Methods to detect error sources and their application at the TPS

For a low-emittance photon light source, beam stability is a very important property to attain a high-quality photon beam. While it is hard to avoid beam perturbations in a storage ring, it is more important to quickly find the source locations and to remove or eliminate the sources as soon as possible. In this report, we develop a method to identify the locations of multiple sources. For a source with a particular frequency, the relative phase between sources can also be obtained. This method has been a useful tool during TPS operation and its methodology and practical applications are described in this report.