Analytical modeling and experimental verification of oscillatory ponderomotive instabilities in closed-loop superconducting rf cavities

Superconducting radio-frequency (SRF) cavities with high-loaded-Q are susceptible to ponderomotive instabilities arising from nonlinear electromechanical coupling. Under low-level rf feedback control, stability analysis is challenging and has, until now, lacked comprehensive experimental verification. In this work, we linearize the coupled cavity electromagnetic and mechanical equations about the operating point, deriving explicit small-signal stability criteria for both open- and closed-loop operation. A characteristic equation approach is used to map the oscillatory instability threshold in the detuning–gradient plane. Time-domain simulations confirm the predicted onset of self-excited oscillations at these thresholds. Furthermore, experiments on a 162.5 MHz SRF linac (CAFE2) show that the observed oscillation onset agrees with our analytical predictions within a small margin. By combining analytical modeling, numerical simulation, and direct experimentation, this study providescomprehensive validation of oscillatory ponderomotive instability theory under feedback control, offering practical guidance for the stable operation of high-gradient SRF accelerators.