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Beam-Beam Effects for LHC and LHC Upgrade Scenarios

Beam-Beam Effects for LHC and LHC Upgrade Scenarios. Frank Zimmermann US-LARP Beam-Beam Workshop SLAC, 2007. We acknowledge the support of the European Community-Research Infrastructure Activity under the FP6

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Beam-Beam Effects for LHC and LHC Upgrade Scenarios

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  1. Beam-Beam Effects for LHC and LHC Upgrade Scenarios Frank Zimmermann US-LARP Beam-Beam Workshop SLAC, 2007 We acknowledge the support of the European Community-Research Infrastructure Activity under the FP6 "Structuring the European Research Area" programme (CARE, contract number RII3-CT-2003-506395)

  2. LHC beam-beam effects • incoherent beam-beam effects • lifetime & dynamic aperture • PACMAN effects • bunch-to-bunch variation • coherent effects • oscillations and instabilities (W. Herr, LHC Design Report, Chapter 5)

  3. beam-beam issues in LHC versions • nominal LHCdesign criterion, head-on collisions, crossing angle, alternating crossing, long-range beam-beam effects, halo collision, tune footprints, dispersion, noise, strong-strong effects • early-separation upgradecrab cavity, low-distance parasitic encounters, crab waist collisions, emittance growth due to crab noise • large Piwinski angle upgradenew regime for hadron colliders, crab waist collisions, tune shift, wire compensation, emittance growth due to wire noise

  4. two high luminosity IPs (IP1 ATLAS & IP5 CMS) two lower-luminosity IPs (IP2 ALICE & IP8 LHCb)

  5. long-range separation at IP1 & 5 3 different crossing angles; 30 LR collisions T. Sen et al, LHC’99

  6. design criterion (J. Gareyte, J.-P. Koutchouk) avoid resonances < order 13 & |QH-QV|~0.01 → nominal total tune spread (up to 6s in x&y) from all IPs and over all bunches, including long-range effects, should be less than 0.01-0.012 notes: • this limiting value comes from SPS & Tevatron; • 6s is empirical to match results of Ritson & Chou for “ultimate” LHC, |QH-QV|~0.005, and the total tune spread should be less than 0.015-0.017

  7. nominal 7-TeV collision parameters 3 “head-on” collisions with crossing angle 1 halo collision with 5-s separation at IP2 60 long-range collisions with on average ~9.5 separation 60 negligible long-range collisions

  8. crossing angle “Piwinski angle” qc/2 luminosity reduction factor nominalLHC effective beam size s→s/Rf note: the tune shift is reduced by roughly the same factor

  9. Impact of crossing angle? Lepton colliders: Strong-strong beam-beam simulations predict an increase in the KEKBbeam-beam tune shift limit by a factor 2-3 for head-on collision compared with the present crossing angle. This is the primary motivation for installing crab cavities. [K. Ohmi] Hadron Colliders:RHIC operates with crossing angles of +/- 0.5 mrad due to limited BPM resolution and diurnal orbit motion. Performance of proton stores is very irreproducible and frequently occurring lifetime problems could be related to the crossing angle, but this is not definitely proven. [W. Fischer] Tevatron controls crossing angle to better than 10 mrad, and for angles of 10-20 mrad no lifetime degradation is seen. [V. Shiltsev]

  10. Experiment at SPS Collider K. Cornelis, W. Herr, M. Meddahi, “Proton Antiproton Collisions at a Finite Crossing Angle in the SPS”, PAC91 San Francisco f~0.45 qc=500 mrad f>0.7 qc=600 mrad small emittance

  11. head-on & long-range tune shifts head-on tune shift (with Piwinski angle f~0) long-range tune shift for nominal LHC:

  12. tune footprints & alternating crossing total LHC tune footprint for regular and PACMAN bunch [courtesy H. Grote] tune footprints due to head-on and long-range collisions in IP1 and IP5 [courtesy H. Grote] DQ from LR collisions is approximately cancelled by alternating crossing [D. Neuffer, S. Peggs, SSC-63 (1986)]

  13. diffusive aperture due to LR encounters, new regime of hadron beam-beam “diffusive aperture” with independent of b* and energy J. Irwin, SSC-223 (1989) Y. Papaphilippou & F.Z., PRST-AB 2, 104001 (1999) Y. Papaphilippou & F.Z., PRST-AB 5, 074001 (2002) for nominal LHC: xsep~9.5s, xda~6s

  14. current dependence of dynamic aperture Y. Papaphilippou & F.Z., PRST-AB 2, 104001 (1999)

  15. dynamic aperture with beam-beam and field errors collision 7 TeV injection 450 GeV significant reduction of dynamic aperture due to LR beam-beam; even small field errors lead to losses when beam-beam present; benefits of triplet correction much reduced H. Grote, L.H.A. Leunissen, Y. Luo, F. Schmidt

  16. recent tune & angle scans - particle losses over 1M turns traces of resonances 10th 13th 16th 3rd x/y asymmetry W. Herr, D. Kaltchev, 2007

  17. bunch-to-bunch emittance variation two consequences: • reduces normalized separation for larger bunches • head-on collisions with unequal beam size will lead to particle losses from larger bunches → bunch-to-bunch variation should not exceed 10% (about the best the injectors can do); same tolerance for intensity

  18. LHC filling pattern lack of 4-fold symmetry → some bunches encounter abort gap in IP2 or 8 and have missing head-on collisions; in addition IP8 is displaced by 11.22 m and also 3 bunches in each train miss head-on collisions in IP2

  19. Beam-Beam Equivalence Classes for LHCr [J. Jowett, LHC’99] All encounters in the straight sections are taken into account. Each bunch in the LHC is represented as a dot. The angular co-ordinate is the initial position of the bunch around the circumference. There is a one-to-one correspondence between beam-beam equivalence class and the radius in the plot. The classes are sorted according to the population of the class. Thus, classes containing a single bunch, of which there are several, lie towards the centre of the plot.Tomake adjacent classes easier to distinguish they are also colored differently (although the colours are used several times over at clearly distinguishable radii).Here there are 171 equivalenceclasses. only ~half of the bunches are regular

  20. PACMAN effects • expect bunch-to-bunch variation of orbit, tune and chromaticity • partial compensation by alternating crossing in IP1 and 5

  21. bunch-to-bunch orbit variation orbit displacements at IP1 beam1 beam1 beam2 beam2 HH crossing HV crossing only half of bunch pattern shown; collisions are head-on in the other plane; in addition ground motion ay separate the two beams by 5s during 8 hours W. Herr

  22. bunch-to-bunch Q, Q’ variation HH crossing HV crossing HV crossing HH crossing first 3 bunches in each train abort gap W. Herr

  23. intermediate comments • alternating crossing ~ kind of beam-beam compensation • vertical dispersion from crossing angle cannot easily be corrected; SBR strength from crossing angle comparable to that from dispersion [H. Leunissen, LHC’99] • alternating crossing vs equal-plane crossing→ tune shift & resonance excitation • role of phase advance between IPs → LRBB resonance excitation, off-momentum b beating, nonlinear chromaticity • wire compensation (dc, pulsed)

  24. emittance growth from noise • noise sources: ground motion, power converter ripple, transverse feedback, rf, wire compensator, crab cavity • emittance growth due to random beam-beam offset including decoherence and feedback [Y. Alexahin]: where g is a feedback gain factor (typically g~0.2), |x| the total beam-beam tune-shift parameter assumed equal 0.01, sx* the horizontal IP beam size, nIP the number of IPs (taken to be two), and s0~0.645 • emittance growth < 1%/hr: → Dx < 2.6 nm for g=0.2, Dx < 0.6 nm for g=0.0 consistent with simulations by K. Ohmi

  25. LHC ground motion asymmetric IR optics enhances low-f effect “high” frequency 1.5x LEP “low” frequency 10x LEP E. Keil, CERN SL/97-61 (AP)

  26. coherent beam-beam effects • unlike SPS and Tevatron, LHC will operate in the strong-strong regime • Y. Alexahin predicted that Landau damping of the p mode may be lost • Landau damping can be restored by symmetry breaking • different intensities • different tunes • broken symmetry for multiple interaction regions or by overlap with synchrotron sidebands

  27. frequency spectrum of dipole oscillations p mode s mode continuum equal intensity intensity ratio 0.55 p mode not Landau damped p mode Landau damped M.P. Zorzano & F.Z., PRST-AB 3, 044401 (2000) W. Herr, M.P. Zorzano, F. Jones, PRST-AB 4, 054402 (2002)

  28. Landau damping from beam-beam nominal LHC: LR in IP1 and IP5 ultimate LHC: HO+LR in IP1 and IP5 W. Herr and L. Vos LHC Project Note 316 (2003) max. octupoles 0.0012

  29. strong-strong emittance growth? • coherent beam-beam mode coupling yields instability [A. Chao, R. Ruth, Part.Accel.16:201-216,1985] • together with Landau damping “virtual” instabilities could lead to continuous emittance growth (A. Chao, private communication)

  30. from 4 to 2 IPs: “ultimate” LHC ~0.01 ~0.01 ~0.01 ~0.01 tune footprint up to 6s with 2 IPs tune footprint up to 6s with 2 IPs at ultimate intensity nominal tune footprint up to 6s with 4 IPs L=1034 cm-2s-1 L=2.3x1034 cm-2s-1 SPS, Tevatron, RHIC experience: beam-beam limit ↔ total tune shift DQ~0.01 going from 4 to 2 IPs we can increase ATLAS&CMS luminosity by factor 2.3 this and all following upgrade studies were based on assumption of only 2 IPs PAF/POFPA Meeting 20 November 2006

  31. large Piwinski angle (LPA) early separation (ES)

  32. early separation (ES) large Piwinski angle (LPA) • double bunch spacing • longer & more intense bunches with fPiwinski~ 2 • b*~25 cm • no elements inside detectors • long-range beam-beam wire compensation → novel operating regime for hadron colliders • stay with ultimate LHC beam (1.7x1011 protons/bunch, 25 spacing) • squeeze b* to ~10 cm in ATLAS & CMS • add early-separation dipoles in detectors starting at ~ 3 m from IP; accept 4 long-range collisions at 4-5s separation • possibly also add quadrupole-doublet inside detector at ~13 m from IP • and add crab cavities stronger triplet magnets optional Q0 larger-aperture triplet D0 dipole small-angle crab cavity wire compensator ultimate bunches & near head-on collision long bunches & nonzero crossing angle & wire compensation

  33. ES luminosity boost by crab cavities 5s separation at 4 closest encounters 3.5 m from IP b*=11 cm

  34. how serious are 4 parasitic collisions at 4-5 s? RHIC experiments in 2005 and 2006 single off-center collision 24 GeV 100 GeV (W. Fischer et al.) one collision with 5-6s offset strongly increases RHIC beam loss rate; worse at smaller offsets PAF/POFPA Meeting 20 November 2006

  35. Tevatron 2006 how serious are 4 parasitic collisions at 4-5 s? removal of two 5-s collisions at … increased luminosity by 15-30% (V. Shiltsev) PAF/POFPA Meeting 20 November 2006

  36. Upgrade Option: Flat Beam Collisions • Crossing plane = plane where the beam size is larger at IP (i.e. smaller in the triplet) • To gain aperture in the triplet (smaller crossing angle and better matching between beam-screen and beam aspect ratio, see next slide) • To gain in luminosity (geometric loss factor ~ 1) Luminosity calculated for two head-on colliding round beams r.m.s. bunch length (7.5 cm in collision for the nominal LHC) S. Fartoukh, LHC-MAC, 16 June 2006 Full X-angle in s units (9.5 s’*for the nominal LHC) flat beams were first proposed by US-LARP, S. Peggs, T. Sen, et al

  37. Potential of Flat Beam: Aperture • Triplet beam screen orientation for H/V crossing • In all cases, the average b-b separation is set to 9.5*sx/y(for H/V crossing) Effect of decreasing the beam aspect ratio at the IP (and increasing the vert. X-angle) Effect of increasing the beam aspect ratio at the IP (and decreasing the vert. X-angle) • Find the optimum match between beam-screen and beam aspect ratio S. Fartoukh, LHC-MAC, 16 June 2006

  38. Head-on beam-beam for flat beams  independent of r provided inversion of the beam aspect ratio from IR1 to IR5 as in the present case: Nominal tune at zero intensity: (.31/0.32) Flat beam case 4:IR1 contribution for bx* = 88 cm, by* = 30 cm Nominal :one IR with for bx* = by* = 55 cm Flat beam case 4:IR5 contribution IR5 for by* = 88 cm, bx* = 30 cm Combined contribution (slight degradation due to the reduction of the X-angle in the flat beam case) Individual contribution of IR1 and IR5 S. Fartoukh, LHC-MAC, 16 June 2006

  39. Long-range beam-beam for flat beams: • Tune shiftonly partially compensated by the H/V separation scheme with flat beam: • Beam-beam tune spread and driven resonances further amplified by highb at the parasitic encounters, e.g. the non-resonant beam-beam driven anharmonicity coefficients scale as S. Fartoukh, LHC-MAC, 16 June 2006 stronger LR effect should be compensated!

  40. Beam-beam tune footprint at 6s atnominal intensity for nominal case (blue) compared to two flat beam cases (red) DQ ~2. 10-2 Flat beam case: r~1.7, b*~51cm L~1.2 L0, aperture saturated (n1=7) After Q-adjustment DQx,y = 5.5 10-3 • ~ 40-50% bigger ! • case limited to ~ 60-70% of nominal intensity LR compensation would help 20% improvement of tune spread, loosing only 20% of lumi and gaining aperture DQ ~ 1.6 10-2 After Q-adjustment DQx,y ~ 3.3 10-3 Other flat beam case: r~1.45, b*~61cm L~L0, aperture maximized (n1=8) • ~ 20-25% bigger ! • case limited to ~80-85% of nominal intensity S. Fartoukh, LHC-MAC, 16 June 2006

  41. 1’000’000-turn dynamic aperture atnominal intensity for nominal case (blue) and flat beam case (red): • Net reduction by ~ 40% from 6-7s to 4-5 s for the min. DA. • No possibility of further improvement via a tiny tune scan. stronger LR effect must be compensated! • DA almost exactly follows the change in the b-b tune spread S. Fartoukh, LHC-MAC, 16 June 2006,

  42. upgrade option: crab waist initiated and led by LNF in the frame of FP7; first beam tests at DAFNE later in 2007 Hamiltonian minimizes b at s=-x/qc implementation: add sextupoles at right phase distance from IP focal plane

  43. summary – LHC b-b compensation SPS tests; RHIC? SPS + RHIC tests • alternating crossing or not? • IP1-5 phase advance • LR wire compensation • DC, pulsed, noise, small distance (EL?) • crab cavity • noise, space, local or global • head-on compensation (EL) • potential loss of Landau damping • large Piwinski angle • self compensation • effect of few collisions at 4-5s separation • flat beams (easier wire?, crab waists) • hadron beam crab waist KEKB; still needs hadron beam test! needs beam test! needs beam test! both need beam test! DAFNE; still needs hadron beam test!

  44. Thanks! Yuri Alexahin, Rama Calaga, Alex Chao, Ulrich Dorda, Stephane Fartoukh, Wolfram Fischer, Jacques Gareyte, Hans Grote, Werner Herr, Albert Hofmann, Wolfgang Hofle, John Irwin, John Jowett, Dobrin Kaltchev, Eberhard Keil, Jean-Pierre Koutchouk, Peter Leunissen, Yun Luo, Kazuhito Ohmi, Katsunobu Oide, Yannis Papaphilippou, Steve Peggs, Dave Ritson,Walter Scandale, Tanaji Sen, Frank Schmidt, Vladimir Shiltsev, Rogelio Tomas, Luc Vos, Jorg Wenninger, Kaoru Yokoya, Xiaolong Zhang, Maria-Paz Zorzano, …

  45. some references • J. Poole and F. Zimmermann, eds., Proceedings of Workshop on beam-beam effects in Large Hadron Colliders, CERN/SL 99-039 (AP) (1999). • J. Gareyte, Beam-Beam Design Criteria for LHC, Proc. LHC’99 • O. Bruning et al, LHC Design Report, Vol. 1, Chapter 5 (beam-beam section by W. Herr), CERN-2004-003 • Y. Alexahin, On the Landau damping and decoherence of transverse dipole oscillations in colliding beams, Part. Accel. 59, 43 (1998). • W. Chou and D. Ritson, Dynamic aperture studies during collisions in the LHC, CERN LHC Project Report 123 (1997). • L. Leunissen, Influence of vertical dispersion and crossing angle on the performance of the LHC, CERN LHC Project Report 298 (1999). • Y. Papaphilippou, F. Zimmermann, Weak-strong beam-beam simulations for the Large Hadron Collider, PRST-AB 2:104001, 1999 • Y. Papaphilippou & F. Zimmermann, Estimates of diffusion due to long-range beam-beam collisions, PRST-AB 5:074001, 2002. • M.P. Zorzano, F. Zimmermann, Coherent beam-beam oscillations at the LHC, PRST-AB 3:044401, 2000. • W. Herr, M.P. Zorzano and F. Jones A Hybrid Fast Multipole Method applied to beam-beam collisions in the strong strong regime, PRST-AB 4, 054402 (2001) • H. Grote, L. Leunissen, F. Schmidt, LHC Dynamic Aperture at Collision, LHC Project Note 197 (1999). • J. Jowett, Collision Schedules and Bunch Filling Schemes in the LHC, CERN LHC Project Note 179 (1999). • M.P.Zorzano, T.Sen, Emittance growth for the LHC beams due to head-on beam-beam interaction and ground motion , LHC Project Note 222 (2000). • W. Herr, L. Vos, Tune distributions and effective tune spread from beam-beam interactions and the consequences for Landau damping in the LHC, LHC Project Note 316, 2003 • W. Herr, M.-P. Zorzano, Coherent Dipole Modes for Multiple Interaction Regions, LHC Project Report 462 (2001) • Y. Alexahin, A study of the Coherent Beam-Beam Effect in the framework of the Vlasov Perturbation Theory, NIM A 380, 253 (2002) • W. Herr, R. Paparella, Landau Damping of Coherent Modes by Overlap with Synchrotron Sidebands, CERN LHC Project Note 304, 2002 • W. Herr, Features and Implications of Different LHC Crosing Schemes, LHC Project Report 628 (2003) • Y. Alexahin, On the Emittance Growth due to Noise in Hadron Colliders and Methods of its Suppression, NIM A 391, 73 (1996). PAF/POFPA Meeting 20 November 2006

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