Application of beam-based optimization 225
DA optimization at MAX-IV and NSLS-II: DA optimization with
RCDS was also successfully applied on the MAX-IV storage ring [91]. MAXIV is the first storage ring light source that adopted an multi-bend achromat
(MBA) lattice. It currently has the lowest emittance among all storage ring
light sources. In the MAX-IV experiments, the objective function was the fractional beam loss of the stored beam under a fixed horizontal kick. The tuning
knobs are five sextupole families and three octupole families. The chromaticity
response matrix of the sextupoles was used to construct three combined knobs
that do not change chromaticities. There were a total of 6 free knobs. RCDS
steadily improved the DA over 4 iterations. The DA was increased roughly
from 5 mm to 7 mm (measured at the center of a long straight section), while
the chromaticities remained about the same. The optimized lattice also has
an significantly improved momentum acceptance, which reached the design
goal of 4.5%.
On the NSLS-II storage ring, DA optimization with RCDS using sextupole
knobs improved the DA by more than 20% [123]. It was found that the horizontal tune shift with amplitude was reduced by more than a factor of two in
the optimized lattice.
8.4.2 Local momentum aperture optimization
If the local momentum aperture (LMA) is smaller than the RF bucket height,
it becomes the limiting factor for the Touschek lifetime. In such cases, online
optimization may be done to enlarge the LMA. The tuning knobs for the LMA
are usually the same as those for the DA optimization. The objective function
can be the beam loss rate for a Touschek scattering dominated beam. The
Touschek loss rate is strongly dependent on the momentum aperture, δ A , with
1
τ T
roughly proportional to δ
−3
A . As shown in Eq. 8.2, it is also proportional
to the charge density. In the LMA optimization experiment, it is critical to
separate the charge density factor out from the loss rate in order to target
only the LMA.
In an experiment, the bunch charge constantly changes as a consequence of
the beam loss that causes a finite lifetime. In addition, the bunch length varies
with the bunch charge due to bunch lengthening through the longitudinal
impedance. To avoid a significant impact from bunch lengthening, the bunch
charge may be replenished frequently so that it is roughly constant. When
sextupole strengths are changed, the vertical emittance could also be altered,
as vertical orbit offsets in sextupoles are a source of linear coupling errors. To
mitigate the impact of vertical emittance variation, it is desirable to keep a
constant orbit (with orbit feedback) that is as close to the sextupole centers
as possible. It would also be helpful to slightly increase the coupling ratio with
skew quadrupoles, such that coupling variations due to sextupoles are small
compared to the initial vertical emittance. If the diagnostics are available,
a preferred approach is to measure the vertical emittance and factor out its
effect from the objective function.
DA optimization at MAX-IV and NSLS-II: DA optimization with
RCDS was also successfully applied on the MAX-IV storage ring [91]. MAXIV is the first storage ring light source that adopted an multi-bend achromat
(MBA) lattice. It currently has the lowest emittance among all storage ring
light sources. In the MAX-IV experiments, the objective function was the fractional beam loss of the stored beam under a fixed horizontal kick. The tuning
knobs are five sextupole families and three octupole families. The chromaticity
response matrix of the sextupoles was used to construct three combined knobs
that do not change chromaticities. There were a total of 6 free knobs. RCDS
steadily improved the DA over 4 iterations. The DA was increased roughly
from 5 mm to 7 mm (measured at the center of a long straight section), while
the chromaticities remained about the same. The optimized lattice also has
an significantly improved momentum acceptance, which reached the design
goal of 4.5%.
On the NSLS-II storage ring, DA optimization with RCDS using sextupole
knobs improved the DA by more than 20% [123]. It was found that the horizontal tune shift with amplitude was reduced by more than a factor of two in
the optimized lattice.
8.4.2 Local momentum aperture optimization
If the local momentum aperture (LMA) is smaller than the RF bucket height,
it becomes the limiting factor for the Touschek lifetime. In such cases, online
optimization may be done to enlarge the LMA. The tuning knobs for the LMA
are usually the same as those for the DA optimization. The objective function
can be the beam loss rate for a Touschek scattering dominated beam. The
Touschek loss rate is strongly dependent on the momentum aperture, δ A , with
1
τ T
roughly proportional to δ
−3
A . As shown in Eq. 8.2, it is also proportional
to the charge density. In the LMA optimization experiment, it is critical to
separate the charge density factor out from the loss rate in order to target
only the LMA.
In an experiment, the bunch charge constantly changes as a consequence of
the beam loss that causes a finite lifetime. In addition, the bunch length varies
with the bunch charge due to bunch lengthening through the longitudinal
impedance. To avoid a significant impact from bunch lengthening, the bunch
charge may be replenished frequently so that it is roughly constant. When
sextupole strengths are changed, the vertical emittance could also be altered,
as vertical orbit offsets in sextupoles are a source of linear coupling errors. To
mitigate the impact of vertical emittance variation, it is desirable to keep a
constant orbit (with orbit feedback) that is as close to the sextupole centers
as possible. It would also be helpful to slightly increase the coupling ratio with
skew quadrupoles, such that coupling variations due to sextupoles are small
compared to the initial vertical emittance. If the diagnostics are available,
a preferred approach is to measure the vertical emittance and factor out its
effect from the objective function.