Dynamic Lorentz force detuning (LFD) in the 324 MHz superconducting double-spoke cavities for the China Spallation Neutron Source Phase-II (CSNS-II) linac is investigated through combined modeling, simulation, and cryomodule experiments. A modal ponderomotive coupling model is established and validated against multiphysics finite-element analysis and measurements up to 9 MV/m with 1.2 ms pulses at 50 Hz. Intra-pulse detuning reconstructed from low-level RF (LLRF) waveforms agrees with full-pulse detuning inferred from piezo-sensor signals, and FFT analysis identifies dominant mechanical modes consistent with simulated eigenfrequencies. Beyond single-cavity behavior, inter-cavity mechanical coupling through a shared cryomodule and support system is experimentally verified: RF excitation of one cavity induces measurable vibration and frequency perturbation in the adjacent cavity, confirmed independently by LLRF and piezo diagnostics. Active compensation is implemented with piezo tuners using a parameterized half-sine feedforward waveform. Parameters are first optimized by systematic scanning and then refined on-line using a Proximal Policy Optimization (PPO) agent interacting with the real cavity via a gymnasium/pyepics interface. After 1 0 4 training steps, the PPO-optimized waveform reduces the effective detuning metric by about 37% relative to the initial policy, matching or surpassing the best manually scanned setting while improving robustness to operating-condition variations.
Liu et al. (Mon,) studied this question.