Independent component analysis for beam measurement

Independent component analysis (ICA) has been used for data mining in many branches of science. In beam physics, ICA can be applied to analyze the turn-by-turn beam position monitor (BPM) data of the transverse beam motion. Transverse beam motion consists of both linear betatron motion and the nonlinear motions which can be excited by higher order nonlinear magnetic elements. The diagnosis of the linear betatron motion has been developed by other methods like the model independent analysis (MIA) which is essentially built upon the principal component analysis (PCA). However, the detection and analysis of the nonlinear optics of an accelerator has never been effectively addressed. With the introduction of the ICA method which is inherently superior over the other traditional multivariate statistical methods like PCA or factor analysis, one can gain better accuracy in the linear betatron motion analysis and make the nonlinear optics diagnosis feasible.;The narrow-band filtering of ICA provides us with accurate interpretation of both the linear and nonlinear betatron motions, especially the x2nu motion as we show in this thesis. For linear betatron oscillation, ICA can extract the betatron amplitude function and phase advance with high precision. For the nonlinear motion, the x 2nu motion uncovered by ICA agrees very well the analytical result derived from the Hill's equation. Based upon the study of both linear and nonlinear optics using ICA method, we finally propose two methods of beam-based measurement of the higher order nonlinear magnetic elements.