Application of beam-based optimization 221
Septum
unkicked
kicked
stored beam
injected beam
DA
bump
D
x
Figure 8.11 Illustration of off-axis injection for a storage ring.
efficiency to have the highest sensitivity over the DA, the boundary should
better be in the dense part of the beam.
The tuning knobs for the DA are usually the power supply setpoints for
the sextupole magnets. Sextupoles are the sources of the nonlinearity in the
beam motion and are hence effective knobs to change the DA. The purpose of
including sextupoles in the lattice is to correct the chromaticities. Any change
to the sextupole setting should not significantly change the chromaticity values. Some storage rings have harmonic sextupoles, which are located in areas
with a zero dispersion. The harmonic sextupoles do not change the chromaticities and are free tuning knobs for the nonlinear beam dynamics. More often
is the case in which all sextupoles are at dispersive locations; in some cases
harmonic sextupoles become chromatic sextupoles after the linear lattices are
modified for emittance reduction. In such cases, care should be taken to not
change the chromaticities during the DA optimization.
There are usually a small number of sextupoles in each lattice cell placed
symmetrically about the cell center. Sextupoles at the symmetric points of
the same cell and sextupoles at the same location of different cells may be
powered by a serial power supply. Sextupoles on the same power supply are
collectively referred to as a sextupole family. At the minimum, there are only
two sextupole families, which are required for chromaticity correction and
leave no free knobs for DA optimization. In the other extreme, all sextupoles
could be powered individually. There would be tens or hundreds of sextupole
knobs, potentially more than the optimization algorithms can handle in online
applications. In such a case, the sextupoles need to be grouped for the number
of knobs to be reduced to an acceptable level (e.g., 10 to 30). Typically the
sextupoles are grouped such that the each family consists of a number of
magnets that are symmetrically distributed around the ring. In some cases, the
sextupoles may be already grouped and powered in several families according
to their locations. Some storage rings have octupole magnets in the lattice for
controlling the nonlinear dynamics behavior [91]. They should also be included
as nonlinear dynamics tuning knobs.
Septum
unkicked
kicked
stored beam
injected beam
DA
bump
D
x
Figure 8.11 Illustration of off-axis injection for a storage ring.
efficiency to have the highest sensitivity over the DA, the boundary should
better be in the dense part of the beam.
The tuning knobs for the DA are usually the power supply setpoints for
the sextupole magnets. Sextupoles are the sources of the nonlinearity in the
beam motion and are hence effective knobs to change the DA. The purpose of
including sextupoles in the lattice is to correct the chromaticities. Any change
to the sextupole setting should not significantly change the chromaticity values. Some storage rings have harmonic sextupoles, which are located in areas
with a zero dispersion. The harmonic sextupoles do not change the chromaticities and are free tuning knobs for the nonlinear beam dynamics. More often
is the case in which all sextupoles are at dispersive locations; in some cases
harmonic sextupoles become chromatic sextupoles after the linear lattices are
modified for emittance reduction. In such cases, care should be taken to not
change the chromaticities during the DA optimization.
There are usually a small number of sextupoles in each lattice cell placed
symmetrically about the cell center. Sextupoles at the symmetric points of
the same cell and sextupoles at the same location of different cells may be
powered by a serial power supply. Sextupoles on the same power supply are
collectively referred to as a sextupole family. At the minimum, there are only
two sextupole families, which are required for chromaticity correction and
leave no free knobs for DA optimization. In the other extreme, all sextupoles
could be powered individually. There would be tens or hundreds of sextupole
knobs, potentially more than the optimization algorithms can handle in online
applications. In such a case, the sextupoles need to be grouped for the number
of knobs to be reduced to an acceptable level (e.g., 10 to 30). Typically the
sextupoles are grouped such that the each family consists of a number of
magnets that are symmetrically distributed around the ring. In some cases, the
sextupoles may be already grouped and powered in several families according
to their locations. Some storage rings have octupole magnets in the lattice for
controlling the nonlinear dynamics behavior [91]. They should also be included
as nonlinear dynamics tuning knobs.