Bunch-by-bunch BPM data analysis at HEPS

An important diagnostic method for beam dynamics characterization in synchrotron radiation light sources is presented. By directly sampling beam position monitor (BPM) signals using an adequate performing oscilloscope, the transverse beam position and longitudinal phases (arrival times) of individual bunches could be resolved with unprecedented precision. A novel technique for extracting longitudinal phase information from oscilloscope data is detailed, achieving a resolution of 0.1 ps. Triggered by the injection timing signal, the oscilloscope captures transient dynamics during beam injection, enabling the derivation of critical parameters such as the longitudinal tune and residual oscillation amplitude, which are essential for optimizing the injection efficiency. The singular-value decomposition (SVD) method was applied on the acquired bunch-by-bunch transverse and longitudinal data, revealing the dominant physical modes (e.g., betatron and synchrotron oscillations) through their associated singular values. Furthermore, the SVD-based approach demonstrates the potential for identifying coupled-bunch instabilities by isolating collective beam motion components. This work establishes a versatile framework for advanced beam diagnostics, combining high temporal resolution, multi-dimensional parameter extraction, and instability analysis, thereby providing critical insights for accelerator performance optimization.