Contents vii
Chapter 5 Linear optics measurement and correction - II 121
5.1 OPTICS MEASUREMENT WITH HARMONIC ANALYSIS
122
5.1.1 Phase advance measurement
122
5.1.2 Precise tune determination from turn-by-turn
BPM data
124
5.1.3 Determination of beta functions with phase
advances
127
5.2 GLOBAL ANALYSIS OF TURN-BY-TURN BPM DATA
129
5.2.1 A model for the turn-by-turn BPM data
130
5.2.2 Principal component analysis (PCA)
131
5.2.3 Independent component analysis (ICA)
137
5.3 OPTICS CORRECTION WITH TURN-BY-TURN DATA
143
5.3.1 Fitting optics functions to lattice model
143
5.3.2 Fitting turn-by-turn data directly to
lattice model
147
5.4 OTHER METHODS FOR OPTICS CORRECTION
151
5.5 SUMMARY FOR LINEAR OPTICS CORRECTION
152
Chapter 6 Coupling and nonlinear dynamics correction 153
6.1 COUPLING MEASUREMENT AND CORRECTION
METHODS
154
6.1.1 Off-diagonal blocks of orbit response matrix
154
6.1.2 Amplitude and phase of normal modes via ICA 155
6.1.3 Other methods of coupling correction
157
6.2 COUPLING CORRECTION EXPERIMENTS
158
6.3 CORRECTION OF NONLINEAR DYNAMICS ERRORS
161
Section III Beam-based Optimization
Chapter 7 Online optimization algorithms
169
7.1 GENERAL CONSIDERATIONS OF ONLINE
OPTIMIZATION
170
7.1.1 Need for online optimization of accelerators
170
7.1.2 Formulating online optimization problem
171