1. Crab cavity voltage in HL1.3
R. De Maria
WP2 Meeting 12/6/2017

2. Introduction
Crab cavities generates a correlation at IP between the arrival time and the transverse position to maximize luminosity.
x(s=IP-s0,z)≈px s0 – R12Vcrab sin(ω z/c) where z=s-ct
crabbing angle: θcrab= 2 R12Vcrab ω z/c crossing angle: θxing= 2 px
luminosity is maximal when θcrab~1.1 θxing
In the local scheme, two crab cavities in between are need to cancel the correlation outside.
cancellation cannot be perfect since phase advance is close but not exactly π
matching voltage done to reduce the maximum leakage in machine (crabbing leaks in the other IPs, e.g σ)
L. Medina

3. Crabbing angle and voltage for 2 cavities
HLLHCV1.2 (2cav) H V
Θxing [µrad]
374
379
ACFA/B LB1 [MV]
3.4
ACFA/B RB1 [MV]
3.18
3.37
ACFA/B LB2 [MV]
-3.18
-3.37
ACFA/B RB2 [MV]
-3.4
Left
Right
HLLHCV1.2 (2cav) βx βy
ACFB LB1 [m]
3548
3651
ACFA LB1 [m]
3589
3768
ACFA RB2 [m]
4208
3739
ACFB RB2 [m]
4085
3698
Beam 2 optics βx<->βy

4. Crabbing angle and voltage for 2 cavities
HLLHCV1.3 H V
Θxing [µrad]
378
385
ACFA/B LB1 [MV]
3.4
ACFA/B RB1 [MV]
3.18
3.37
ACFA/B LB2 [MV]
-3.18
-3.37
ACFA/B RB2 [MV]
-3.4
Left
Right
HLLHCV1.3 βx βy
ACFB LB1 [m]
3615
3713
ACFA LB1 [m]
3656
3830
ACFA RB2 [m]
4268
3805
ACFB RB2 [m]
4145
3764
Beam 2 optics βx<->βy

5. Crabbing angle and voltage for 2 cavities
HLLHCV1.3 H V
Θxing [µrad]
379
384
ACFA/B LB1 [MV]
3.4
ACFA/B RB1 [MV]
3.18
3.37
ACFA/B LB2 [MV]
-3.18
-3.37
ACFA/B RB2 [MV]
-3.4
Left
Right
Symmetric layout for Point 1 and Point 5, optimize both H and V crossing.
Possible improvements at some cost:
Dissimmetrize IR1/5 layout for specific crossing plane.
Dissimmetrize IR1/5 optics for specific crossing plane.
Reduce margin for Q7.
Lift optics constraints (e.g. dispersion in the arc)