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

Through our earlier papers, we have shown that reactor noise in accelerator-driven systems (ADS) is different from that in critical or radioactive source-driven subcritical systems due to periodically pulsed source and its non-Poisson character. We have developed a theory of reactor noise for ADS, taking into account the non-Poisson character of the source. Various noise descriptors, such as Rossi-alpha, Feynman-alpha (or variance to mean), power spectral density, and cross power spectral density, have been derived for a periodically pulsed source, including correlation between different pulses and finite pulses of different shapes. For mathematical simplicity, the theory was restricted to the case of prompt neutrons only. Recently, we extended the theory to the delayed neutron case and derived Feynman-alpha and Rossi-alpha formulae by considering the source to be a periodically pulsed non-Poisson source, without correlations between different pulses. The present paper extends the treatment to account for the possibility of correlations between pulses. Feynman-alpha and Rossi-alpha formulas are derived by considering the source to be a periodic sequence of delta function non-Poisson pulses, with exponential correlations.