Study of the optimal amplitude extraction algorithm for cavity BPM

Cavity Beam Position Monitor (CBPM) adopting a resonant cavity structure and using the characteristic modes excited by the electron beam to measure the beam parameters, has the advantage of high position resolution and is widely used in Free-electron Laser (FEL) facilities. The wake field of different modes carries different bunch information, the amplitude and phase of the signals of different modes can be extracted through the signal processing method to obtain the characteristic parameters of the source bunch. In the application of bunch charge and position measurement, the accurate amplitude extraction method for cavity BPM signal is the primary issue to be considered when designing the data acquisition and processing system. In this paper, through theoretical analysis and numerical simulation, it is proved that the optimal algorithm of amplitude extraction for CBPM exists, and the dependence between the data processing window size and the decay time of the cavity BPM under the optimal design is given. In addition, the relationship between the optimized amplitude extraction uncertainty and the noise-to-signal ratio, sampling rate of data acquisition and processing system, and the decay time of the cavity BPM is also proposed, which can provide clear guidance for the design and optimization of the CBPM system. Accordingly, the CBPM system in Shanghai Soft X-ray FEL (SXFEL) facility is optimized, and the resolution improved from 273 nm to 177 nm at the bunch charge of 500 pC.