152 Beam-based Correction and Optimization for Accelerators
matrix the Courant-Snyder parameters can be calculated. Using the transfer
matrices between two locations, the phase advances can also be determined.
These derived data can then be fitted to the lattice model to determine the
quadrupole errors. One may also fit the lattice by directly comparing the
transfer matrices between the model and the measurements.
5.5 SUMMARY FOR LINEAR OPTICS CORRECTION
Linear optics correction for storage rings has been an extensively researched
area. LOCO, the method of fitting the orbit response matrix [102], was an
early success, which became the standard method for optics correction on
electron storage rings. The constrained fitting technique was an important
development [49, 50] for the method as it solved the degeneracy problem
that caused the original fitting method to fail for many machines and limited
the precision of optics correction. The improved fitting method is the default
method in the LOCO code [95] in the form of the scaled Levenberg-Marquardt
method.
One limitation of the LOCO method is that the measurement of the orbit
response matrix is time consuming. For the SPEAR3 ring it takes 10 minutes
to measure one data set. For large rings or rings with slow ramping correctors, the time would be considerably longer. A new approach that uses fast
correctors to modulate the beam orbit at different frequencies can substantially reduce the data taking time (e.g., from 1 hour reduced to 2 minutes
for NSLS-II) as the responses of multiple correctors can be simultaneously
measured [124].
In recent years, as turn-by-turn BPMs are widely used on new rings, methods based on simultaneous turn-by-turn BPM data have been developed and
studied at many facilities [58, 3, 61, 116, 109, 125, 47]. Most methods rely
on the accurate phase measurements from the turn-by-turn BPM data, which
are used to fit the lattice model. There have been a number of studies that
compare the performances of LOCO and turn-by-turn BPM data-based methods [1, 110, 84]. The ICA-based fitting method was found to have a comparable
accuracy with LOCO in the NSLS-II study [110].
In one-pass systems, the betatron phase advance-based methods cannot be
applied as there is no temporal betatron oscillation. The method of directly
fitting the beam position data to the lattice model can be used in this case [61].
It has been demonstrated with experiments on the LCLS [128].
matrix the Courant-Snyder parameters can be calculated. Using the transfer
matrices between two locations, the phase advances can also be determined.
These derived data can then be fitted to the lattice model to determine the
quadrupole errors. One may also fit the lattice by directly comparing the
transfer matrices between the model and the measurements.
5.5 SUMMARY FOR LINEAR OPTICS CORRECTION
Linear optics correction for storage rings has been an extensively researched
area. LOCO, the method of fitting the orbit response matrix [102], was an
early success, which became the standard method for optics correction on
electron storage rings. The constrained fitting technique was an important
development [49, 50] for the method as it solved the degeneracy problem
that caused the original fitting method to fail for many machines and limited
the precision of optics correction. The improved fitting method is the default
method in the LOCO code [95] in the form of the scaled Levenberg-Marquardt
method.
One limitation of the LOCO method is that the measurement of the orbit
response matrix is time consuming. For the SPEAR3 ring it takes 10 minutes
to measure one data set. For large rings or rings with slow ramping correctors, the time would be considerably longer. A new approach that uses fast
correctors to modulate the beam orbit at different frequencies can substantially reduce the data taking time (e.g., from 1 hour reduced to 2 minutes
for NSLS-II) as the responses of multiple correctors can be simultaneously
measured [124].
In recent years, as turn-by-turn BPMs are widely used on new rings, methods based on simultaneous turn-by-turn BPM data have been developed and
studied at many facilities [58, 3, 61, 116, 109, 125, 47]. Most methods rely
on the accurate phase measurements from the turn-by-turn BPM data, which
are used to fit the lattice model. There have been a number of studies that
compare the performances of LOCO and turn-by-turn BPM data-based methods [1, 110, 84]. The ICA-based fitting method was found to have a comparable
accuracy with LOCO in the NSLS-II study [110].
In one-pass systems, the betatron phase advance-based methods cannot be
applied as there is no temporal betatron oscillation. The method of directly
fitting the beam position data to the lattice model can be used in this case [61].
It has been demonstrated with experiments on the LCLS [128].