A multi-region multi-energy formalism for the Feynman-alpha formulas

• 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.

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-αα 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.