10 The Largest Accelerators and Colliders of Their Time
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electron beams. As in HERA, an equilibrium polarization of at least 50% has been
shown to be achievable in eRHIC at the highest electron beam operation energy
of 18 GeV. This performance will enable to maintain a high level of average
polarization of 80% with the initial polization of the the electron beam of 85%
if the stored electron bunches are replaced every 6 min on average [177].
10.5.2.5 Lessons Learned from HERA Dynamic Aperture
The dynamic aperture optimization in the HERA electron ring after the year
2000 was accomplished with only two sextupole families for the correction of
chromaticity. Correction of higher order chromaticity which is due to the strong
contribution of the interaction region quadrupole magnets to the chromaticity and
the corresponding strong off-momentum distortion of the optical functions (betabeat) is necessary to confine the beam tune foot print and to avoid destabilizing
resonances.
The straight forward correction of off-momentum beta-beats with more families
of sextupoles was avoided thereby avoiding large peak strengths of the sextupole
magnets, which would have deteriorated the dynamic aperture. Instead, the horizontal and vertical betatron phase differences between the North and the South
interaction points were chosen to be an odd integer of π/2. The off-momentum beta
beat caused by the low beta quadrupoles of one IR was intrinsically canceled by
the correponding beta beat of the other IR. This way, the nonlinear tuneshift with
momentum was minimized.
The HERA chromatic correction scheme [184] also suppressed the generation of driving terms of the higher order nonlinear synchro-betatron resonances
Q x + 3 cot Q s =integer which otherwise would have affected the beam stability
at the low tune values needed for high polarization operation.
Last but not least, the HERA chromatic correction scheme reduced the magnet
currents of the sextupoles circuits which would have been required using the multifamily scheme. The HERA scheme is being carried over to eRHIC which is planned
to be operated with two collidng beam detectors as well. The eRHIC chromatic
correction scheme is an important constituent of the design which enables highest
luminosity values.
10.5.2.6 HERA IR Magnet Design
In order to achieve hightest luminosity, the HERA interaction regions have been
re-designed to allow for very small beta functions at the IP. The change was
implemented in the year 2000 and HERA operated with about 3.5 times the design
luminosity in the years 2004–2007.
This upgrade included accelerator magnets that were placed inside the colliding
beam detectors H1 and ZEUS, and in particular inside the solenoidal detector fields
of up to 5 T. Obviously, no magnetic steel was allowable inside the solenoid fields
639
electron beams. As in HERA, an equilibrium polarization of at least 50% has been
shown to be achievable in eRHIC at the highest electron beam operation energy
of 18 GeV. This performance will enable to maintain a high level of average
polarization of 80% with the initial polization of the the electron beam of 85%
if the stored electron bunches are replaced every 6 min on average [177].
10.5.2.5 Lessons Learned from HERA Dynamic Aperture
The dynamic aperture optimization in the HERA electron ring after the year
2000 was accomplished with only two sextupole families for the correction of
chromaticity. Correction of higher order chromaticity which is due to the strong
contribution of the interaction region quadrupole magnets to the chromaticity and
the corresponding strong off-momentum distortion of the optical functions (betabeat) is necessary to confine the beam tune foot print and to avoid destabilizing
resonances.
The straight forward correction of off-momentum beta-beats with more families
of sextupoles was avoided thereby avoiding large peak strengths of the sextupole
magnets, which would have deteriorated the dynamic aperture. Instead, the horizontal and vertical betatron phase differences between the North and the South
interaction points were chosen to be an odd integer of π/2. The off-momentum beta
beat caused by the low beta quadrupoles of one IR was intrinsically canceled by
the correponding beta beat of the other IR. This way, the nonlinear tuneshift with
momentum was minimized.
The HERA chromatic correction scheme [184] also suppressed the generation of driving terms of the higher order nonlinear synchro-betatron resonances
Q x + 3 cot Q s =integer which otherwise would have affected the beam stability
at the low tune values needed for high polarization operation.
Last but not least, the HERA chromatic correction scheme reduced the magnet
currents of the sextupoles circuits which would have been required using the multifamily scheme. The HERA scheme is being carried over to eRHIC which is planned
to be operated with two collidng beam detectors as well. The eRHIC chromatic
correction scheme is an important constituent of the design which enables highest
luminosity values.
10.5.2.6 HERA IR Magnet Design
In order to achieve hightest luminosity, the HERA interaction regions have been
re-designed to allow for very small beta functions at the IP. The change was
implemented in the year 2000 and HERA operated with about 3.5 times the design
luminosity in the years 2004–2007.
This upgrade included accelerator magnets that were placed inside the colliding
beam detectors H1 and ZEUS, and in particular inside the solenoidal detector fields
of up to 5 T. Obviously, no magnetic steel was allowable inside the solenoid fields