10 The Largest Accelerators and Colliders of Their Time
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Fig. 10.8 Orbit and spin tracking through the four helical magnets of a Siberian Snake. The spin
tracking shows the reversal of the vertical polarization. The spin rotation axis is in the horizontal
plane and is pointing 45 ◦ away from the beam direction
spin rotation axes. This configuration yields a spin tune Q s = 0.5 and a vertical
stable spin direction around the ring. Here, spin tune is defined as the number
of spin precessions in one orbital revolution. Since the betatron tunes in circular
accelerators are kept away from half integer to keep the beam stable, both intrinsic
and imperfection depolarizing spin resonances at Gγ = kP ± Q y and Gγ = k are
avoided [79]. Here, G is the anomalous g factor, γ is the Lorentz factor, k is an
integer, P is the super-periodicity of the accelerator, and Q y is the vertical betatron
tune.
The accurate measurement of the beam polarization is required for set-up and
operation of the polarized proton collider. Very small angle elastic scattering in the
Coulomb-Nuclear interference region offers the possibility for an analyzing reaction
with a high figure-of-merit, which is not expected to be strongly energy dependent
[80]. For polarized beam commissioning in RHIC an ultra-thin carbon ribbon is
used as an internal target, and the recoil carbon nuclei are detected to measure both
vertical and radial polarization components. The detection of the recoil carbon with
silicon detectors using both energy and time-of-flight information shows excellent
particle identification. It was demonstrated that this polarimeter can be used to
monitor polarization of the high energy proton beams in an almost non-destructive
manner and that the carbon fiber target could be scanned through the circulating
beam to measure beam and polarization profiles. A polarized atomic hydrogen jet
was also installed as an internal target for small angle proton-proton scattering
which allows the absolute calibration of the beam polarization to better than 5%.
Figure 10.9 shows circulating beam current, luminosity and measured circulating
beam polarization of a typical store with a beam energy of 100 GeV. The maximum
peak luminosity achieved with 100 GeV proton beams is about 50 × 10 30 cm −2 s −1
and store beam polarization of about 55% calibrated at 100 GeV with the absolute
polarimeter mentioned above. To preserve beam polarization in RHIC during
acceleration and storage the vertical betatron tune has to be controlled to better than
0.005 and the orbit has to be corrected to better than 1 mm rms to avoid depolarizing
“snake” resonances.
During acceleration from 100 GeV to the maximum RHIC energy of 250 GeV,
several very strong depolarizing spin resonances need to be crossed [81]. In
a first running period an average store polarization of 34% was measured at
250 GeV again calibrated with the absolute polarimeter. The peak luminosity
607
Fig. 10.8 Orbit and spin tracking through the four helical magnets of a Siberian Snake. The spin
tracking shows the reversal of the vertical polarization. The spin rotation axis is in the horizontal
plane and is pointing 45 ◦ away from the beam direction
spin rotation axes. This configuration yields a spin tune Q s = 0.5 and a vertical
stable spin direction around the ring. Here, spin tune is defined as the number
of spin precessions in one orbital revolution. Since the betatron tunes in circular
accelerators are kept away from half integer to keep the beam stable, both intrinsic
and imperfection depolarizing spin resonances at Gγ = kP ± Q y and Gγ = k are
avoided [79]. Here, G is the anomalous g factor, γ is the Lorentz factor, k is an
integer, P is the super-periodicity of the accelerator, and Q y is the vertical betatron
tune.
The accurate measurement of the beam polarization is required for set-up and
operation of the polarized proton collider. Very small angle elastic scattering in the
Coulomb-Nuclear interference region offers the possibility for an analyzing reaction
with a high figure-of-merit, which is not expected to be strongly energy dependent
[80]. For polarized beam commissioning in RHIC an ultra-thin carbon ribbon is
used as an internal target, and the recoil carbon nuclei are detected to measure both
vertical and radial polarization components. The detection of the recoil carbon with
silicon detectors using both energy and time-of-flight information shows excellent
particle identification. It was demonstrated that this polarimeter can be used to
monitor polarization of the high energy proton beams in an almost non-destructive
manner and that the carbon fiber target could be scanned through the circulating
beam to measure beam and polarization profiles. A polarized atomic hydrogen jet
was also installed as an internal target for small angle proton-proton scattering
which allows the absolute calibration of the beam polarization to better than 5%.
Figure 10.9 shows circulating beam current, luminosity and measured circulating
beam polarization of a typical store with a beam energy of 100 GeV. The maximum
peak luminosity achieved with 100 GeV proton beams is about 50 × 10 30 cm −2 s −1
and store beam polarization of about 55% calibrated at 100 GeV with the absolute
polarimeter mentioned above. To preserve beam polarization in RHIC during
acceleration and storage the vertical betatron tune has to be controlled to better than
0.005 and the orbit has to be corrected to better than 1 mm rms to avoid depolarizing
“snake” resonances.
During acceleration from 100 GeV to the maximum RHIC energy of 250 GeV,
several very strong depolarizing spin resonances need to be crossed [81]. In
a first running period an average store polarization of 34% was measured at
250 GeV again calibrated with the absolute polarimeter. The peak luminosity