Correction of β-beating due to beam-beam for the LHC and its impact on dynamic aperture

Transcription

1 Correction of β-beating due to beam-beam for the LHC and its impact on dynamic aperture WEOAB2 Luis Medina1,2, R. Toma s2, J. Barranco3, X. Buffat1, Y. Papaphilippou1, T. Pieloni3 1 Universidad de Guanajuato, Leo n, Mexico CERN-BE-ABP, Geneva, Switzerland 3 EPFL, Laussane, Switzerland lmedinam@cern.ch 2 8th International Particle Accelerator Conference 17 May 217 This work is supported by the European Circular Energy-Frontier Collider Study, H22 programme under grant agreement no , by the Swiss State Secretariat for Education, Research and Innovation SERI, and by the Beam project (CONACYT), Mexico.

2 Introduction

3 Beam-beam effects When the bunches of two beams of a particle collider come into proximity, they interact electromagnetically and give rise to beam-beam (BB) effects Tune shift Tune spread β-beating Beam stability and dynamic aperture Etc. 2 / 16

4 Motivation: beam-beam effects in the LHC and HL-LHC 2 IPs 2 IPs LHC: ξ bb =.1 (total) HL-LHC: ξ bb =.2.3 (total) 8 % β-beating 15 % to 23 % β-beating Impact on performance ±9 % β change for HL-LHC Direct repercussion on luminosity luminosity imbalance between the main experiments Impact on protection system 3 / 16

5 Compensation techniques Other compensation techniques: Electron beam lens Current-bearing wires Correction of β-beating by compensation of the BB linear kick with local magnets First step for a correction scheme involving higher multipoles in view of the HL-LHC First measurements and preliminary test in the LHC (P. Gonçalves et. al., TUPVA3) βy/βy [%] βx/βx [%] Measured εn 2% larger εn Location s [m] 25 3 Simulation βx/βx [%] βy/βy [%] Location s [m] Measurement 4 / 16

6 Beam-beam kick y r s 1 s s 2 x r Radial distance from the test particle to the center of the opposite beam, r = x 2 + y 2 d σ N Beam size (assumed round) Bunch population { x y } = 2Nr γ { 1 r 2 x y } [ 1 exp ( r 2 2σ 2 )] r γ d Classical particle radius Relativistic Lorentz factor Beam separation 5 / 16

7 Example: LHC interaction region 12 Left 6.5 GeV, ppb β* = 4 cm, θ/2 = 14 µrad, ε n = 2.5 µrad Right 8 4 X [cm] IP S [m] 6 / 16

8 Example: LHC interaction region beams 12 Left 6.5 GeV, ppb β* = 4 cm, θ/2 = 14 µrad, ε n = 2.5 µrad Right 8 4 X [cm] Beam 1 Beam 2 IP S [m] 6 / 16

9 Example: LHC interaction region matching section 12 Left 6.5 GeV, ppb β* = 4 cm, θ/2 = 14 µrad, ε n = 2.5 µrad Right 8 4 Q4 Q4 X [cm] -4-8 Beam 1 Beam 2 IP S [m] 6 / 16

10 Example: LHC interaction region dipoles 12 Left 6.5 GeV, ppb β* = 4 cm, θ/2 = 14 µrad, ε n = 2.5 µrad Right 8 4 X [cm] -4-8 Beam 1 Beam 2 IP5 D2 D1 D1 D S [m] 6 / 16

11 Example: LHC interaction region inner triplet 12 Left 6.5 GeV, ppb β* = 4 cm, θ/2 = 14 µrad, ε n = 2.5 µrad Right 8 4 X [cm] -4-8 Beam 1 Beam 2 IP5 Q2 Q2 Q3 Q1 Q1 Q S [m] 6 / 16

12 Example: LHC interaction region beam envelope 12 Left 6.5 GeV, ppb β* = 4 cm, θ/2 = 14 µrad, ε n = 2.5 µrad Right 8 4 X [cm] -4 Beam 1 Beam 2 IP σ-envelope S [m] 6 / 16

13 Head-on and long-range beam-beam expansion

14 Head-on (HO) beam-beam Linearisation of kick for small amplitudes: { } { x r y = Nr x r γσ 2 y Same effect on both planes } Beam-beam parameter as a measure of the induced tune shift: ξ bb d( r ) dr Horizontal and vertical β 4π = Nr β 4πγσ 2 r / ( 2Nr /γ ) [σ -1 ] Beam-beam kick -.6 Quadrupole kick Radial position r [σ] 7 / 16

15 Head-on (HO) beam-beam: LHC 12 Left 6.5 GeV, ppb β* = 4 cm, θ/2 = 14 µrad, ε n = 2.5 µrad Right 8 4 HO-BB X [cm] -4 Beam 1 Beam 2 IP σ-envelope S [m] 8 / 16

16 Long-range (LR) beam-beam: LHC (16 collisions per IP side) 12 Left 6.5 GeV, ppb β* = 4 cm, θ/2 = 14 µrad, ε n = 2.5 µrad Right 8 4 X [cm] -4 Beam 1 Beam 2 IP LR-BB LR-BB 5σ-envelope S [m] 8 / 16

17 Long-range (LR) beam-beam Taylor expansions up to second order around (d, ) (horizontal crossing): x = K +(K 1 +K 1) x +(K 2 +K 2)( x) 2 K 2 ( y) 2, y = K 1 y 2K 2 x y, where K i and K i are functions of E d exp ( d 2 ) 2σ 2 (See Appendix A) 9 / 16

18 LR-BB for large separation Taylor expansions up to second order around (d, ) (horizontal crossing): x = K +(K 1 +K 1) x +(K 2 +K 2)( x) 2 K 2 ( y) 2, y = K 1 y 2K 2 x y, where K i and K i are functions of E d exp ( d 2 ) 2σ 2 (See Appendix A) 9 / 16

19 LR-BB for large separation: pure quadrupolar/sextupolar terms Taylor expansions up to second order around (d, ) (horizontal crossing): x = K +(K 1 +K 1) x +(K 2 +K 2)( x) 2 K 2 ( y) 2, y = K 1 y 2K 2 x y, where K i and K i are functions of E d exp ( d 2 ) 2σ 2 (See Appendix A) 9 / 16

20 Procedure and results

21 Procedure Re-matching of optics (β x,y, α x,y ) at the start / IP / end of each IR (separately) Eight degrees of freedom per beam per IP Eight variables: 4 left-right pairs of magnets Re-matching of β [km] Horizontal LHCB1 Vertical Tunes to (64.31, 59.32) Chromaticities to S [m] 1 / 16

22 Choice of magnets Correction in both beams Magnet strengths for counter-rotating beams: K n ( 1) n K n (: dipole, 1: quad, etc.) y y y y x x s s s s x x Beam 1 in a QF Beam 2 sees a QD Beam 1 in a SF Beam 2 sees a SF too B F v (Beam 1) v (Beam 2) Quadrupole, octupole, etc. components of the BB cannot be directly compensated for both beams using common magnets. 11 / 16

23 Choice of magnets: Matching quadrupoles for HO 12 Left 6.5 GeV, ppb β* = 4 cm, θ/2 = 14 µrad, ε n = 2.5 µrad Right 8 4 Q4 HO-BB Q4 X [cm] -4 Beam 1 Beam 2 IP σ-envelope S [m] 12 / 16

24 Choice of magnets: Common sextupoles for LR 12 Left 6.5 GeV, ppb β* = 4 cm, θ/2 = 14 µrad, ε n = 2.5 µrad Right 8 4 MCSSX MCSX MCSX MCSSX X [cm] -4 Beam 1 Beam 2 IP LR-BB LR-BB 5σ-envelope S [m] 12 / 16

25 Reduction of RMS β-beating due to HO-BB or LR-BB Before After Before After Horizontal β-beating [%] HO Horizontal Vertical β-beating β-beating [%] [%] HO LR Vertical β-beating [%] IP4 IP5 IP6 IP7 IP8 IP1 IP2 IP4 IP5 IP6 IP7 IP8 IP1 IP2 Longitudinal position Longitudinal position HO: from 3.67 % / 1.91 % to.3 % /.15 % (Hor./Ver.) LR: from 2.69 % / 3.84 % to.4 % /.4 % 13 / 16

26 Reduction of RMS β-beating due to HO-BB and LR-BB Reduction of RMS β-beating to <.15 % Tunes reduced by.1, chromaticities increased by 2 units Re-matched to nominal Correction with an identical process for the opposite beam Similar results Before After Before After Horizontal β-beating [%] HO+LR Vertical β-beating [%] HO+LR IP4 IP5 IP6 IP7 IP8 IP1 IP2 Longitudinal position IP4 IP5 IP6 IP7 IP8 IP1 IP2 Longitudinal position 14 / 16

27 Stability of the HO-BB and LR-BB correction Correcting sextupole strengths have opposite sign to the sextupolar term of the BB kick. Non-linear elements Long-term stability? Dynamic aperture (DA), via single-particle tracking. Little impact on DA > 5.5σ for all angles Minimum dynamic aperture [σ] Before LHCB1 SixDesk - SixTrack 1 6 turns After I oct = A 2 units of chromaticity Angle [deg] 15 / 16

28 Conclusions and outlook

29 Conclusions and Outlook Beam-beam interactions can limit the machine performance. Luminosity imbalance, machine protection Induced β-beating can be corrected, at least partially, by matching local magnet strenghts to the multipolar terms of the BB kick expansion. Successful application to the current LHC optics (RMS beating < 1 %) Linear HO corrected with matching quadrupoles LR quadrupolar term corrected via sextupole feed-down Compensation scheme involving common sextupoles has negligible impact on DA. First measurements and test of correction in LHC anyalsis on-going Extension to higher orders, and to the HL-LHC: Compensation of beam-beam octupolar component via feed-down from decapoles (not present in the LHC) 16 / 16

30 Thank you 16 / 16