Abstract
Crab cavities are proposed to be used for a luminosity upgrade of the Large Hadron Collider (LHC). Crab cavities are rf cavities operated in a transverse dipole mode, which imparts on the beam particles a transverse kick that varies with the longitudinal position along the bunch. The crab cavity introduces another kind of dispersion to the particles which is $z$ dependent, and thus could complicate the beam dynamics and have an impact on the LHC collimation system. As for LHC, the off-momentum beta-beat and dispersion-beat already compromise the performance of the collimation system; the crab dispersion introduced by global crab cavities might do the same, and should be carefully evaluated. In this paper, we present a definition for the crab dispersion, and study its impact on the LHC collimation system.
Highlights
INTRODUCTIONThe design luminosity of the Large Hadron Collider (LHC) is 1034 cmÀ2 sÀ1 at the two high-luminosity proton-proton experiments ATLAS (located at interaction point 1, or IP1) and CMS (located at IP5), with a center-ofmass energy of 14 TeV [1]
The design luminosity of the Large Hadron Collider (LHC) is 1034 cmÀ2 sÀ1 at the two high-luminosity proton-proton experiments ATLAS and CMS, with a center-ofmass energy of 14 TeV [1]
From formula (13), we observe that the deviation of the closed orbit from the z-dependent crab dispersion is proportional to the crabbing angle =2, and that it is modulated by the angular frequency of the crab cavity and the longitudinal coordinate z, as sinð!z=cÞ=!
Summary
The design luminosity of the Large Hadron Collider (LHC) is 1034 cmÀ2 sÀ1 at the two high-luminosity proton-proton experiments ATLAS (located at interaction point 1, or IP1) and CMS (located at IP5), with a center-ofmass energy of 14 TeV [1]. Namely the early-separation scheme and the full crab crossing (FCC). Scheme, crab cavities are an essential ingredient of the upgrade. Crab cavities (CC) have been proposed for both linear [2] and circular colliders [3], to restore an effective headon collision at the IP. The crab cavity gives rise to a z-dependent transverse kick on the beam particles, as well as to a change in the longitudinal momentum. The required horizontal kick from the crab cavity can be written as (assuming horizontal beam-beam crossing). The angular frequency of the crab cavity, z the longitudinal coordinate of the particle with respect to the bunch center, c the velocity of light, and x the horizontal coordinate. The crab cavity introduces an x-dependent longitudinal kick, Ápz
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