Coupling and nonlinear dynamics correction 163
Realizing the design performance of the nonlinear beam dynamics on the
real machine is also very challenging and will be more challenging for the
future diffraction limited storage rings as these rings will be more nonlinear
and have more error sources. Developing methods to compensate the negative
impact of lattice errors to the nonlinear beam dynamics is critical for the
success of future storage rings and can also benefit the operation of existing
rings.
The nonlinear beam dynamics performance of a storage ring depends
strongly on the linear optics. Correction of linear errors is essential. For third
generation light sources, optics correction often leads to improvements in the
dynamic aperture and the momentum acceptances. However, there will always
be residual optics errors. Even when the beta functions and phase advances
at the BPMs are at the ideal design values, their values at the sextupoles
may differ from the design. The strengths of the nonlinear magnets in the real
machine may be different from the design model due to calibration errors.
The nonlinear fields in dipole and quadrupole magnets and the higher order
multipoles in sextupoles due to systematic and random errors may not be
included in the model. Therefore, correction of the nonlinear lattice features
toward the design is necessary.
Nonlinear beam dynamics measurement and correction:
Naturally, it is desirable to apply the beam-based correction approach to
correct the nonlinear beam dynamics toward the design. As for the cases of
linear errors correction, this requires
• control parameters (i.e., knobs) that have a direct impact to the nonlinear dynamics,
• beam diagnostics that can effectively measure the nonlinear beam dynamics behavior, and
• a method that deduces the required adjustments of the knobs from the
measurements.
The knobs are typically the strengths of the nonlinear magnets in the lattice,
i.e., sextupoles and octupoles (if present in the lattice). The fitting results
for these knobs can be used to correct the machine. If the goal is to identify
sources of discrepancies between the model and the machine, additional multipole components in the model (such as sextupole, octupole, and decapole
components of the dipole and quadrupole magnets) can be included as fitting
parameters. The diagnostics need to detect features of the beam dynamics
that are relevant to the nonlinear beam dynamics performance and can be
compared to the design model. These features could be higher order chromaticities, the tune shifts with amplitudes, and the resonance driving terms
(RDTs). The least-square fitting approach can be used to calibrate the lattice
model with the measurements [9, 8].
Tune shifts with amplitudes and RDTs can be measured with turn-by-turn
BPMs. As shown in Eqs. (2.116)-(2.117), the spectral lines of the turn-by-turn
Realizing the design performance of the nonlinear beam dynamics on the
real machine is also very challenging and will be more challenging for the
future diffraction limited storage rings as these rings will be more nonlinear
and have more error sources. Developing methods to compensate the negative
impact of lattice errors to the nonlinear beam dynamics is critical for the
success of future storage rings and can also benefit the operation of existing
rings.
The nonlinear beam dynamics performance of a storage ring depends
strongly on the linear optics. Correction of linear errors is essential. For third
generation light sources, optics correction often leads to improvements in the
dynamic aperture and the momentum acceptances. However, there will always
be residual optics errors. Even when the beta functions and phase advances
at the BPMs are at the ideal design values, their values at the sextupoles
may differ from the design. The strengths of the nonlinear magnets in the real
machine may be different from the design model due to calibration errors.
The nonlinear fields in dipole and quadrupole magnets and the higher order
multipoles in sextupoles due to systematic and random errors may not be
included in the model. Therefore, correction of the nonlinear lattice features
toward the design is necessary.
Nonlinear beam dynamics measurement and correction:
Naturally, it is desirable to apply the beam-based correction approach to
correct the nonlinear beam dynamics toward the design. As for the cases of
linear errors correction, this requires
• control parameters (i.e., knobs) that have a direct impact to the nonlinear dynamics,
• beam diagnostics that can effectively measure the nonlinear beam dynamics behavior, and
• a method that deduces the required adjustments of the knobs from the
measurements.
The knobs are typically the strengths of the nonlinear magnets in the lattice,
i.e., sextupoles and octupoles (if present in the lattice). The fitting results
for these knobs can be used to correct the machine. If the goal is to identify
sources of discrepancies between the model and the machine, additional multipole components in the model (such as sextupole, octupole, and decapole
components of the dipole and quadrupole magnets) can be included as fitting
parameters. The diagnostics need to detect features of the beam dynamics
that are relevant to the nonlinear beam dynamics performance and can be
compared to the design model. These features could be higher order chromaticities, the tune shifts with amplitudes, and the resonance driving terms
(RDTs). The least-square fitting approach can be used to calibrate the lattice
model with the measurements [9, 8].
Tune shifts with amplitudes and RDTs can be measured with turn-by-turn
BPMs. As shown in Eqs. (2.116)-(2.117), the spectral lines of the turn-by-turn