A multi-region multi-energy formalism for the Feynman-alpha formulas. (February 2015) - Malinovitch, T.; Dubi, C.
Highlights: A formalism of N regions and M groups for the Feynman- α method is introduced. Using a space-energy cell notation the expressions are simplified significantly. A simple way to incorporate the detectors in the system is used. The results have been verified by a Monte Carlo simulation in a two-region case. Abstract: The stochastic transport equation, describing the dynamics in time of the neutron population in a nuclear system, is used to gain expressions for the higher moments of the neutron population in a sub-critical system. Such expressions are the bone structure of the so called Feynman- α method to analyze noise experiments, aimed to determine the reactivity of sub-critical systems. In the present study, a general formalism for the stochastic transport equation in an N regions system, under the M energy groups approximation will be introduced. In particular, expressions for the Feynman variance to mean (or the Feynman-Y function) under the above mentioned restriction will be sought by using the steady state mode of the solution.