Application of Hilbert-transform-phase-space-reconstruction in HLS Bunch-by-bunch system

The authors introduce the phase space reconstruction method based on Hilbert transform to comprehensively analyse the Bunch-by-bunch measurement record. The analyzing results include one beam position monitor (BPM) phase space reconstruction, bunch oscillation's phase information, mode diagnosing, tune evolvement regressed from phase space and the damping rate of the mode and bunch oscillation. The new method to calculate the tune evolvement exhibits a very high resolution both in time domain and frequency domain without any time domain average. The exponential fit to the mode and bunch oscillation damping curve are also exhibited in this paper. (authors)