The forward equation of probability balance for neutrons in a medium with randomly time-varying properties: Space and angle dependence

The recent contributions to combined zero-power and at-power neutron noise analysis by Pazsit and Pal [Pazsit, I., Pal, L., 2008, Neutron Fluctuations, a Treatise on the Physics of Branching Processes. Elsevier Science Ltd.] have been restricted to the point model approximation. In this paper we extend that work and develop a set of equations which allows a full description of the space and angle variations of the neutron fluctuations to be calculated. These equations are based upon the forward Kolmogorov formalism as developed by Govorkov [Govorkov, A.B., 1962a. Statistical scattering of pulse amplitudes in fast neutron pulse reactors. Translated from Atomnaya Energiya 13, 152; Govorkov, A.B., 1962b. Statistical reactor kinetic equations. Translated from Atomnaya Energiya 17, 474.]. The nature of the randomly time-varying medium is described by a dichotomic Markov process and this is incorporated into the moment equations by the use of a stochastic ansatz for the first and second moments of the probability distribution. The result of these calculations is a pair of coupled integro-differential equations for the second moment from which the variance of the neutron density may be found.