92 Beam-based Correction and Optimization for Accelerators
There are many error sources that can cause deviations of the linear optics
from the design. Quadrupole magnets could have strength errors due to manufacturing errors, magnetic field calibration errors, or power supply regulation
errors. Horizontal orbit offsets in sextupole magnets, which can be caused by
magnet misalignment, introduce quadrupole components from the feed-down
effect. Other types of magnets, such as dipole or sextupole magnets, could
have random quadrupole errors due to manufacturing errors. Inaccurate lattice modeling could introduce discrepancies between the model and the real
machine. Insertion devices could contribute to linear optics errors through the
quadrupole components in their residual field integrals or the dynamical effects
that arise from the transverse field roll-off and the sinusoidal trajectories [103].
Impedances could also cause optics errors for an intense beam.
With linear optics errors, the betatron tunes are usually shifted from the
design values. The lattice functions lose the periodicity. Because of the beta
beating and betatron phase beating, the sextupole cancellation scheme could
lose effectiveness, causing degradation of the nonlinear beam dynamics performance. Correction of the linear optics toward the design has many benefits.
Similar to orbit correction, correction of linear optics requires a correction
target, measurements that characterize the optics errors, and knobs to compensate the errors. The correction target is typically the design optics, which
is often represented by a lattice model with which the linear optics functions,
such as the Courant-Snyder parameters, the betatron phase advances, and the
dispersion functions, can be computed.
To correct the linear optics errors, measurements must be conducted to
sample the linear optics and determine the errors. Magnetic field measurement
on an operating accelerator is not realistic; even if it can be done, it cannot
resolve all differences between the machine and the design as some differences
are visible only to the beam (e.g., the dynamic ID effect and the impedance
effect) and some differences come from the model (e.g., hard-edge approximation of the magnetic field profiles). Beam-based measurements can reveal the
linear optics of the machine as the beam experiences. Using information derived from beam-based measurements to correct the linear optics can restore
the optics condition for the beam.
In the case of orbit correction, the errors that need correction can be readily determined since the orbit is measured directly with BPMs. The linear
optics, however, cannot be directly obtained. Indirect measurements are generally necessary to determine the linear optics. Processing data taken in these
measurements to extract the optics errors and to derive the required knob
changes for correction is a fundamental challenge in linear optics correction.
Closed-orbit response matrix [77, 76, 44, 25, 21, 102] and turn-by-turn BPM
data [15, 19, 119, 118, 58, 61, 116, 125, 117] are two basic types of measurements that are used for linear optics measurement and correction. The
measured dispersion function is often used as supplemental data.
Beta functions in circular accelerators can also be determined by measuring tune shifts due to quadrupole modulation [48]. In this method, the
There are many error sources that can cause deviations of the linear optics
from the design. Quadrupole magnets could have strength errors due to manufacturing errors, magnetic field calibration errors, or power supply regulation
errors. Horizontal orbit offsets in sextupole magnets, which can be caused by
magnet misalignment, introduce quadrupole components from the feed-down
effect. Other types of magnets, such as dipole or sextupole magnets, could
have random quadrupole errors due to manufacturing errors. Inaccurate lattice modeling could introduce discrepancies between the model and the real
machine. Insertion devices could contribute to linear optics errors through the
quadrupole components in their residual field integrals or the dynamical effects
that arise from the transverse field roll-off and the sinusoidal trajectories [103].
Impedances could also cause optics errors for an intense beam.
With linear optics errors, the betatron tunes are usually shifted from the
design values. The lattice functions lose the periodicity. Because of the beta
beating and betatron phase beating, the sextupole cancellation scheme could
lose effectiveness, causing degradation of the nonlinear beam dynamics performance. Correction of the linear optics toward the design has many benefits.
Similar to orbit correction, correction of linear optics requires a correction
target, measurements that characterize the optics errors, and knobs to compensate the errors. The correction target is typically the design optics, which
is often represented by a lattice model with which the linear optics functions,
such as the Courant-Snyder parameters, the betatron phase advances, and the
dispersion functions, can be computed.
To correct the linear optics errors, measurements must be conducted to
sample the linear optics and determine the errors. Magnetic field measurement
on an operating accelerator is not realistic; even if it can be done, it cannot
resolve all differences between the machine and the design as some differences
are visible only to the beam (e.g., the dynamic ID effect and the impedance
effect) and some differences come from the model (e.g., hard-edge approximation of the magnetic field profiles). Beam-based measurements can reveal the
linear optics of the machine as the beam experiences. Using information derived from beam-based measurements to correct the linear optics can restore
the optics condition for the beam.
In the case of orbit correction, the errors that need correction can be readily determined since the orbit is measured directly with BPMs. The linear
optics, however, cannot be directly obtained. Indirect measurements are generally necessary to determine the linear optics. Processing data taken in these
measurements to extract the optics errors and to derive the required knob
changes for correction is a fundamental challenge in linear optics correction.
Closed-orbit response matrix [77, 76, 44, 25, 21, 102] and turn-by-turn BPM
data [15, 19, 119, 118, 58, 61, 116, 125, 117] are two basic types of measurements that are used for linear optics measurement and correction. The
measured dispersion function is often used as supplemental data.
Beta functions in circular accelerators can also be determined by measuring tune shifts due to quadrupole modulation [48]. In this method, the