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Prospective for Flat Beam Optics

S. Fartoukh AB/ABP, LHC MAC no. 19, 15-17 June 2006 Acknowledgment for technical support and fruitful discussions: W. Herr, B. Jeanneret, E. McIntosh, F. Schmidt, F. Zimmermann. Prospective for Flat Beam Optics. Potential of flat beam optics :

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Prospective for Flat Beam Optics

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  1. S. Fartoukh AB/ABP, LHC MAC no. 19, 15-17 June 2006 Acknowledgment for technical support and fruitful discussions: W. Herr, B. Jeanneret, E. McIntosh, F. Schmidt, F. Zimmermann Prospective for Flat Beam Optics • Potential of flat beam optics: • Pushing the Luminosity (by decreasing the X-angle) • Maximizing the triplet aperture (by matching the beam aspect ratio to the triplet beam-screen) • Illustration via a few specific cases: • Nominal (round beam) • Flat beam: optimized for luminosity at constant aperture • Flat beam : optimized for aperture at constant luminosity • Investigation of possible limitations: • Chromatic correction and triplet field imperfection • Beam-beam • Conclusions and future plans

  2. Potential of Flat Beam: Luminosity • Flat beam means • The Xing plane is always the plane where the beam size is the largest at the IP (i.e. the smallest in the triplet) • To gain aperture in the triplet (smaller X-angle requested and better matching between beam-screen and beam aspect ratio, see next slide) • To gain in luminosity (geometric loss factor closer to unity) 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 s units (9.5 s’*for the nominal LHC) S. Fartoukh, LHC-MAC, 16 June 2006, p. 2/20

  3. 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 between beam-screen and beam aspect ratio S. Fartoukh, LHC-MAC, 16 June 2006, p. 3/20

  4. A few specific cases • Strategy: • Consider the nominal case (round beam with b*= 55cm) as the reference case for luminosity, aperture and beam-beam: case 1. • Working at constant b* = 55 cm, find the maximum IP beam aspect ratiormax allowed by triplet aperture: case 2. • Working at constant b*, find the optimum beam aspect ratio for aperture, 1 < rop <rmax : case 3 leading also to a luminosity gain (smaller X-angle for flat beam, see previous slides). • At this stage two possible choices: • Convert the aperture gain of case 3 into luminosity by furtherdecreasing the smallest b* (triplet aperture re-saturated): case 4. • Convert the luminosity gain of case 3 into aperture by re-increasing the smallest b* (back to the nominal lumi): case 5. S. Fartoukh, LHC-MAC, 16 June 2006, p. 4/20

  5. A few specific cases ymax~ 6.5 mm • Case 1: Nominal LHC, example of IR1 (round beam) Beam1 in IR1 bx,max~ 4.4 km by,max~ 4.4 km Beam2 In IR1 Vertical crossing a = 285 mrad Round beam r = 1 bx* = by* = 55 cm n1 ~ 7 (small aperture limitation fixed by triplet sorting) S. Fartoukh, LHC-MAC, 16 June 2006, p. 5/20

  6. xmax~ 5 mm • Case 2:max. possible aspect ratio to preserve aperture r =2at constant b* Beam1 in IR1 bx,max~ 2.2 km by,max~ 8.8 km  L increased by 13% thank to the reduction of the X-angle Beam2 in IR1 Flat beam r = 2 bx* = 110 cm, by* = 27.5 cm n1 ~ 7 (even slightly better than the nominal case) Horizontal crossing a = 285/r1/2 = 201 mrad S. Fartoukh, LHC-MAC, 16 June 2006, p. 6/20

  7. xmax~ 5.5 mm • Case 3: Still working at constant b*, the triplet aperture is optimized forr ~ 1.6 Beam1 in IR1 bx,max~ 2.7 km by,max~ 7.0 km  L still higher by 10% w.r.t. to nominal, n1 ~ 7.5 Beam2 in IR1 Horizontal crossing slighly increased to a = 285/r1/2 = 225mrad Flat beam r = 1.6 bx* = 88 cm, by* = 34.4 cm n1 ~ 7.5! S. Fartoukh, LHC-MAC, 16 June 2006, p. 7/20

  8. xmax~ 5.5 mm Beam1 in IR1 • Case 4: Re-saturating the triplet aperture by reducing further by* to 30 cm keeping constant bx* bx,max~ 2.7 km by,max~ 8.1 km  L increased by 18% w.r.t. to nominal, n1 ~ 7 Beam2 in IR1 Flat beambx* = 88 cm, by* = 30 cm • Horizontal crossing • = 225mrad (unchanged w.r.t. previous case) n1 ~ 7 S. Fartoukh, LHC-MAC, 16 June 2006, p. 8/20

  9. xmax~ 5.5 mm bx,max~ 2.7 km by,max~ 5.8 km Beam1 in IR1 • Case 5: back to the nominal lumi to gain aperture by increasing by* to 42 cm keeping constant bx*  L unchanged w.r.t. to nominal, but n1~ 8 Beam2 in IR1 Flat beambx* = 88 cm, by* = 42 cm • Horizontal crossing • = 225mrad (unchanged w.r.t. previous case) n1 ~ 8! S. Fartoukh, LHC-MAC, 16 June 2006, p. 9/20

  10. Summary table(note case 5 further split into 2 sub-cases) • All these configurations are achievable with the nominal LHC hardware (layout, power supply, optics antisymmetry, b.s. orientation in the MQX’triplets). • The last 3 cases will be studied in more detail. S. Fartoukh, LHC-MAC, 16 June 2006, p. 10/20

  11. Investigation of possible limitations • Chromatic correction:  Q’ correction is a non-issue with the actual LHC sextupole scheme: SF and SD powered at 31% and 51% in the worst case (case 2: b* =27.5 cm in one of the two planes  bmax =8.8 km).  Q’’ and off-momentumbeta-beat correction  Enough sextupole strength even for two IR’s with b*=25 cm in both planes (see S.Fartoukh, LPR 308).  Remark: IR phasing by p/2 does no longer work for flat beams (induces only a partial compensation since the aspect ratio is inverted from IP1 to IP5). S. Fartoukh, LHC-MAC, 16 June 2006, p. 11/20

  12. Triplet imperfections: • Dynamic aperture vs phase space angle f for nominal(bmax =4.4 km) and flat beam case 4 (bmax =8.1 km) using measured MQX error table. • Net loss but nice results (DA > 10s even w/o triplet correction) due to the high field quality of MQX magnets, much better than expected. S. Fartoukh, LHC-MAC, 16 June 2006, p. 12/20

  13. Beam-beam (1/4):  Head-on: 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, p. 13/20

  14. Beam-beam (2/4): • Parasitic beam-beam • Tune shiftonly partially compensated by the H/V separation scheme with flat beam: • Beam-beam tune spread and driven resonances even more 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, p. 14/20

  15. Beam-beam tune footprint at 6s atnominal intensity for nominal case (blue) compared to the two flat beam cases 4 and 5a(red) DQ ~2. 10-2 Flat beam case 4: 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 4 limited to ~ 60-70% of nominal intensity 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 Flat beam case 5a: r~1.45, b*~61cm L~L0, aperture maximized (n1=8) • ~ 20-25% bigger ! • Case 5a limited to ~80-85% of nominal intensity S. Fartoukh, LHC-MAC, 16 June 2006, p. 15/20

  16. 1’000’000 turns Dynamic aperture atnominal intensity for nominal case (blue) compared to the flat beam case 4 (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. • The DA follows almost exactly the scaling of the b-b tune spread which further confirmed the intensity limitation given for case 4 and case 5a. S. Fartoukh, LHC-MAC, 16 June 2006, p. 16/20

  17. Increasing the b-b sep. from to 9.5 to 11s(flat beam case 5b) at the expense of re-saturating the triplet aperture and loosing 3% of lumi DQ ~1.2 10-2 No more tails!  some advantages not yet quantified, e.g. - robustness vs. CO and b* at IP1 and IP5. (some limitation in case of round beam with H/V scheme) - easiness to accommodate the footprint in the resonance grid (e.g. closest to the diag.).  DA almost recovered.  Possible improvement via fine tune scan …still missing. S. Fartoukh, LHC-MAC, 16 June 2006, p. 17/20

  18. Conclusions • The LHC experimental insertions are very flexible. • Extremely good Field Quality of the triplet magnets.  will allow to produce and test a large variety of flat beam collision optics: (range given by the triplet beam screen aperture).  if needed, will allow V-H, H-V, V-V or H-H crossing scheme with round-round, flat-flat, round-flat or flat-round beam optics in IR1 and IR5. • While strong (parasitic) beam-beam limitations occur at nominal intensity, staging the IP beam aspect ratio with intensity allows • To push the lumi by up to 20% at max. b* (aperture saturated) and medium intensity: < 60% of nom. intensity  see flat beam case 4, with r~ 1.7. • Up to ~ 80% of the nominal intensity,to enlarge the triplet aperture by 15% (n1=8 instead of 7) at constant lumi, e.g. in case of direct or indirect problem (impedance) related to collimation  see case 5a, with r ~ 1.45. 3. To enlarge the b-b separation by ~ 15-20% at full intensity, constant aperture but slightly reduced lumi, e.g. in case of unexpected beam-beam related difficulties  see case 5b, with r ~ 1.45 and b-b sep. of ~11s. S. Fartoukh, LHC-MAC, 16 June 2006, p. 18/20

  19. Future plans • A fully optimized flat beam configuration at nominal intensity has still to be done, basically • finding the optimum tune for case 5b. • fine optics adjustment to strictly stick to the nominal luminosity. • A dedicated study for the partial self beam-beam compensation induced by image current must be done (flat beam closer to the beam-screen wall compared to round beam). • The potential of flat beam optics for LHC upgrade has to be seriously envisaged, with the nominal LHC as bench-marker. • Clearly beneficial for both lumi and aperture in case of parasitic beam-beam compensation by wires (so-called BBLR from J.P. Koutchouk). • Clearly beneficial for luminosity for the option “quadrupole first” when the large X-angle imposed by round beam leads to an intrinsic loss of luminosity by ~ 40-50% for b*= 20-25 cm. S. Fartoukh, LHC-MAC, 16 June 2006, p. 19/20

  20. Beam-beam separation in IR1 and IR5 ATLAS Nominal case (black) Flat beam case 2 (red) Flat beam cases 4 and 5a (green) Flat beam case 5b (blue) ..In millimeter ..In beam size CMS Min. separation of 8 s for flat beam case 5b Min. separation of only 6.5 s for round and flat Beam case 4 and 5a S. Fartoukh, LHC-MAC, 16 June 2006, p. 20/20

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