Feynman-Alpha and Rossi-Alpha Formulas with Delayed Neutrons for Subcritical Reactors Driven by Pulsed Non-Poisson Sources

In our earlier papers, we developed a theory of reactor noise for accelerator-driven systems (ADSs). It was shown that reactor noise in ADSs is different from that in critical or radioactive source-driven subcritical systems because of the periodically pulsed source and its non-Poisson character. Various noise descriptors, such as Rossi alpha, Feynman alpha (or variance to mean), power spectral density, and cross-power spectral density, were derived, for a periodically pulsed source, including correlation between different pulses and finite pulses of different shapes. Throughout the work we restricted ourselves to the case of prompt neutrons only. In the present paper, we extend the theory to the delayed neutron case. Feynman-alpha and Rossi-alpha formulas are derived by considering the source to be a periodically pulsed non-Poisson source, without correlations between different pulses. Each pulse is assumed to be a delta function. The calculations are carried out in the time domain that leads to closed-form expressions for these descriptors.