1. Frank Zimmermann, LARP Beam-Beam, SLAC, July 2077 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. Frank Zimmermann, LARP Beam-Beam, SLAC, July 2077 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. Frank Zimmermann, LARP Beam-Beam, SLAC, July 2077 beam-beam issues in LHC versions nominal LHC design criterion, head-on collisions, crossing angle, alternating crossing, long-range beam-beam effects, halo collision, tune footprints, dispersion, noise, strong-strong effects early-separation upgrade crab cavity, low-distance parasitic encounters, crab waist collisions, emittance growth due to crab noise large Piwinski angle upgrade new regime for hadron colliders, crab waist collisions, tune shift, wire compensation, emittance growth due to wire noise

4. Frank Zimmermann, LARP Beam-Beam, SLAC, July 2077 two high luminosity IPs (IP1 ATLAS & IP5 CMS) two lower- luminosity IPs (IP2 ALICE & IP8 LHCb)

5. Frank Zimmermann, LARP Beam-Beam, SLAC, July 2077 long-range separation at IP1 & 5 T. Sen et al, LHC’99 3 different crossing angles; 30 LR collisions

6. Frank Zimmermann, LARP Beam-Beam, SLAC, July 2077 design criterion (J. Gareyte, J.-P. Koutchouk) avoid resonances < order 13 & |Q H -Q V |~0.01 → nominal total tune spread (up to 6  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; 6  is empirical to match results of Ritson & Chou for “ultimate” LHC, |Q H -Q V |~0.005, and the total tune spread should be less than 0.015-0.017

7. Frank Zimmermann, LARP Beam-Beam, SLAC, July 2077 nominal 7-TeV collision parameters **  offsetangle IP10.55 m 16.7  m 0 285  rad (y) [9.4  ] IP210 m 70.9  m355  m [5  ] 300  rad (y) [42.3  ] IP50.55 m 16.7  m 0 285  rad (x) [9.4  ] IP810 m 70.9  m 0 400  rad (x) [56.4  ] 3 “head-on” collisions with crossing angle 1 halo collision with 5-  separation at IP2 60 long-range collisions with on average ~9.5 separation 60 negligible long-range collisions

8. Frank Zimmermann, LARP Beam-Beam, SLAC, July 2077 “Piwinski angle” luminosity reduction factor nominal LHC crossing angle  c /2 effective beam size  →  /R  note: the tune shift is reduced by roughly the same factor

9. Frank Zimmermann, LARP Beam-Beam, SLAC, July 2077 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  rad, and for angles of 10-20  rad no lifetime degradation is seen. [V. Shiltsev] Lepton colliders: Strong-strong beam-beam simulations predict an increase in the KEKB beam-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] Impact of crossing angle?

10. Frank Zimmermann, LARP Beam-Beam, SLAC, July 2077 Experiment at SPS Collider K. Cornelis, W. Herr, M. Meddahi, “Proton Antiproton Collisions at a Finite Crossing Angle in the SPS”, PAC91 San Francisco  ~0.45  >0.7  c =500  rad  c =600  rad small emittance

11. Frank Zimmermann, LARP Beam-Beam, SLAC, July 2077 head-on tune shift (with Piwinski angle  ~0) long-range tune shift head-on & long-range tune shifts for nominal LHC:

12. Frank Zimmermann, LARP Beam-Beam, SLAC, July 2077 tune footprints due to head-on and long-range collisions in IP1 and IP5 [courtesy H. Grote] total LHC tune footprint for regular and PACMAN bunch [courtesy H. Grote]  Q from LR collisions is approximately cancelled by alternating crossing [D. Neuffer, S. Peggs, SSC-63 (1986)] tune footprints & alternating crossing

13. Frank Zimmermann, LARP Beam-Beam, SLAC, July 2077 “diffusive aperture” diffusive aperture due to LR encounters, new regime of hadron beam-beam with independent of  * and energy for nominal LHC: x sep ~9.5 , x da ~6  J. Irwin, SSC-223 (1989) Y. Papaphilippou & F.Z., PRST-AB 2, 104001 (1999) Y. Papaphilippou & F.Z., PRST-AB 5, 074001 (2002)

14. Frank Zimmermann, LARP Beam-Beam, SLAC, July 2077 Y. Papaphilippou & F.Z., PRST-AB 2, 104001 (1999) current dependence of dynamic aperture

15. Frank Zimmermann, LARP Beam-Beam, SLAC, July 2077 H. Grote, L.H.A. Leunissen, Y. Luo, F. Schmidt dynamic aperture with beam-beam and field errors injection 450 GeV collision 7 TeV 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

16. Frank Zimmermann, LARP Beam-Beam, SLAC, July 2077 recent tune & angle scans - particle losses over 1M turns W. Herr, D. Kaltchev, 2007 traces of resonances x/y asymmetry 13th 16th 3rd 10th

17. Frank Zimmermann, LARP Beam-Beam, SLAC, July 2077 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. Frank Zimmermann, LARP Beam-Beam, SLAC, July 2077 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. Frank Zimmermann, LARP Beam-Beam, SLAC, July 2077 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 equivalence classes. Beam-Beam Equivalence Classes for LHCr [J. Jowett, LHC’99] only ~half of the bunches are regular

20. Frank Zimmermann, LARP Beam-Beam, SLAC, July 2077 PACMAN effects expect bunch-to-bunch variation of orbit, tune and chromaticity partial compensation by alternating crossing in IP1 and 5

21. Frank Zimmermann, LARP Beam-Beam, SLAC, July 2077 bunch-to-bunch orbit variation beam1 beam2 beam1 beam2 orbit displacements at IP1 HH crossingHV crossing W. Herr only half of bunch pattern shown; collisions are head-on in the other plane; in addition ground motion will separate the two beams by 5  during 8 hours

22. Frank Zimmermann, LARP Beam-Beam, SLAC, July 2077 bunch-to-bunch Q, Q’ variation HV crossing HH crossing W. Herr first 3 bunches in each train abort gap

23. Frank Zimmermann, LARP Beam-Beam, SLAC, July 2077 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  beating, nonlinear chromaticity wire compensation (dc, pulsed)

24. Frank Zimmermann, LARP Beam-Beam, SLAC, July 2077 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), |  | the total beam-beam tune-shift parameter assumed equal 0.01,  x * the horizontal IP beam size, n IP the number of IPs (taken to be two), and s 0 ~0.645 emittance growth < 1%/hr: →  x < 2.6 nm for g=0.2,  x < 0.6 nm for g=0.0 consistent with simulations by K. Ohmi

25. Frank Zimmermann, LARP Beam-Beam, SLAC, July 2077 LHC ground motion asymmetric IR optics enhances low-f effect “high” frequency “low” frequency E. Keil, CERN SL/97-61 (AP) 1.5x LEP 10x LEP

26. Frank Zimmermann, LARP Beam-Beam, SLAC, July 2077 coherent beam-beam effects unlike SPS and Tevatron, LHC will operate in the strong-strong regime Y. Alexahin predicted that Landau damping of the  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. Frank Zimmermann, LARP Beam-Beam, SLAC, July 2077  mode  mode continuum equal intensity intensity ratio 0.55 frequency spectrum of dipole oscillations  mode not Landau damped  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. Frank Zimmermann, LARP Beam-Beam, SLAC, July 2077 Landau damping from beam-beam max. octupoles0.00012 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)

29. Frank Zimmermann, LARP Beam-Beam, SLAC, July 2077 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. Frank Zimmermann, LARP Beam-Beam, SLAC, July 2077PAF/POFPA Meeting 20 November 2006 from 4 to 2 IPs: “ultimate” LHC nominal tune footprint up to 6  with 4 IPs tune footprint up to 6  with 2 IPs tune footprint up to 6  with 2 IPs at ultimate intensity L=10 34 cm -2 s -1 L=2.3x10 34 cm -2 s -1 SPS, Tevatron, RHIC experience: beam-beam limit ↔ total tune shift  Q~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 ~0.01

31. Name Event Date Name Event Date 31 Frank Zimmermann, LARP Beam-Beam, SLAC, July 2077 parametersymbolnominalultimateES upgradeLPA upgrade transverse emittance  [  m] 3.753.753.75 protons per bunch N b [10 11 ] 1.151.71.74.9 bunch spacing  t [ns] 25252550 beam current I [A] 0.580.860.861.22 longitudinal profile GaussGaussGaussFlat rms bunch length  z [cm] 7.557.557.5511.8 beta* at IP1&5  [m] 0.550.50.080.25 full crossing angle  c [  rad] 2853150381 Piwinski parameter  c  z /(2*  x *) 0.640.7502.0 hourglass reduction 0.860.99 peak luminosity L [10 34 cm -2 s -1 ] 12.315.510.7 peak events per crossing 1944294403 initial lumi lifetime  L [h] 22142.24.5 effective luminosity (T turnaround =10 h) L eff [10 34 cm -2 s -1 ] 0.460.912.42.5 T run,opt [h] 21.217.06.69.5 effective luminosity (T turnaround =5 h) L eff [10 34 cm -2 s -1 ] 0.561.153.63.5 T run,opt [h] 15.012.04.66.7 e-c heat SEY=1.4(1.3) P [W/m] 1.07 (0.44) 1.04 (0.59) 0.36 (0.1) SR heat load 4.6-20 K P SR [W/m] 0.170.250.250.36 image current heat P IC [W/m] 0.150.330.330.78 gas-s. 100 h (10 h)  b P gas [W/m] 0.04 (0.38) 0.06 (0.56) 0.09 (0.9) extent luminous region  l [cm]4.54.33.75.3 comment D0 + crab (+ Q0)wire comp. early separation (ES) large Piwinski angle (LPA)

32. Name Event Date Name Event Date 32 Frank Zimmermann, LARP Beam-Beam, SLAC, July 2077 early separation (ES) stay with ultimate LHC beam (1.7x10 11 protons/bunch, 25 spacing) stay with ultimate LHC beam (1.7x10 11 protons/bunch, 25 spacing) squeeze  * to ~10 cm in ATLAS & CMS squeeze  * to ~10 cm in ATLAS & CMS add early-separation dipoles in detectors starting at ~ 3 m from IP; accept 4 long- range collisions at 4-5  separation add early-separation dipoles in detectors starting at ~ 3 m from IP; accept 4 long- range collisions at 4-5  separation possibly also add quadrupole-doublet inside detector at ~13 m from IP possibly also add quadrupole-doublet inside detector at ~13 m from IP and add crab cavities and add crab cavities ultimate bunches & near head-on collision stronger triplet magnets D0 dipole small-angle crab cavity optional Q0 large Piwinski angle (LPA) double bunch spacing double bunch spacing longer & more intense bunches with  Piwinski ~ 2 longer & more intense bunches with  Piwinski ~ 2  *~25 cm  *~25 cm no elements inside detectors no elements inside detectors long-range beam-beam wire compensation long-range beam-beam wire compensation → novel operating regime for hadron colliders wire compensator larger-aperture triplet long bunches & nonzero crossing angle & wire compensation

33. Name Event Date Name Event Date 33 Frank Zimmermann, LARP Beam-Beam, SLAC, July 2077 ES luminosity boost by crab cavities 5  separation at 4 closest encounters 3.5 m from IP  *=11 cm

34. LHC Upgrade Beam Parameters, Frank ZimmermannFrank Zimmermann, LARP Beam-Beam, SLAC, July 2077PAF/POFPA Meeting 20 November 2006 RHIC experiments in 2005 and 2006 single off-center collision one collision with 5-6  offset strongly increases RHIC beam loss rate; worse at smaller offsets (W. Fischer et al.) 24 GeV 100 GeV how serious are 4 parasitic collisions at 4-5  ?

35. LHC Upgrade Beam Parameters, Frank ZimmermannFrank Zimmermann, LARP Beam-Beam, SLAC, July 2077PAF/POFPA Meeting 20 November 2006 Tevatron 2006 removal of two 5-  collisions at … increased luminosity by 15-30% (V. Shiltsev) how serious are 4 parasitic collisions at 4-5  ?

36. Frank Zimmermann, LARP Beam-Beam, SLAC, July 2077 Upgrade Option: Flat Beam Collisions –Crossing plane = plane where the beam size is larger at IP (i.e. smaller in the triplet) 1.To gain aperture in the triplet (smaller crossing angle and better matching between beam-screen and beam aspect ratio, see next slide) 2.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) Full X-angle in  units (9.5  ’   for the nominal LHC) S. Fartoukh, LHC-MAC, 16 June 2006 flat beams were first proposed by US-LARP, S. Peggs, T. Sen, et al

37. Frank Zimmermann, LARP Beam-Beam, SLAC, July 2077 Potential of Flat Beam: Aperture Triplet beam screen orientation 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)  In all cases, the average b-b separation is set to 9.5*  x/y (for H/V crossing)  Find the optimum match between beam-screen and beam aspect ratio S. Fartoukh, LHC-MAC, 16 June 2006

38. Frank Zimmermann, LARP Beam-Beam, SLAC, July 2077 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: S. Fartoukh, LHC-MAC, 16 June 2006 Individual contribution of IR1 and IR5 Combined contribution (slight degradation due to the reduction of the X-angle in the flat beam case) Nominal :one IR with for  x  =  y  = 55 cm Flat beam case 4:IR5 contribution IR5 for  y  = 88 cm,  x  = 30 cm Flat beam case 4:IR1 contribution for  x  = 88 cm,  y  = 30 cm Nominal tune at zero intensity: (.31/0.32)

39. Frank Zimmermann, LARP Beam-Beam, SLAC, July 2077 Long-range beam-beam for flat beams:  Tune shift only partially compensated by the H/V separation scheme with flat beam:  Beam-beam tune spread and driven resonances further amplified by high  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. Frank Zimmermann, LARP Beam-Beam, SLAC, July 2077  Beam-beam tune footprint at 6  at nominal intensity for nominal case (blue) compared to two flat beam cases (red) Flat beam case: r~1.7    51cm L~1.2 L 0, aperture saturated (n1=7) Other flat beam case: r~1.45    61cm L~L 0, aperture maximized (n1=8)  Q ~2. 10 -2  Q ~ 1.6 10 -2 20% improvement of tune spread, loosing only 20% of lumi and gaining aperture After Q-adjustment  Q x,y = 5.5 10 -3 S. Fartoukh, LHC-MAC, 16 June 2006 After Q-adjustment  Q x,y ~ 3.3 10 -3 ~ 40-50% bigger !  case limited to ~ 60-70% of nominal intensity ~ 20-25% bigger !  case limited to ~80-85% of nominal intensity LR compensation would help

41. Frank Zimmermann, LARP Beam-Beam, SLAC, July 2077  1’000’000-turn dynamic aperture at nominal intensity for nominal case (blue) and flat beam case (red): S. Fartoukh, LHC-MAC, 16 June 2006,  Net reduction by ~ 40% from 6-7  to 4-5  for the min. DA.  No possibility of further improvement via a tiny tune scan.  DA almost exactly follows the change in the b-b tune spread stronger LR effect must be compensated!

42. Frank Zimmermann, LARP Beam-Beam, SLAC, July 2077 upgrade option: crab waist minimizes  at s=-x/  c focal plane implementation: add sextupoles at right phase distance from IP initiated and led by LNF in the frame of FP7; first beam tests at DAFNE later in 2007 Hamiltonian

43. Frank Zimmermann, LARP Beam-Beam, SLAC, July 2077 summary – LHC b-b compensation alternating crossing or not? IP1-5 phase advance; chromaticity 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 4-5  separation flat beams (easier wire?, crab waists) hadron beam crab waist KEKB; still needs hadron beam test! both need beam test! Tevatron, needs more beam tests! needs beam test! SPS tests; RHIC? SPS + RHIC tests DAFNE; still needs hadron beam test!

44. Frank Zimmermann, LARP Beam-Beam, SLAC, July 2077 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. LHC Upgrade Beam Parameters, Frank ZimmermannFrank Zimmermann, LARP Beam-Beam, SLAC, July 2077PAF/POFPA Meeting 20 November 2006 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).