Stochastic transport theory of neutron and photon coupled fields: neutron and photon counting statistics in nuclear assemblies

The behavior of neutrons and gamma rays in a nuclear reactor or configuration of fissile material can be represented as a stochastic process. The observation of this stochastic process is usually achieved by measuring the fluctuations of the neutron and gamma ray population on the system. The general theory of the stochastic neutron field has been developed to a high degree. However, the theory of the stochastic nature of the gamma rays and neutrons couples the two processes. The generalized probability balances are developed from which the first and higher moments of the neutron and gamma rays fields are obtained. The paper also provides a description of the probability generating functions for both photon and neutron detectors that are the foundations for measurements of the fluctuations. The formalism developed in this paper for the representation of the statistical descriptors of the neutron-photon coupled field is applicable for many neutron noise analysis measurements.