166 Beam-based Correction and Optimization for Accelerators
the diffraction limited storage rings, making it more difficult for the method to
work where it is needed the most. Radiation damping in high energy storage
rings also limits the number of usable turns.
Second, the imperfections of the BPMs will affect the RDT measurements.
These include the nonlinear response of the BPMs to beam position and the
random BPM noise or other contaminating noise sources. The nonlinear BPM
response distorts the apparent nonlinear beam motion and interferes with
the spectral lines. The random BPM noise introduces errors to the RDTs or
even completely swamps the weak spectral lines. The decoherence and BPM
imperfections affect the precision of RDT measurements. The errors in the first
order RDTs driven by sextupoles could be high enough to make the results
not useful for correction. The relative errors in higher order RDTs originated
from interactions of multiple sources would be much larger.
Third, there are not enough independent knobs for the correction of the
many RDTs. In theory, if linear and nonlinear lattice elements in the machine
are identical to the design model, RDTs of all orders are automatically equal
between the machine and the model. In reality, there are residual optics errors
in the machine and there are also physics effects not accounted for in the
model (such as fringe fields, insertion device perturbations, etc.) and hence
the RDTs will be different. Compensation of all the relevant RDTs will likely
require more nonlinear magnets than are available.
Another issue for the RDT-based correction approach is that the correction
of measurable RDTs would not necessarily bring improvement to the nonlinear dynamics performance. The dynamic aperture of a storage ring may be
limited by one or more higher order resonances which are not visible on the
BPM signals. For example, one limiting resonance in the APS-U lattice is
the 6th order resonance 2ν x + 4ν y = p. The correction may likely introduce
changes to the lattice such that other resonances become performance limiting. Furthermore, chromatic resonances are difficult to measure and correct
and hence the local momentum apertures may not be under control.
the diffraction limited storage rings, making it more difficult for the method to
work where it is needed the most. Radiation damping in high energy storage
rings also limits the number of usable turns.
Second, the imperfections of the BPMs will affect the RDT measurements.
These include the nonlinear response of the BPMs to beam position and the
random BPM noise or other contaminating noise sources. The nonlinear BPM
response distorts the apparent nonlinear beam motion and interferes with
the spectral lines. The random BPM noise introduces errors to the RDTs or
even completely swamps the weak spectral lines. The decoherence and BPM
imperfections affect the precision of RDT measurements. The errors in the first
order RDTs driven by sextupoles could be high enough to make the results
not useful for correction. The relative errors in higher order RDTs originated
from interactions of multiple sources would be much larger.
Third, there are not enough independent knobs for the correction of the
many RDTs. In theory, if linear and nonlinear lattice elements in the machine
are identical to the design model, RDTs of all orders are automatically equal
between the machine and the model. In reality, there are residual optics errors
in the machine and there are also physics effects not accounted for in the
model (such as fringe fields, insertion device perturbations, etc.) and hence
the RDTs will be different. Compensation of all the relevant RDTs will likely
require more nonlinear magnets than are available.
Another issue for the RDT-based correction approach is that the correction
of measurable RDTs would not necessarily bring improvement to the nonlinear dynamics performance. The dynamic aperture of a storage ring may be
limited by one or more higher order resonances which are not visible on the
BPM signals. For example, one limiting resonance in the APS-U lattice is
the 6th order resonance 2ν x + 4ν y = p. The correction may likely introduce
changes to the lattice such that other resonances become performance limiting. Furthermore, chromatic resonances are difficult to measure and correct
and hence the local momentum apertures may not be under control.