A special branching process with two particle types

Journal article, 2011

Traditional theories of neutron fluctuations in subcritical stationary multiplying systems with analytical solutions disregard the energy dependence of the neutrons, i.e. they treat only one type of neutrons in the branching process. In several recent applications, such as certain coincidence measurements in nuclear safeguards and Accelerator-Driven reflected fast-reactor Systems (ADS), energy dependence of the neutrons must be included into the description. The simplest of such models, still allowing analytical solutions, is to distinguish between two types of neutrons, fast and thermal, corresponding to the two-group theory of traditional reactor physics. The purpose of the present paper is to extend the traditional theory of neutron fluctuations to two neutron types, fast and thermal. We will consider the special case when branching is only induced by one of the two types, giving rise to the progeny of the other type only (thermal fission generating fast neutrons). Stationary injection of neutrons by an extraneous source, as well as the detection process, are taken into account. The results obtained have applications in current problems of nuclear safeguards and reactivity measurements in ADS.