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Online beam phase and current calibration for rf cavities under closed-loop operation

Feng Qiu1,2,*, Rihua Zeng3, Chengye Xu1, Shihui Wei1, Lijuan Yang1, Zhaojie Chen1,2, Yilin Miao1,2, Muyuan Wang4, Cecilia Maiano4 et al.

Paolo Pierini4 and Yuan He1,2,†

  • *Contact author: qiufeng@impcas.ac.cn
  • †Contact author: hey@impcas.ac.cn
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Phys. Rev. Accel. Beams 29, 062802 – Published 29 June, 2026

DOI: https://doi.org/10.1103/jrx8-jhrm

Abstract

Leveraging the interaction between the beam and the radio-frequency (rf) cavity to measure the beam phase reduces tuning time and mitigates slow drifts induced by ambient conditions. An online phase-measurement approach based on beam-induced rf transients was previously demonstrated at DESY using superconducting rf cavities in an electron accelerator under open-loop operation. However, open-loop operation is unsuitable for high-current proton or heavy-ion linacs due to elevated risks of beam loss and trips. This work proposes two novel schemes that operate under closed-loop conditions. The first, a virtual open-loop (VOL) method, solves the cavity difference equation to remove the contribution of feedback (and/or feedforward) control from the cavity field, thereby recovering the beam-loading signal under an equivalent open-loop condition from which the beam parameters are determined. The second, a steady-state (SS) method, determines the beam parameters (i.e., beam current and phase) when beam-loading and cavity-detuning compensation are sufficient and infers the beam phase and current by computing the vector difference of steady-state forward voltages with and without beam. Both approaches were systematically validated on the buncher cavity at the European Spallation Source (ESS), showing agreement with independent beam diagnostics, with phase error within ±0.5° and current error within ±4%. The methods enable real-time, accurate beam-phase measurement during closed-loop operation and are readily extensible to other high-power accelerator systems.

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Phys. Rev. Accel. Beams 29, 062802– Published 29 June, 2026
  • Received 18 November 2025
  • Accepted 21 May 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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