed neutrons are also taken into account. Due to the complexity of the description, only the expectation of the neutron number is calculated. The concept of criticality of a time-varying system is also generalized to systems with delayed neutrons. The temporal behaviour of the expectation of the number of neutrons and its asymptotic properties are displayed and discussed.