Theoretical Derivation of a Unique Combination Number Hidden in the Higher-Order Neutron Correlation Factors Using the Pál-Bell Equation

Tomohiro Endo, Fuga Nishioka, Akio Yamamoto, Kenichi Watanabe, Cheol Ho Pyeon

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
JournalNuclear Science and Engineering
DOIs
Publication statusAccepted/In press - 2022

All Science Journal Classification (ASJC) codes

  • Nuclear Energy and Engineering

Fingerprint

Dive into the research topics of 'Theoretical Derivation of a Unique Combination Number Hidden in the Higher-Order Neutron Correlation Factors Using the Pál-Bell Equation'. Together they form a unique fingerprint.

Cite this