Impact of feedback loop parameter settings on the stability margin in a double radio-frequency system

Abstract: Most synchrotron light storage rings are equipped with a higher harmonic cavity (HHC) and are currently predominantly used to increase beam life. With the enhancement of the beam current intensity, it is necessary to consider instability problems that may be caused by heavy beam loading effects. In this study, we incorporated a HHC into the small-signal Pedersen mathematical model and used system signal analysis to investigate the mode-zero Robinson instability driven by the passive superconducting harmonic cavity (PSHC) and active superconducting harmonic cavity (ASHC) fundamental modes. To further study and alleviate this instability, we introduced direct radio-frequency feedback (DRFB), an automatic voltage control loop (AVC), and a phase-lock loop (PLL) into the model, discussed the impact of the feedback loop parameter settings on the stability margin, and provided suggestions for parameter settings.