vi Contents
2.7 LATTICE MODELING AND PARTICLE TRACKING
59
2.7.1 Tracking different types of accelerator elements
59
2.7.2 Calculation of lattice functions and beam
parameters
63
Section II Beam-based Correction
Chapter 3 Orbit and trajectory correction
69
3.1 ACCELERATOR COMPONENTS FOR ORBIT
CORRECTION
70
3.1.1 Beam position monitors
70
3.1.2 Orbit correctors
73
3.2 BEAM-BASED ALIGNMENT
74
3.3 ORBIT CORRECTION
76
3.3.1 Orbit correction with SVD
78
3.3.2 Orbit correction with weights on BPMs
84
3.3.3 Other methods for global orbit correction
86
3.3.4 Local orbit correction
89
Chapter 4 Linear optics measurement and correction - I
91
4.1 BEAM MEASUREMENTS FOR LINEAR OPTICS
93
4.1.1 Sampling linear optics with transverse
beam profile
93
4.1.2 Sampling linear optics with beam orbit
94
4.2 FITTING ORBIT RESPONSE MATRIX TO LATTICE
MODEL
98
4.2.1 Measured orbit response matrix
99
4.2.2 Model orbit response matrix
101
4.2.3 Least-square fitting setup
102
4.2.4 Gauss-Newton method
103
4.2.5 Error analysis
105
4.2.6 Optics correction and an example
106
4.2.7 Constrained least-square fitting
109
4.2.8 Application of constrained fitting for
optics correction
117