626
K. Hübner et al.
10.4.7 Beam Optics
The luminosity of a ring collider is inversely proportional to the vertical β-function
at the IP as shown in Eq. (10.4). The B-factories have used the smallest β ∗
y as a
ring collider so far. Generally speaking, a small β ∗
y means higher chromaticity and
higher nonlinearity arisen from sextupoles for the chromaticity correction. Thus the
design of the ring lattice needs special care to ensure the dynamic aperture. One
technique applied for KEKB was non-interleaved sextupole pairs separated by a
−I transformation that cancel the geometric nonlinearity of the sextupoles up to
the second order [145]. Although the idea was very old but the reason why the
application to a real ring had to wait until the B-factories was probably the necessary
computer power to optimize the sextupole setting, as it requires a large number of
sextupole families to extend the momentum acceptance. For instance, KEKB had 54
families of sextupole pairs. The relative betatron phase advance between the pairs
became adequate by using the 2.5π cell structure in the case of KEKB arc section
[146].
Another technique to enlarge the dynamic aperture was to place a special
chromaticity correction section near the IP. The beam optics became somewhat
similar to that for linear colliders in this case. KEKB designed such a section for
the vertical correction, while PEP–II horizontal for their LERs.
These schemes worked as expected for the B-factories, and expected to work
for future super B-factories and light sources. Once the chromaticity correction is
solved, the next source of the nonlinearity is the fringe field of the final quadrupole
and the geometric nonlinearity at the IP [147], which may be mitigated by additional
octupoles placed at the final quadrupoles.
The x-y coupling and the residual vertical dispersion all over the ring were
one of the keys to achieve a high luminosity by reducing the vertical emittance.
Various techniques have been applied for such optics measurements and corrections
[148–150]. A counter solenoid to the detector solenoid was also effective to reduce
the coupling source in the case of KEKB. This was also important in the case of
crab crossing where the luminosity performance was sensitive to the chromatic x-y
coupling as described later.
10.4.8 Beam Diagnostics and Control
A number of beam diagnostic methods were developed and applied for the Bfactories:
• Beam position monitors (BPMs) with a resolution better than 1 μm in the average
mode. In some cases turn-by-turn or bunch-by-bunch electronics were equipped
[151]. In the case of KEKB, the gain imbalance of the electrodes through the
electronics was calibrated using a beam-mapping technique [152]. The design
K. Hübner et al.
10.4.7 Beam Optics
The luminosity of a ring collider is inversely proportional to the vertical β-function
at the IP as shown in Eq. (10.4). The B-factories have used the smallest β ∗
y as a
ring collider so far. Generally speaking, a small β ∗
y means higher chromaticity and
higher nonlinearity arisen from sextupoles for the chromaticity correction. Thus the
design of the ring lattice needs special care to ensure the dynamic aperture. One
technique applied for KEKB was non-interleaved sextupole pairs separated by a
−I transformation that cancel the geometric nonlinearity of the sextupoles up to
the second order [145]. Although the idea was very old but the reason why the
application to a real ring had to wait until the B-factories was probably the necessary
computer power to optimize the sextupole setting, as it requires a large number of
sextupole families to extend the momentum acceptance. For instance, KEKB had 54
families of sextupole pairs. The relative betatron phase advance between the pairs
became adequate by using the 2.5π cell structure in the case of KEKB arc section
[146].
Another technique to enlarge the dynamic aperture was to place a special
chromaticity correction section near the IP. The beam optics became somewhat
similar to that for linear colliders in this case. KEKB designed such a section for
the vertical correction, while PEP–II horizontal for their LERs.
These schemes worked as expected for the B-factories, and expected to work
for future super B-factories and light sources. Once the chromaticity correction is
solved, the next source of the nonlinearity is the fringe field of the final quadrupole
and the geometric nonlinearity at the IP [147], which may be mitigated by additional
octupoles placed at the final quadrupoles.
The x-y coupling and the residual vertical dispersion all over the ring were
one of the keys to achieve a high luminosity by reducing the vertical emittance.
Various techniques have been applied for such optics measurements and corrections
[148–150]. A counter solenoid to the detector solenoid was also effective to reduce
the coupling source in the case of KEKB. This was also important in the case of
crab crossing where the luminosity performance was sensitive to the chromatic x-y
coupling as described later.
10.4.8 Beam Diagnostics and Control
A number of beam diagnostic methods were developed and applied for the Bfactories:
• Beam position monitors (BPMs) with a resolution better than 1 μm in the average
mode. In some cases turn-by-turn or bunch-by-bunch electronics were equipped
[151]. In the case of KEKB, the gain imbalance of the electrodes through the
electronics was calibrated using a beam-mapping technique [152]. The design