A Study On Beam Loading Effects In The SSRF Storage Ring

There are three major problems in operation of the storage ring RF system in Shanghai Synchrotron Radiation Facility(SSRF).The first one is that superconducting cavity frequently quench which is caused by multipacting effects when the accelerating voltage is high.The second one is that the RF system fails to maintain high beam current operation when the accelerating voltage is low.The third one is that the disturbance signal and measurement noise signal is hard to be suppressed by the RF feedback system.The disturbance signal and measurement noise will spoil the synchrotron spectrum through beam longitudinal motion.After comparing the solution of domestic and overseas accelerators,we believe that all the three problems mentioned above can be solved by properly designed feedback loops.This paper presents the whole derivation process of the multi-cavity coupled model for the SSRF storage ring RF system which is based on Pedersen model.The arithmetic expression of the low level RF(LLRF)system control algorithm in the SSRF storage ring which is compatible with Pedersen model is also presented in this paper.To obtain the experiment data for the loop analysis results,we embedded a digital transfer function measurement system into the LLRF system of the SSRF storage ring.The consistency between experimental results and simulation results is high.The nonlinear effect,that the conversion from amplitude modulation to phase modulation increases with the increasing incident carrier power,which is parasitized in the LLRF system is discovered during transfer function measurement.The nonlinear effect,that the gain of amplitude modulation decreases and the gain of phase modulation distorts with frequency with increasing incident carrier power,which is parasitized in the high level RF system is also discovered during transfer function measurement.These are important supplements to the classical Pedersen model and will be the base for the error model construction.Two loop analysis models which are applied on different beam loading situation are presented in this paper.The one is the effective complex field single input single output(SISO)model for slight beam loading effect,which can be used for stability analysis and transfer function calculation through generalized complex field Nyquist diagram directly.The other is the multi-input multi-output(MIMO)model for heavy beam loading effect,which can be used for stability analysis through generalized Nyquist criterion.The suppression effect for disturbance signal and measurement noise can be analyzed by the calculated transfer function from different nodes.The loop analysis result indicates that the stability of RF system is determined by loop stability.Beam current can be high when the beam loading phase is positive and the limit is determined by the system robustness.The equivalence between direct feedback loop and the classical proportional-integral(PI)controller is proved by loop analysis.A qualitative explaination using description method for the RF system self-excited phenomenon is presented by comparing two self-excited phenomenon in heavy beam loaded RF system and loop-closed large phase-mismatched LLRF system in this paper.Through MIMO control theory,the failure to offer sufficient suppression for the ill-conditioned RF system disturbance signal and measurement noise in low-voltage high-current operation with current diagonal control structure is explained in this paper.A systematic research for the beam loading effect in the RF system with feedback loop is presented in this paper,and it will offer experiment data and theory material for low-voltage high-current operation or large accelerator construction in the future.