Model Independent Analysis of Beam Dynamics in Accelerators

In this paper, we address fundamental issues in BPM-based observations and present methods to analyze beam dynamics in an accelerator. Our analysis methods do not rely on any particular machine model, and therefore are referred to as Model Independent Analysis (MIA). There are two major parts in MIA. One is noise reduction and degree-of-freedom analysis using a singular value decomposition of a BPM-reading matrix. The other is a physical base decomposition of the BPM-reading 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 is a statistical analysis of BPM readings which can be collected non-invasively during normal machine operation, and can lead to better understanding and control of beams.