Proposal and applicability of estimated criticality lower-limit multiplication factor using the bootstrap method

ABSTRACT

To judge whether an application system is a subcritical state or not based on numerical results of the effective neutron multiplication factor ${\mathrm{k}}_{\mathrm{e}\mathrm{f}\mathrm{f}}$, an evaluation method of the estimated criticality lower-limit multiplication factor (ECLLMF) using the bootstrap method is newly proposed. By utilizing numerical results of ${\mathrm{k}}_{\mathrm{e}\mathrm{f}\mathrm{f}}$ for critical benchmark-problems that are selected depending on neutronic similarity to the application system, the ECLLMF should be carefully and conservatively estimated based on uncertainties of ${\mathrm{k}}_{\mathrm{e}\mathrm{f}\mathrm{f}}$ due to a criticality safety analysis code, experimental uncertainty, and covariance matrix of the nuclear data library. Furthermore, the frequency distribution of ${\mathrm{k}}_{\mathrm{e}\mathrm{f}\mathrm{f}}$ for these problems does not necessarily obey an ideal normal distribution. Using a resampling technique called ‘bootstrap method,’ the proposed method can reasonably estimate the ECLLMF considering the uncertainties and nuclear data-induced correlation between each critical benchmark-problem without the assumption of normality. To investigate the applicability of the proposed method, the approach-to-criticality experiment was carried out at the Kyoto University Critical Assembly (KUCA). Comparison of numerical results of ${\mathrm{k}}_{\mathrm{e}\mathrm{f}\mathrm{f}}$ and the ECLLMF using the bootstrap method indicated that the proposed method was able to judge an actual subcritical core as subcritical state.

KEYWORDS:

• subcriticality
• estimated criticality lower-limit multiplication factor
• bootstrap method
• critical experiment
• KUCA
• uncertainty
• criticality calculation
• covariance
• nuclear data
• benchmark

Acknowledgments

This work was supported by the Japan Society for the Promotion of Science (JSPS) Grant-in-Aid for Scientific Research (C) (19K05328). The authors are grateful to all the staff at KUCA for their assistance during the educational experiments for graduate students.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Japan Society for the Promotion of Science [19K05328].