Measurement of the cavity-loaded quality factor in superconducting radio-frequency systems with mismatched source impedance

The accurate measurement of parameters such as the cavity-loaded quality factor (QL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Q_\textrm{L}$$\end{document}) and half bandwidth (f0.5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f_{0.5}$$\end{document}) is essential for monitoring the performance of superconducting radio-frequency cavities. However, the conventional “field decay method" employed to calibrate these values requires the cavity to satisfy a “zero-input" condition. This can be challenging when the source impedance is mismatched and produce nonzero forward signals (Vf\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V_\textrm{f}$$\end{document}) that significantly affect the measurement accuracy. To address this limitation, we developed a modified version of the “field decay method" based on the cavity differential equation. The proposed approach enables the precise calibration of f0.5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f_{0.5}$$\end{document} even under mismatch conditions. We tested the proposed approach on the SRF cavities of the Chinese Accelerator-Driven System Front-End Demo Superconducting Linac and compared the results with those obtained from a network analyzer. The two sets of results were consistent, indicating the usefulness of the proposed approach.