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The Feynman-alpha method is a neutron noise technique that is used toestimate the prompt neutron period of fissile assemblies. The method andquantity are of widespread interest including in applications such as nuclearcriticality safety, safeguards and nonproliferation, and stockpile stewardship;the prompt neutron period may also be used to infer the $k_\text{eff}$multiplication factor. The Feynman-alpha method is predicated ontime-correlated neutron detections that deviate from a Poisson random variabledue to multiplication. Traditionally, such measurements are diagnosed withone-region point kinetics, but two-region models are required when the fissileassembly is reflected. This paper presents a derivation of the two-region pointkinetics Feynman-alpha equations based on a double integration of theRossi-alpha equations, develops novel propagation of measurement uncertainty,and validates the theory. Validation is achieved with organic scintillatormeasurements of weapons-grade plutonium reflected by various amounts of copperto achieve $k_\text{eff}$ values of 0.83-0.94 and prompt periods of 5-75 ns.The results demonstrate that Feynman-alpha measurements should use thetwo-region model instead of the one-region model. The simplified one-regionmodel deviates from the validated two-region models by as much as 10\% in theestimate of the prompt neutron period, and the two-region model reduces to theone-region model for small amounts of reflector. The Feynman-alpha estimates ofthe prompt neutron period are compared to those of the Rossi-alpha approach.The comparative results demonstrate that the Feynman-alpha method is moreprecise than the Rossi-alpha method and more accurate for $k_\text{eff}<0.92$,whereas the Rossi-alpha method is generally more accurate for highermultiplications.

On the Feynman-alpha Method for Reflected Fissile Assemblies