74 Beam-based Correction and Optimization for Accelerators
fast orbit disturbances. In machines that require high orbit stability, such as
synchrotron light sources, orbit correctors with fast responses are needed.
Orbit errors are caused by deviations of the bending fields along the beam
path from the design condition. The bending field deviations are the sources of
orbit errors. Ideally, the error sources should be corrected locally at the source
points, such that no orbit distortion occurs elsewhere. However, in reality, local
correction is often not practical. This is because the error sources cannot be
identified or no adjustment to the bending field can be made to compensate
the errors at the locations. In such cases, global orbit correction through a
distribution of orbit correctors is desired.
The differential orbit shift caused by a small change to the corrector
strength is the orbit response of the orbit corrector. Orbit responses at the
BPMs can be measured by changing the corrector current by a small amount
and monitoring the orbit shifts. The orbit responses at multiple BPMs of multiple orbit correctors can be arranged in a matrix, called the orbit response
matrix, whose element is given by
R ij =
∆x i
∆θ j
,
(3.5)
where ∆x i is the orbit change at BPM i for a kick angle, ∆θ j , at corrector
j. With M BPMs and N correctors, the dimension of the orbit response
matrix is M × N . The orbit response matrix can be used to predict the orbit
changes when the orbit correctors are varied. Conversely, knowing the desired
orbit changes, the orbit response matrix can be used to calculate the required
changes to the orbit corrector strengths.
3.2 BEAM-BASED ALIGNMENT
For orbit correction, a target orbit given in terms of BPM readings is needed.
The design orbit would be the natural choice for the target orbit. However,
it is not straightforward to determine the design orbit on the BPMs. The
vacuum chambers, to which the BPMs are attached, have alignment errors.
The BPM buttons have mechanical errors in the sizes and positions. The BPM
electronics also have errors in signal processing. Therefore, a BPM reading of
zero does not represent the design orbit, nor does it represent the mechanical
center of the BPM.
On the other hand, since all the magnets have alignment errors from their
design positions, the design orbit is not necessarily the ideal orbit for the beam
for the purpose of optimizing beam performance. At certain locations of the
beam line, the beam position affects the experiments that use the beam. For
example, the position and angle of the electron beam in an insertion device
affect the photon beam position. For such locations, the target particle beam
orbit on the BPMs would be determined by the requirements of the user
experiments. In other areas of the beam path, however, there is some freedom
in choosing the target orbit. In general, the target orbit should be chosen for
fast orbit disturbances. In machines that require high orbit stability, such as
synchrotron light sources, orbit correctors with fast responses are needed.
Orbit errors are caused by deviations of the bending fields along the beam
path from the design condition. The bending field deviations are the sources of
orbit errors. Ideally, the error sources should be corrected locally at the source
points, such that no orbit distortion occurs elsewhere. However, in reality, local
correction is often not practical. This is because the error sources cannot be
identified or no adjustment to the bending field can be made to compensate
the errors at the locations. In such cases, global orbit correction through a
distribution of orbit correctors is desired.
The differential orbit shift caused by a small change to the corrector
strength is the orbit response of the orbit corrector. Orbit responses at the
BPMs can be measured by changing the corrector current by a small amount
and monitoring the orbit shifts. The orbit responses at multiple BPMs of multiple orbit correctors can be arranged in a matrix, called the orbit response
matrix, whose element is given by
R ij =
∆x i
∆θ j
,
(3.5)
where ∆x i is the orbit change at BPM i for a kick angle, ∆θ j , at corrector
j. With M BPMs and N correctors, the dimension of the orbit response
matrix is M × N . The orbit response matrix can be used to predict the orbit
changes when the orbit correctors are varied. Conversely, knowing the desired
orbit changes, the orbit response matrix can be used to calculate the required
changes to the orbit corrector strengths.
3.2 BEAM-BASED ALIGNMENT
For orbit correction, a target orbit given in terms of BPM readings is needed.
The design orbit would be the natural choice for the target orbit. However,
it is not straightforward to determine the design orbit on the BPMs. The
vacuum chambers, to which the BPMs are attached, have alignment errors.
The BPM buttons have mechanical errors in the sizes and positions. The BPM
electronics also have errors in signal processing. Therefore, a BPM reading of
zero does not represent the design orbit, nor does it represent the mechanical
center of the BPM.
On the other hand, since all the magnets have alignment errors from their
design positions, the design orbit is not necessarily the ideal orbit for the beam
for the purpose of optimizing beam performance. At certain locations of the
beam line, the beam position affects the experiments that use the beam. For
example, the position and angle of the electron beam in an insertion device
affect the photon beam position. For such locations, the target particle beam
orbit on the BPMs would be determined by the requirements of the user
experiments. In other areas of the beam path, however, there is some freedom
in choosing the target orbit. In general, the target orbit should be chosen for