Model independent analysis of beam centroid dynamics in accelerators

Fundamental issues in Beam-Position-Monitor (BPM)-based beam dynamics observations are studied in this dissertation. The major topic is the Model-Independent Analysis (MIA) of beam centroid dynamics. Conventional beam dynamics analysis requires a certain machine model, which itself often needs to be refined by beam measurements. Instead of using any particular machine model, MIA relies on a statistical analysis of the vast amount of BPM data that often can be collected non-invasively during normal machine operation. There are two major parts in MIA. One is noise reduction and degrees-of-freedom analysis using a singular value decomposition of a BPM-data matrix, which constitutes a principal component analysis of BPM data. The other is a physical base decomposition of the BPM-data matrix based on the time structure of pulse-by-pulse beam and/or machine parameters. The combination of these two methods allows one to break the resolution limit set by individual BPMs and observe beam dynamics at more accurate levels. A physical base decomposition is particularly useful for understanding various beam dynamics issues. MIA improves observation and analysis of beam dynamics and thus leads to better understanding and control of beams in both linacs and rings.; Another important topic discussed in this dissertation is the measurement of a nonlinear Poincaré section (one-turn) map in circular accelerators. Although many kinds of nonlinear beam dynamics experiments have been conducted, no direct measurement of a nonlinear map has been reported for a ring in normal operation mode. This dissertation analyzes various issues concerning map measurements and shows that it is possible to measure the Poincaré section map (in terms of Taylor series) of a circular accelerator to a surprisingly high order and accuracy based on present BPM technology. MIA can overcome the inherent limit of BPM resolution. Nonlinear map measurements will advance understanding of the beam dynamics of a ring because the beam dynamics in a ring is intrinsically nonlinear and the one-turn map plays a basic role in characterizing and analyzing this type of system.