TY - JOUR
T1 - Theoretical Derivation of a Unique Combination Number Hidden in the Higher-Order Neutron Correlation Factors Using the Pál-Bell Equation
AU - Endo, Tomohiro
AU - Nishioka, Fuga
AU - Yamamoto, Akio
AU - Watanabe, Kenichi
AU - Pyeon, Cheol Ho
N1 - Funding Information:
This work was supported by the Japan Society for the Promotion of Science (JSPS) Grant-in-Aid for Scientific Research (C) [Grant Number 19K05328]. We sincerely dedicate this study to Lénárd Pál, the pioneer of neutron-detection probability theory. This work was partly conducted under the Visiting Researcher’s Program of the Kyoto University. The authors are grateful to all the technical staff of KUCA for their assistance during the experiments.
Funding Information:
We sincerely dedicate this study to Lénárd Pál, the pioneer of neutron-detection probability theory. This work was partly conducted under the Visiting Researcher’s Program of the Kyoto University. The authors are grateful to all the technical staff of KUCA for their assistance during the experiments.
Publisher Copyright:
© 2022 The Author(s). Published with license by Taylor & Francis Group, LLC.
PY - 2023
Y1 - 2023
N2 - The Pál-Bell equation is a backward-type master equation that describes the probability generating function (PGF) of neutron counts in a neutron multiplication system. Thanks to the Pál-Bell equation with the two-forked and the fundamental mode approximations, an analytical solution of PGF of neutron counts in a source-driven subcritical system can be theoretically derived. This theoretical derivation clarifies that the unique combination number of double factorial (2n−3)!! does exist in the ratio of the higher-order neutron correlation factors measured in a critical state even for any kind of fissile and moderator materials. Additionally, the unique combination numbers are experimentally validated for the order 3 ≤ n ≤ 6 through reactor noise measurements in actual subcritical systems. This knowledge can be used to judge whether a target system is in a deep subcritical state or to roughly estimate the magnitude of subcriticality, based on the factorial moments of the measured reactor noise in a zero-power state.
AB - The Pál-Bell equation is a backward-type master equation that describes the probability generating function (PGF) of neutron counts in a neutron multiplication system. Thanks to the Pál-Bell equation with the two-forked and the fundamental mode approximations, an analytical solution of PGF of neutron counts in a source-driven subcritical system can be theoretically derived. This theoretical derivation clarifies that the unique combination number of double factorial (2n−3)!! does exist in the ratio of the higher-order neutron correlation factors measured in a critical state even for any kind of fissile and moderator materials. Additionally, the unique combination numbers are experimentally validated for the order 3 ≤ n ≤ 6 through reactor noise measurements in actual subcritical systems. This knowledge can be used to judge whether a target system is in a deep subcritical state or to roughly estimate the magnitude of subcriticality, based on the factorial moments of the measured reactor noise in a zero-power state.
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U2 - 10.1080/00295639.2022.2049992
DO - 10.1080/00295639.2022.2049992
M3 - Article
AN - SCOPUS:85128733060
SN - 0029-5639
VL - 197
SP - 176
EP - 188
JO - Nuclear Science and Engineering
JF - Nuclear Science and Engineering
IS - 2
ER -