The Feynman-alpha method is a neutron noise technique that is used to estimate the prompt neutron period of fissile assemblies. The method and quantity are of widespread interest including in applications such as nuclear criticality safety, safeguards and nonproliferation, and stockpile stewardship; the prompt neutron period may also be used to infer the $k_{\mathrm{eff}}$ multiplication factor. The Feynman-alpha method is predicated on time-correlated neutron detections that deviate from a Poisson random variable due to multiplication. Traditionally, such measurements are diagnosed with one-region point kinetics, but two-region models are required when the fissile assembly is reflected. This paper presents a derivation of the two-region point kinetics Feynman-alpha equations based on a double integration of the Rossi-alpha equations, develops novel propagation of measurement uncertainty, and validates the theory. Validation is achieved with organic scintillator measurements of weapons-grade plutonium reflected by various amounts of copper to achieve $k_{\mathrm{eff}}$ values of 0.83–0.94 and prompt periods of 5–75 ns. The results demonstrate that Feynman-alpha measurements should use the two-region model instead of the one-region model. The simplified one-region model deviates from the validated two-region models by as much as 10% in the estimate of the prompt neutron period, and the two-region model reduces to the one-region model for small amounts of reflector. The Feynman-alpha estimates of the prompt neutron period are compared to those of the Rossi-alpha approach. The comparative results demonstrate that the Feynman-alpha method is more precise than the Rossi-alpha method and more accurate for $k_{\mathrm{eff}}<0.92$, whereas the Rossi-alpha method is generally more accurate for higher multiplications. The uncertainty propagation developed in this work should be used for all Feynman-alpha measurements and will therein improve fitting accuracy and appropriate precision estimates.

Feynman-alpha方法是一种中子噪声技术，用于估计裂变组件的迅速中子周期。这种方法和数量受到广泛关注，包括在核临界安全性，保障和防扩散以及库存管理等应用中；迅速的中子周期也可以用来推断${ķ}_{\mathrm{效}}$乘法因子。Feynman-alpha方法基于与时间相关的中子检测，该检测由于乘法而偏离了Poisson随机变量。传统上，使用一区点动力学来诊断此类测量，但是当反映裂变组合时，则需要两区模型。本文提出了基于Rossi-α方程的双重积分的两区域点动力学Feynman-α方程的推导，开发了测量不确定度的新型传播方法，并验证了该理论。通过有机闪烁体测量武器级p（通过各种数量的铜来反射）来实现验证，${ķ}_{\mathrm{效}}$值为0.83–0.94，提示周期为5–75 ns。结果表明，Feynman-alpha测量应使用两区域模型而不是一区域模型。简化的一区模型与已验证的二区模型在中子瞬变周期估计中的偏差高达10％，并且对于少量反射体，二区模型简化为一区模型。迅速中子周期的费曼-阿尔法估计值与罗西-阿尔法方法的估计值进行了比较。比较结果表明，Feynman-alpha方法比Rossi-alpha方法更精确，并且对于${ķ}_{\mathrm{效}}<0.92$，而Rossi-alpha方法通常对于更高的乘法更为准确。这项工作中发展的不确定性传播应用于所有费曼-阿尔法测量，并将在其中提高拟合精度和适当的精度估计。