Feynman-α and Rossi-α analyses for a subcritical reactor system driven by a pulsed spallation neutron source in Kyoto University Critical Assembly

ABSTRACT

For a subcritical reactor system driven by a periodically pulsed spallation neutron source in Kyoto University Critical Assembly (KUCA), the Feynman-α and the Rossi-α neutron correlation analyses were carried out to determine the prompt-neutron decay constant and quantitatively to confirm a non-Poisson characteristics of the neutron source. In these correlation analyses, a non-negligible contribution of delayed neutrons and a non-Poisson character of the source were considered, and each pulse was assumed to be a delta function. When a neutron counter was placed closely to the reactor core, the prompt-neutron decay constant determined from the present Feynman-α analysis well agreed with that done from a previous analysis for the same subcritical system driven by an inherent neutron source. However, the decay constant determined from the present Rossi-α analysis was in poor agreement with that done from the above previous analysis. This disagreement originated from an inevitable excitation of a higher mode. In the Rossi-α counting probability distribution, the excitation deformed a sharp cusp arising from the delta function to a smooth convex shape. When the data around the convex top were masked for least-squares fitting of the present Rossi-α formula, the disagreement could be successfully resolved. Compared with the previous Feynman-α and Rossi-α analyses under the Poisson inherent source, the non-Poisson spallation source definitely enhanced the respective prompt-neutron correlation amplitudes. The enhancement rate increased with an increase in subcriticality. Moreover, the Degweker’s factor (m₂-m₁²)/m₁² of 0.067 ± 0.011, which indicated a non-Poisson character of the present spallation source, could be determined from the present correlation analysis and the non-zero value of the factor convinced us that the present source had a different statistical distribution from the Poisson.

KEYWORDS:

• KUCA
• ADS
• spallation source
• Feynman-α
• Rossi-α
• non-Poisson
• MVP

Acknowledgments

The present work was performed as a joint research program of the KUCA at the Institute for Integrated Radiation and Nuclear Science, Kyoto University.

Disclosure statement

No potential conflict of interest was reported by the authors.

Nomenclature

$A_i$	=	residues of zero-power reactor transfer function
f	=	pulse repetition frequency [Hz]
[fT]	=	largest integer less than or equal to fT
G(s)	=	zero-power reactor transfer function
$m_1$	=	first factorial moment of source multiplicity distribution (average number of neutrons in a pulsed bunch)
$m_2$	=	second factorial moment of source multiplicity distribution
N	=	number of protons in a pulse bunch
R	=	average count rate [1/s] $Y_i=2\frac{\overline{\nu \left(\nu -1\right)}}{{\bar{\nu }}^2}\frac{A_{i}G\left({\alpha }_i\right)}{{\alpha }_i}\left[s^2\right]$
Greek	=
${\alpha }_p$	=	prompt-neutron decay constant [1/s]
${\alpha }_i$	=	ith-delayed-neutron decay constant [1/s]
$\epsilon$	=	detection efficiency of a neutron counter
$\bar{\nu }$	=	first factorial moment of number of neutrons generated in fission event
$\overline{\nu \left(\nu -1\right)}$	=	second factorial moment of number of neutrons generated in fission event
$\overline{{\nu }_{sp}}$	=	first factorial moment of number of neutrons produced by spallation event
$\overline{{\nu }_{sp}\left({\nu }_{sp}-1\right)}$	=	second factorial moment of number of neutrons produced by spallation event
${\lambda }_d$	=	probability per unit time that a neutron is detected by a neutron counter [1/s]
${\lambda }_f$	=	probability per unit time that a neutron induces a fission event [1/s]
$\mathrm{\Lambda }$	=	generation time [s]
$\rho$	=	reactivity