Crab dispersion and its impact on the CERN Large Hadron Collider collimation

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.

Figure 1

Crab dispersion and off-momentum dispersion for nominal LHC optics.

Figure 2

Crab dispersion and off-momentum dispersion for lowbetamax collision optics.

Figure 3

The orbit deviation at IP5 with a linear crab kick (ideally low crab frequency), for two different crossing angles.

Figure 4

Comparison of crab dispersive orbit between theoretical results (blue) and LHC simulation (red).

Figure 5

Off-momentum phase space cut at the primary collimator TCP.C6L7.B1 (with $D_x=0.38\mathrm{m}$).

Figure 6

Off-momentum phase space cut at the primary collimator TCP.6L3.B1 (with $D_x=2.2\mathrm{m}$).

Figure 7

Phase space cut from purely off-momentum beat, revealing the hierarchy of primary (TCP), secondary (TCSG), tertiary (TCTH), beam dump (TCDQ) horizontal collimators, and shower absorbers (TCLA).

Figure 8

Phase space cut with crab dispersion from the primary collimator TCP.6L3.B1.

Figure 9

Phase space cut from crab dispersion (for $n_{\beta ,\mathrm{cut}}$ between $5\sigma$ and $11\sigma$), with the hierarchy of primary (TCP), secondary (TCSG), tertiary (TCTH), beam dump (TCDQ) horizontal collimators, and shower absorbers (TCLA).

Figure 10

Total orbit deviation versus energy offset ${\delta }_p$, at the primary collimator TCP.C6L7.B1, with both off-momentum dispersion and crab dispersion.

Figure 11

CC disturbed phase space cut, with the hierarchy of primary (TCP), secondary (TCSG), tertiary (TCTH), beam dump (TCDQ) horizontal collimators, and shower absorbers (TCLA): longitudinal slice with $z=1{\sigma }_z$ (top left); longitudinal slice with $z=2{\sigma }_z$ (top right); longitudinal slice with $z=3{\sigma }_z$ (bottom left); longitudinal slice with $z=4{\sigma }_z$ (bottom right).

Figure 12

Zoomed view of Fig. 11 (top left), longitudinal slice with $z=1{\sigma }_z$.

Figure 13

Minimum phase space distance between different groups of collimators: TCP and TCSG (red); TCSG and TCTH (green); TCSG and TCLA (blue); TCSG and TCDQ (magenta).

Figure 14

Global cleaning inefficiency for LHC top energy, ${\beta }_{\mathrm{IP}1,5}^{*}=0.55\mathrm{m}$, with the 800-MHz global crab cavity: beam halo with $z=1{\sigma }_z$ (blue); beam halo with $z=2{\sigma }_z$ (green); beam halo with $z=3{\sigma }_z$ (magenta); beam halo with $z=4{\sigma }_z$ (cyan).

Figure 15

Local cleaning inefficiency in LHC IR7, without global crab cavity (top energy, ${\beta }_{\mathrm{IP}1,5}^{*}=0.55\mathrm{m}$).

Figure 16

Local cleaning inefficiency in LHC IR7, simulated with the 800-MHz global crab cavity (top energy, ${\beta }_{\mathrm{IP}1,5}^{*}=0.55\mathrm{m}$): beam halo with $z=1{\sigma }_z$ (top left); beam halo with $z=2{\sigma }_z$ (top right); beam halo with $z=3{\sigma }_z$ (bottom left); beam halo with $z=4{\sigma }_z$ (bottom right).