Linear optics measurement and correction - I 107
in tracking simulation to better predict the nonlinear dynamics or collective
effects of the real machine.
More importantly, the fitted quadrupole and skew quadrupole parameters
give the errors of these parameters relative to their design values, which can
be eliminated by adjusting the magnet power supply setpoints. By eliminating the quadrupole errors, the machine linear optics will be corrected toward
the ideal condition. Linear optics errors in a storage ring can cause a reduction of the dynamic aperture and the local momentum apertures. Correction
of linear optics can lead to improvement in the injection efficiency and the
Touschek lifetime. The skew quadrupole errors represent the linear coupling
errors and spurious vertical dispersion in the machine lattice. Correction of
skew quadrupole errors suppresses the linear coupling and vertical dispersion. In an electron storage ring, this will lead to an reduction of the vertical emittance. In this section we consider only linear optics correction with
quadrupole parameters. The BPM and corrector rolls and skew quadrupole
parameters are not required in the fitting setup, although they can be
included.
In optics correction, the required setpoint change for a quadrupole can be
obtained by converting the design gradient, K 0 , and the fitted gradient, K f ,
to currents using magnet calibration data. The difference of the two currents
is the step change required for the quadrupole parameter for optics correction.
If the fitting quadrupole parameter corresponds to a power supply that has a
non-zero setpoint value, the correction can also be done by scaling the present
setpoint by the ratio K 0 /K f .
The application of orbit response matrix fitting for optics correction can
be illustrated with a simulated example on the SPEAR3 ring. In the simulation environment [93] all BPM gains are given a random error drawn from a
Gaussian distribution with σ = 0.02. Gradient errors are introduced to three
QF magnets and three QD magnets. Orbit response matrix data are taken
with the simulator using the method of fixed path length. The corrector kick
corresponding to the step change in the measurement is 0.15 mrad for both
horizontal and vertical correctors. Dispersion is measured by changing the RF
frequency by 1 kHz, corresponding to a momentum deviation of ∆δ = 0.0013.
Both orbit response matrix and dispersion measurements are done in the bipolar mode. Gaussian random BPM errors are added to all measurements. The
BPM noise sigma is assumed to be 1 µm for all BPMs.
There are 57 BPMs, 58 horizontal correctors, and 56 vertical correctors.
The combined orbit response matrix is 114 × 114 in dimension. In this test
we focus on the linear optics correction; the off-diagonal blocks, R xy and
R yx , are not included in the fitting. The horizontal dispersion is included.
Hence the length of the residual vector in the LOCO fitting setup is 6555.
The fitting parameters are BPM gains (57 × 2), corrector gains (58 + 56),
and 78 quadrupole gradients. The quadrupole gradient parameters include 28
QF magnets, 28 QD magnets, 1 QFC serial power supply, and a number of
in tracking simulation to better predict the nonlinear dynamics or collective
effects of the real machine.
More importantly, the fitted quadrupole and skew quadrupole parameters
give the errors of these parameters relative to their design values, which can
be eliminated by adjusting the magnet power supply setpoints. By eliminating the quadrupole errors, the machine linear optics will be corrected toward
the ideal condition. Linear optics errors in a storage ring can cause a reduction of the dynamic aperture and the local momentum apertures. Correction
of linear optics can lead to improvement in the injection efficiency and the
Touschek lifetime. The skew quadrupole errors represent the linear coupling
errors and spurious vertical dispersion in the machine lattice. Correction of
skew quadrupole errors suppresses the linear coupling and vertical dispersion. In an electron storage ring, this will lead to an reduction of the vertical emittance. In this section we consider only linear optics correction with
quadrupole parameters. The BPM and corrector rolls and skew quadrupole
parameters are not required in the fitting setup, although they can be
included.
In optics correction, the required setpoint change for a quadrupole can be
obtained by converting the design gradient, K 0 , and the fitted gradient, K f ,
to currents using magnet calibration data. The difference of the two currents
is the step change required for the quadrupole parameter for optics correction.
If the fitting quadrupole parameter corresponds to a power supply that has a
non-zero setpoint value, the correction can also be done by scaling the present
setpoint by the ratio K 0 /K f .
The application of orbit response matrix fitting for optics correction can
be illustrated with a simulated example on the SPEAR3 ring. In the simulation environment [93] all BPM gains are given a random error drawn from a
Gaussian distribution with σ = 0.02. Gradient errors are introduced to three
QF magnets and three QD magnets. Orbit response matrix data are taken
with the simulator using the method of fixed path length. The corrector kick
corresponding to the step change in the measurement is 0.15 mrad for both
horizontal and vertical correctors. Dispersion is measured by changing the RF
frequency by 1 kHz, corresponding to a momentum deviation of ∆δ = 0.0013.
Both orbit response matrix and dispersion measurements are done in the bipolar mode. Gaussian random BPM errors are added to all measurements. The
BPM noise sigma is assumed to be 1 µm for all BPMs.
There are 57 BPMs, 58 horizontal correctors, and 56 vertical correctors.
The combined orbit response matrix is 114 × 114 in dimension. In this test
we focus on the linear optics correction; the off-diagonal blocks, R xy and
R yx , are not included in the fitting. The horizontal dispersion is included.
Hence the length of the residual vector in the LOCO fitting setup is 6555.
The fitting parameters are BPM gains (57 × 2), corrector gains (58 + 56),
and 78 quadrupole gradients. The quadrupole gradient parameters include 28
QF magnets, 28 QD magnets, 1 QFC serial power supply, and a number of