Linear And Nonlinear Model Calibration Of The Storage Ring With The Turn-by-turn BPM System

Linear and nonlinear model calibration of the storage ring using exactly measured turn-by-turn beam position data is becoming effective tools to achieve high performance of synchrotron light sources. It is great convenient for debugging the storage ring by constructing a full set of model calibration methods, which can greatly reduce the debugging time and make sure that the final state of the beam in the storage ring can be highly consistent with the theoretical design. With the development of the beam position monitor system in the storage ring, all of the beam position monitors have the ability to measure turn-by-turn beam position, which make some new methods can be used for the model calibration of the storage ring. This thesis mainly introduces these new methods, which can calibrate the model by directly analyzing the turn-by-turn beam position but do not need to change the lattice of the storage ting. The physical principles, analysis process and simulation results are presented in this thesis.First, this thesis introduces some methods for linear model calibration. The method of linear optics from orbits (LOCO) which is widely used internationally is introduced at the first. The theory of this method is introduced and the analysis of linear optics is worked out with some sets of data measured from the real storage ring including close orbit response matrix, dispersion function, noise levels of the BPMs and so on. In addition, this thesis also introduces three other methods for linear model calibration, which are linear fit analysis, model independent analysis (MIA) and independent component analysis (ICA). All of these three methods don’t rely on the lattice of the storage ring but only analyze the turn-by-turn data measured from BPM system directly. The physical principles of these three methods are introduced and the processes of the linear model calibration with each method are showed in this thesis.Then, this thesis introduces the method of nonlinear model calibration. The measurement of the corrected chromaticity and tune shift with amplitudes are introduced in this thesis firstly, and then a new method of Spectrum fit analysis for the nonlinear optics analysis is mainly introduced. Spectrum fit analysis is developed from the application of Normal From in turn-by-turn beam position, which present the relationship between amplitude of high order resonant spectrums of a single particle transverse motion and nonlinear resonance driving terms. Because of the effect of decoherence and radiation damping, the transverse movement of the beam with a large number of particles in an electron storage ring is much complex than that of a single particle, and the relationship between the high order spectrums of the beam and the nonlinear resonance driving terms can’t be express with an simple analytical form. So, the Spectrum fit analysis is developed for nonlinear model calibration with high order spectrums. This thesis presents the basic theory and the key technique for the analysis, including the method of numerical analysis of the fundamental frequency (NAFF) and the Levenberg-Marquardt optimization algorithm.At last, all of the methods are theoretically validated with a simulation model. The model of the storage ring is simulated with the AT code, and the lattice adopts the theoretical design of storage ring in Hefei Light source. Each method is used to analyze the turn-by-turn beam position which tracked from the simulation model. All of the results are basically the same with the theoretical design, and the accuracy of each method is theoretically validated in this thesis.