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Beam Physics requirements Triplet and LSS aperture and optics matchability

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  1. Optics challenges for Phase I: Towards a complete solution with new concepts andpossible benefits for the nominal LHC opticsS. Fartoukh for the LIUWG • Beam Physics requirements • Triplet and LSS aperture and optics matchability • A few words on nominal low-b optics • “High gradient” option (135 T/m) • “Medium gradient” option (126 T/m) • “Low gradient” option (112 T/m) • Chromatic aberrations • Off-momentum b-beating and non-linear chromaticity: strategy of correction and implementation. • Vertical & Horizontal spurious dispersion: strategy of correction and results. • Coming back to the aperture: exact evaluation of the off-momentum aperture. • Conclusions S. Fartoukh, LIUWG 28/05/2008

  2. Beam Physics requirements (1/2) • Peak luminosity increased by a factor of 2:  Reduction ofb*from 55 cm to ~ 25 cm(50% increase in lumi) • Beam intensity increased from1.15 to 1.4× 1011 p/bunch (50% increase in lumi) • Sufficient aperture in the triplet, D1 and in the LSS • n1 ~ 79 in the triplet/D1 with a X-angle of 450 mrad (10 s b-b separation with V/H Xing in IP1/5 whichmight simplify into H/H scheme after gaining experience with b-b running the nominal LHC). • Possibility to re-use the actual TCT (max. aperture of 58 mm) and if possible, re-use the TAN and the Y-chamber as-is (or shifted). • Increased beam-clearance in the LSS, n1~9-10 (to be confirmed) might be needed to avoid the implementation of new collimation and protection devices: n1=7 is excluded (which justified the TCT’s to protect the triplet), n1~12 is OK (actual min. value of n1 reached in Q5.R1.b1 for b*=55cm). S. Fartoukh, LIUWG 28/05/2008

  3. Beam Physics requirements (2/2) • Correction of the chromatic aberrations • Target momentum window:dp ~ 1-1.5 ×10-3 (~opening of the momentum collimators @ 7TeV for abort gap cleaning). • Regular behavior of Q(dp), i.e. minimization of non-linear chromaticity Q’’, Q’’’,… (avoid off-momentum particles to be trapped into resonance and erratically lost in the ring, or head-tail instability e.g. during off-momentum measurement). • Minimize the linear and non-linear off-momentum beta-beat in the triplet (aperture) and in the two collimation IR’s (collimation inefficiency) • When applicable, correction of the H & V spurious dispersion induced by the V/H crossing angle in IP1/5 (gain aperture margin) and in IR3 (collimation inefficiency). • Main ingredients: • Use of 32 sextupole families up to the ultimate strength of 600 A (2 sectors per triplet will be needed). • Reasonable (<4-5 mm) V&H orbit bumps in the 4 arcs adjacent to IP1 & 5. • 1. & 2. only works after a substantial modification of the overall LHC optics (rephasing the 8 LHC sectors and non low-beta IR’s)  see next slides. S. Fartoukh, LIUWG 28/05/2008

  4. Triplet and LSS aperture and optics matchability (1/5) • Assumption on the triplet and D1 aperture • 120 mm (unless specified differently) • Available beam clearance(from previous discussions at the LIUWG but would need to be updated for octagonal shape beam-screens  see N. Kos, LIUWG#14): Inner beam-screen dimensions (assuming 2 capillaries and nominal rectellipse shape): Gap/Radius = 42.65 / 50.25 mm for Q2, Q3, D1 32.65 / 40.25 mm for Q1 Values indicated in red might be a bit pessimistic for various reasons and would merit further discussions to gain a couple of mm in both transverse planes S. Fartoukh, LIUWG 28/05/2008

  5. A few words on the nominal LHC low-b optics Aperture and optics matchability (2/5) b_max=4400m Triplet “reciprocal focal distance”: 1/P ~ (a/b)exit ~ 1/1000 m-1 with bexit ~ 2km and aexit = b’exit /2~ 2 at the Q3 exit and entrance n1>12 in the LSS  no tertiary needed n1~7 in the triplet  TCT needed b_Q4=1500m Typical n1 plot in collision in LSS1/5 (from Q13 to Q13) b_Q5=900m • The reciprocal focal distance P will be shown to be an extremely important indicator: • quite independent on b* (up to b* ~1m) but very dependant on the detailed triplet layout. • LSS aperture: low P (i.e. basically larger aexit in the relevant transverse plane) means lower b function and therefore increased aperture in the LSS at constant b* and “constant LSS”. • optics matchability to the arcs: on the other hand, “at constant LSS”, too low Palways makes the matching difficult if not impossible: LSS/DS quad. strength going to 0 (e.g. Q4/Q5) or above nom. (e.g. Q7). S. Fartoukh, LIUWG 28/05/2008

  6. With a ~10% overestimated gradient(historically based on LPR1000)  Two categories of optics, both obtained with a symmetric triplet of slightly different layout and gradient. No quad displacement in the LSS Aperture and optics matchability (3/5) b crossing-point pushed against D2  new b-b wires location to be defined. b crossing-point well in between D1 and D2 as for the nom. optics • Case Ia: • Triplet matched with ~ nominal rec. focal (P = 891 m) • No problem of matchability to the arc (LSS quad. strength well in range, beta<200 m in the DS, natural phase advance  inj. optics easy to find)  Aperture problem expected in the LSS (next slide). • Case Ib: • Triplet matched with stronglyreduced P (P=328 m) • First indications of matchability problems (Q7 close to 200 T/m, Q4/Q5 “goes to zero” ~7-15 T/m), i.e. concept of inner/outer triplet comes back.  Optimized for the LSS aperture (next slide). S. Fartoukh, LIUWG 28/05/2008

  7. Case Ia (beam1): • Margin in the 120 mm triplet/D1 (n1~7.58) • Strong aperture restriction in the TAN (n1<6) • 58 mm max. TCT opening not an issue • Very small or no margin in D2/Q4 • Restriction in Q5 (n1~6.5)  Much too far from the target n1=9 in the LSS (even after beam-screen rotation in D2/Q4/Q5) TCT. (in-going beam in between TAN & D2) IR1 (V-Xing) Q3/D1 TAN D2/Q4 Q5 IR5 (H-Xing) • Case Ib (beam1): • Slightly improved margin in the 120 mm triplet/D1 (n1~88.5) • n1=7 almost reached in the TAN • n1>10 reached in the LSS! IR5 (H-Xing) IR1 (V-Xing) S. Fartoukh, LIUWG 28/05/2008

  8. Summary for cases Ia and Ib (~135 T/m): • Optics with standard (a/b)exit (case Ia) are excluded by the LSS aperture unless LSS magnets (D2/Q4/Q5) are displaced (next cases). • Optics with strongly increased (a/b)exit (case Ib) solve the LSS aperture problem but are at the limit of matchability for MQX gradient lower than ~135 T/m (next cases) • Realistic Case Ib-bis with 110 mm D1/MQX aperture could be an economical solution to envisage (i.e. with nominal LSS), compromising on b* (30-35 cm) if opening the coll. is needed: No margin in the triplet/D1: n1 ~ 6.77 for b*=25 cm (Case Ib with 110 mm aperture assumed for MQX/D1) …But, this corresponds to an non-standard LHC low-beta optics still to be looked at into details (Q4/Q5/Q7 collision strength, squeezed sequence, injection optics) IR1 (V-Xing) IR1 (V-Xing) S. Fartoukh, LIUWG 28/05/2008

  9. With a more realistic gradient for 120 mm: ~126T/m  Againtwo categories of optics: with disp. of D2/Q4/Q5 towards the arcs, or with nom. LSS but strongly reduced triplet focal,to fulfill the LSS aperture constraints. Aperture and optics matchability (4/5) b anomalies start to be visible in the LSS • Case IIb: • Triplet matched with nominal LSS and P further reduced to P=345 m.  Matchability problems: Q7 sticks to 200 T/m, Q4/Q5 “goes to zero”, • The natural IR phase cannot be reached limiting the highest possible injection b* (for a squeeze at constant IR phase).  Sufficient aperture expected in the LSS. • Case IIa: • Triplet matched with P=450 m, and displacing the TAN/D2/Q4 and Q5 • No problem of strength and matchability to the arcs.  inj. optics easy to find (see next slides).  Sufficient aperture expected in the LSS (next slide). S. Fartoukh, LIUWG 28/05/2008

  10. Case IIa (beam1): • Margin in the 120 mm triplet/D1 (n1~7.58) • TAN almost at n1~7 • 58 mm max. TCT opening not an issue  n1>910 reached in the LSS: if needed, b.s. rotation could further increase the beam-clearance in D2/Q4/Q5 TCT. (in-going beam in between TAN & D2) Q3/D1 TAN D2/Q4 Q5 IR5 (H-Xing) IR1 (V-Xing) • Case IIb (beam1): • Margin in the 120 mm triplet/D1 (n1~7.58) • n1~ 67 in the TAN (slight reduction w.r.t. case IIb due to slight change in X-scheme & spurious dispersion) • n1>910 reached in the LSS: if needed, b.s. rotation could further increase the beam-clearance in D2/Q4/Q5  Aperture of Q8.R starts to be visible (due to matchability problem, see previous slide) Q8 and adjacent MB’s IR1 (V-Xing) IR5 (H-Xing) S. Fartoukh, LIUWG 28/05/2008

  11.  Beam-screen rotation could substantially improve the LSS aperture if needed: • Applied to Q4.R & D2.R for beam1, and Q4.L & D2.L for beam2. • Applied to both apertures of the four Q5’s. •  See LPR1050 for more details n1=11 n1=9 TCT. (in-going beam in between TAN & D2) Q3/D1 TAN D2/Q4 Q5 Case IIa-beam1 IR5 (H-Xing) Case IIa-beam1 IR5 (H-Xing) After b.s. rotation in Q5.L, D2,R, Q4.R & Q5.R W/o b.s. rotation in LSS magnets S. Fartoukh, LIUWG 28/05/2008

  12.  Injection optics and aperture for cases IIa and IIb: • Case IIa at injection: • Easy squeeze sequence at constant phase, easy injection optics. • Noparticular aperture problem(with the standard spec. n1=7/6.7 at QF/QD) • b* limited to 14 m@ 450 GeVby the Q5/Q6 aperture (compared to 17 m for the nom. LHC). • bmaxlimited to ~ 250 m in the triplet (as for nom.): FQ non critical at injection Case IIa-IR5-beam1: n1 plot @ 450 GeV for b*= 14 m, qc= 180 mrad and sep. =2 mm • Case IIb at injection: Difficult injection optics and squeeze sequence at constant IR phase • b* limited to 7 m@ 450 GeV, at the limit of the IR tunability at injection (non- natural IR phase ~2.6/2.1) • Noparticular aperture problem(with the standard spec. n1_qf/qd=7/6.7 at inj.) • bmax ~ 460 m in the triplet: FQ @ 450 GeV will have to be optimized Case IIb-IR5-beam1: n1 plot @ 450 GeV for b*= 7 m, qc= 250 mrad and sep. =2 mm S. Fartoukh, LIUWG 28/05/2008

  13. Summary for cases IIa and IIb (120 mm & 126 T/m): • Case IIb (nominal LSS, focalreduced by a factor 3 w.r.t. nom.) is not recommended due to difficult matchability and lack of tunability (poor or zero intersection between the inj. and coll. optics tunability diagrams): - LSS quad at very low gradient (Q4/Q5) and KQ7=200 T/m in collision. - Strong limitation on the injection b* and apparently non-smooth squeeze sequence. • Case IIais expensive but looks to be one possible solution: • Triplet matched with 50% reduction of the rec. focal, with a good matchability and no limitation for the injection b* (but the usual one given by the Q5/Q6 aperture at injection). • LSS aperture partially recovered by moving D2, Q4, Q5 ( n1~9) and possibly further optimized by tilting the b.s ( n1~11).  In both cases, the triplet aperture margin (Dn1~0.51 w.r.t. n1=7) is not be usable by the primary beam if the TAN and therefore the Y chamber are not upgraded. S. Fartoukh, LIUWG 28/05/2008

  14. With a low gradient for 120 mm: ~112T/m No solution found w/o moving Q4 and sufficiently low P to get n1_LSS > 7. • Tricky but possiblesolution with P~400 m can be found by moving LSS magnets. However the LSS aperture (mainly Q5) approaches n1=7. Aperture and optics matchability (5/5) Q5.L Q5.R TAN..R TAN..L 10 mm additional hidden margin for 130 mm aperture triplet/D1 • Matched with P~400 m, only Q4 displaced, and b* =27 cm • b* =27 cm at the limit for the correction of chromatic aberrations ( next chapter) • LSS quad strengths are worrying: KQ8/9~200 T/m, KQT~123 T/m, KQ7~205 T/m • w/o b.s. rotation, Q5 aperture close to n1=7 (would be ~6.5 for b* =25 cm)  MQX margin not usable by the beam if the TAN is not changed • Corrector package combined to the non-IP side of Q3 • reduced intercon. length • no specific impact on the X scheme but orbit correct-ability to be checked. S. Fartoukh, LIUWG 28/05/2008

  15. Chromatic aberrations (1/8)Linear and non-linear chromaticity, off-momentum b-beating • Linear chromaticity: • Nominal LHC: IMQX ~ 350 • Upgrade:IMQX ~ 800 850 • Q’MQX ~ -65 per IR, i.e. ~ DQ’nat. induced by the 8 LHC sectors! • Q’’ and linear off-momentum b-beating (see LPR308): • The off-momentum beta-beating goes with twice the betatron phase and can reach ~100% for d=10-3. • By phasing IR1 and IR5, it can be cancelled in half of the ring but then is almost maximized in the other half for the nom. LHC tunes (0.31/.32): • Cancelling by other means, i.e. sextupoles, the off-momentum beta-beating in the triplet automatically kill the triplet contribution to Q’’. However the sextupoles themselves might induce a non-negligible residual Q’’ (next slides) • Third (higher) order chromaticity Q’’’ and signature by second (higher) order off-momentum b-beating: Depending on the sextupoles settings (i.e. 1 or 2 sextupole sectors to compensate for one triplet) significant Q’’’ and non- linear off-momentum beta-beating can be generated (next slides). S. Fartoukh, LIUWG 28/05/2008

  16. Chromatic aberrations (2/8)Linear and non-linear chromaticity, off-momentum b-beating • W/o specific correction,but the usual compensation of Q’ by the MS’s (one family per plane) - Results obtained plugging directly the case IIa optics and layout into the LHC sequence w/o any rephasing. - Plotting the amplitudes Wx,y of the linear off-momentum b-beating along the machine: IP1 IP3 IP5 IP7 IP1 Optics IIa-Beam2 Optics IIa-Beam1 • Different behaviors beam1/beam2 due to differences between the IR1/5 phase advances ( beam1/beam2 phase split in IR2, IR3, IR7, IR8). The Montague’s functions Wx,y can reach 1’000 in the triplets, IR3 and/or IR7, i.e. ~100% change of the b-functions for d=10-3(even more due to higher order effects). S. Fartoukh, LIUWG 28/05/2008

  17. Chromatic aberrations (3/8)Linear and non-linear chromaticity, off-momentum b-beating • Strategy Ia: with IR phasing (p/2 between IR1 and IR5 and correction of the IR2/3/7/8 b-b phase splits). W ~ 1000 in IR3 W ~ 0 in IR7 and in the new triplets Min. momentum window: d = 10-3 Mon. collimator: d = 1.5×10-3 IP1 IP3 IP5 IP7 IP1 Bucket: d = 0.36×10-3 Optics IIa-Beam1 Wx,y (s) Qx,y(d)  Linear off-momentum b-beat minimized in IR7 but maximized in IR3 collimation inefficiency (mainly relevant in the H-plane for IR3)? • Q’ corrected to 2 units: 40%- 68% of Imax (600A) needed in SF-SD, respectively. • No Q’’, but huge Q’’’(basically, because the phase advance from IP1 to IP5 is no longer p/2 for non-zero d) which is the indication of largenon-linear off-momentum b-beat (next slide). S. Fartoukh, LIUWG 28/05/2008

  18. Db(d)/b(0) [%] • in the triplet of IR1 • Lin. term corrected  Large sec. order • Db(d)/b(0) [%] • in the triplet of IR5 • Lin. term corrected  Large sec. order Optics IIa-Beam1 Optics IIa-Beam1 • Db(d)/b(0) [%] • in IP3 • Lin. term not corrected  Large sec. order • Db(d)/b(0) [%] • in IP7 • Lin. term corrected • Some higher order effects. Optics IIa-Beam1 Optics IIa-Beam1 S. Fartoukh, LIUWG 28/05/2008

  19. Chromatic aberrations (4/8)Linear and non-linear chromaticity, off-momentum b-beating  Strategy Ib: with IR phasing and cabling the sextupole families into two per plane for Q’’’ minimization (unbalance of Q’ correction between sectors): • 31%-51% of Imax (600A) in the SF-SD families of sectors 12, 23, 34 & 45 • 51%-83% of Imax (600A) in the SF-SD families of sectors 56, 67, 78 & 81 Db(d)/b(0) [%] in IP3 Db(d)/b(0) [%] in IP1 Qx,y(d) Min. mom. window: d = 10-3 Db(d)/b(0) [%] in IP5 Db(d)/b(0) [%] in IP7 Optics IIa-Beam1 • Net improvement but not fully satisfactory (IR3!) • Back-up solution to keep in mind S. Fartoukh, LIUWG 28/05/2008

  20. Chromatic aberrations (5/8)Linear and non-linear chromaticity, off-momentum b-beating  Strategy IIa-1: • Using the SF1/2 and SD1/2 families in flip-flop mode in the sectors adjacent to IR1 and IR5 (sectors 81,12,45 and 56) to generate an off-momentum b-beating wave  so-called b’-sectors • MS families used in normal mode in the other sectors to compensate for Q’ Q’-sectors • Strength limitation for the SD’s in the Q’ sector (twice less efficient than the SF’s) but some margin in the b’-sector. • mcell as close as possible to p/2 is needed for efficiency (otherwise decoherence of the b’-wave) and to avoid the generation of residual Q’’ by the MS themselves  Inj. Optics has to be changed and substantial left/right tunability of IR1 & IR5 is needed • Large high order effects (Q’’’, b’’(d)) expected (interleaved scheme with strong source of chrom. errors spaced by p/2 and not p). • The SF2 & SD2 families will change sign during the squeeze in the b’-sector. • The phasing condition is actually a bit more complicate due to non-negligible coupling between the SF and SD families. S. Fartoukh, LIUWG 28/05/2008

  21. Strategy IIa-2: -Problem of strength is solved • Still high order effects expected • (interleaved sources of chromatic errors). • Zero-xing during squeeze  Strategy IIa-2 & IIa-3: • If needed (strength limitation in one of the two type of sectors), partial or full mergingof the Q’ and b’-sector functionalities. • Strategy IIa-3: A priori best scheme but …SD families pushed to 950-1000 A in the b’-sectors (~600 A for SF’s). S. Fartoukh, LIUWG 28/05/2008

  22. Qx,y (d)  huge Q’’’ b’(d) well corrected in IR3 &IR7 and in the triplets but sizeable higher order effects Wx,y (s) • Strategy IIa-1: Illustration by setting the arc cell phase advance to p/2 in all sectors and assuming no limitation for the IR tunability(fake trombone matrices installed in IR1/5 for satisfying the phasing conditions and in IR2/4/6/8 for the overall tune). Db(d)/b(0) [%] in IP3 Db(d)/b(0) [%] in IP7 Db(d)/b(0) [%] in IP5 S. Fartoukh, LIUWG 28/05/2008

  23. Qx,y (d)  Almost linear in the H-plane  Huge Q’’’ in the V-plane Wx,y (s) • Strategy IIa-2 for SD’s and IIa-3 for SF’s: Marginal high order in the H-plane, still sizeable in the V-plane . Db(d)/b(0) [%] in IP7 Db(d)/b(0) [%] in IP3 Db(d)/b(0) [%] in IP5 S. Fartoukh, LIUWG 28/05/2008

  24. Wx,y (s) Qx,y (d)  Almost linear in both planes • Strategy IIa-3 both for SF’s & SD’s: Db(d)/b(0) < 5% over the full d-range. Db(d)/b(0) [%] in IP3 Db(d)/b(0) [%] in IP7 Db(d)/b(0) [%] in IP5 S. Fartoukh, LIUWG 28/05/2008

  25. Same quantitative and qualitative conclusions obtained when trying to interchange the “Q’- and b’-sectors”: strategies IIb, IIc, IId,… • The b’-sectors for the SF’s are the Q’-sectors for the SD’s, and vice-versa • Q’-sectors: 12, 45, 56 & 81 • b’- sectors: 23, 34, 67 & 78 • Q’-sectors: 23, 45, 67 & 81 • b’-sectors: 12, 34, 56 & 78 • The generation of the b’(d)-wave and the correction of the MQX contribution to Q’ needs to be done in the same sectors to get rid of Q’’’, b’’(d),.., and avoid zero-xing of RSF/D during squeeze. • Not allowed due to strength limitation in SD’s , but non-issue for the nominal LHC! S. Fartoukh, LIUWG 28/05/2008

  26. Chromatic aberrations (6/8)Linear and non-linear chromaticity, off-momentum b-beating • Strategy III…last chance: Two b’-sectors per triplet constraining the arc cell and IR phase advances all around the ring. • SD families just strong enough: 600 A required (2% more would be welcome). • No zero-crossing during the squeeze. • Non-interleaved scheme (strong SD or SF spaced by ~p) • small high order effects expected • Injection Optics has to be changed (phasing conditions). In additionthe arc tune-shift quadrupoles (acting independently on both beams) gets a non-zero nominal setting because the left (resp. right) phase advances of IR1 & 5 cannot be equalized for the two beams, i.e. the IR now extends up to Q22 with some impact on the aperture @ 450 GeV(CO budget to be tighten by ~0.3 mm). • The adjustment of the fractional part of the tune becomes tricky, and impose to detune in a subtle way the above phasing conditions: e.g. dephasing sector 45 by –DQ/2 and sector 34 by +3DQ/2 give a tune shift of +DQ while warranting that the b’-wave still arrive with the right phase in the triplet.  Residual but sizeable Q’’ is expected(the b’-wave is not zero at the sextupole)  correctable by the arc MO’s if needed. The SD efficiency and then the minimum achievable b* depend (smoothly) on the working point. S. Fartoukh, LIUWG 28/05/2008

  27. A new phasing configuration of the LHC has been found to allow the b’(d) correction in collision, with controllable and/or correctable side effects (b’’(d), Q’’, Q’’’). • New injection optics re-matched accordingly (courtesy of M.Aiba, M.Giovannozzi, T.Risselada, R.Tomas). • Pushing the MSD’s up to 600A+e allows a full correction of the chromatic aberration up to b*~2527 cm (depending on the MQX aperture) for the nom. LHC working point (.31/.32). • Not all WP’s yet tested, but good indication that none will dramatically affect the min. possibleb*(large vertically tunability IR4 and comfortable margin in the SF strength). • This new injection optics still needs fine tuning and detailed verifications: • Aperture @ 450 GeV: expected loss of Dn1~0.10.2 (~0.5 mm at the highest beta locations). • Linear imperfection (systematic b2 induced beta-beating, a2 correct-ability?..) • DA@ 450 GeV (x-y phase split reduced in the arcs  non-linear driving terms a priori more excited, but magnet sorting at installation and actual field quality better than initially expected). S. Fartoukh, LIUWG 28/05/2008

  28. Db(d)/b(0) [%] in IP1 Db(d)/b(0) [%] in IP3 Wx,y (s) Db(d)/b(0) < 5-10% over the full range. Db(d)/b(0) [%] in IP5 Db(d)/b(0) [%] in IP7 Residual Q’’ (~30007000) (b’(d,s) ≠ 0 at the sextupoles) Q(d) linear after MO correction (~200/450A needed in OF/OD) Qx,y (d) w/o MO Qx,y (d) with MO S. Fartoukh, LIUWG 28/05/2008

  29. Chromatic aberrations (7/8)H & V spurious dispersion induced by the X-schemes • Reminder onthe beam related tolerance budget … about 15 mm for Phase I • Already challenging: all potential gain on paper has to be retro-ceded to the target n1. • Closed orbit: 3 mm • Kept unchanged while a rescaling by a factor 1.7 would be fully justified, a fortiori with one MCBX per plane and per triplet on the NIP-side of Q3. • b-beating: 20% (with no specific budget for off-momentum), i.e. 2 mm for n1=7 and bmax=12.5 km. • Kept unchanged while a rescaling by a factor 2.8 could be justified. • Spurious dispersion from the arcs: 30%, i.e. 4.5 mm for bmax=12.5 km and the usual d=0.86 10-3(i.e. 0.36 for the bucket + 0.5 for off-momentum measurement). … Perhaps d=1.5× 10-3 more suitable for off-momentum protons escaping the momentum collimator? • Overall budget, i.e. Dx,y× d, kept unchanged, at least justified for the V-dispersion, not correctable because arriving at an arbitrary phase in the triplet (see below). • V & H dispersion coming from the V & H Xing-schemes in IR1 & IR5: 5 mm in the worst case  Is exported in a given plane from one triplet to the other, at a specific phase.  Two triplets of a given IR combine in phase: effect • Can reach ~6 m for worst phase advances between IR1 and IR5. • Correctable at the source in the H-plane (IR5) via IR-rematching but no IR knobs to correct in the V-plane. • H & V arc orbit bumps tested in the past w/o success: not enough MCB strength, huge orbit in the arcs ( e.g. P. Leunissen 1999). • The new proposed LHC phasing scheme allows to revisit the above conclusion. S. Fartoukh, LIUWG 28/05/2008

  30. IR1 & 5 optics IIa (beam1) – V6.500 optics IR1&5 optics IIa (beam1)– New LHC optics IP1 IP5 IP1 Dxy(s) w/o X-scheme (arc-regular from Q13 to Q13 and matched to zero in IP1,2,5 &8) Dxy(s) w/o X-scheme (arc-regular from Q22 to Q22 and matched to zero in IP1,2,5 &8) H-dispersion generated on purpose in IR3 • A bit better but still! • ~4m in MQX (both beams) • Some perturbation in IR3&7 • With X-scheme • ~ 5 - 6 m in MQX (beam1-2) • substantially modified in IR3/7 S. Fartoukh, LIUWG 28/05/2008

  31. H- Xing in IR5 Closed H-orbit bumps in sectors 45 & 56 Dx & Dy back to 020 cm in the triplets of IR1 & IR5 Closed V-orbit bumps in sectors 12 & 81 V- Xing in IR1 • Small H & V closed orbit (< 3-4mm) generated at the beginning of the IR1 &5 adjacent sectors (1 MCBH/V) and closed at the end (2MCBH or 2 MCBV). • Generate an H & V dispersion wave arriving with the right phase at the triplet to compensate for the effect of the X-angle. • Perfectly works in both planes and for both beams and allow to keep the same optics in IR1 & IR5 with the nominal H&V alternated crossing scheme. • ~3.55 mm, i.e. Dn1~1-1.5 can be retro-ceded to the beam to reach n1~9 in the triplet for 120 mm aperture. • … but with a non-zero nominal CO in the arcs, orthogonal fine tuning knobs must be defined (for orbit, tune, coupling, b*, Dx,y ,Q’ and b’(d))Robustness, operational aspects. S. Fartoukh, LIUWG 28/05/2008

  32. Chromatic aberrations (8/8)Off-momentum aperture (low-b optics II-a, new LHC phasing config.) Mechanical aperture calculated “old style” (e.g. w/o taking into account the b(d) variation) Calculated with exact orbit and twiss parameters for non-zero d (i.e. including linear and non-linear b(d) and dispersion) Before b’(d) and dispersion correction d = +0.86×10-3 d = - 0.86×10-3 Before dispersion correction After b’(d) and dispersion correction After dispersion correction d = + 0.86×10-3 d = - 0.86×10-3 • After b’(d) and dispersion correction, n1 is only smoothly dependant on d. • n1(d) > 8.5-9 both in the triplet and the LSS, but the TAN. S. Fartoukh, LIUWG 28/05/2008

  33. Conclusions (1/2)Open questions and to do list • TheLSS apertureis the main limiting factor. • What is the min. acceptable n1 in the LSS @ 7 TeV w/o additional absorber? • (1)..n1LSS =7+e , (2) n1LSS =9-10 or (3) n1LSS >>10?? • Could be checked quickly with the nominal LHC optics by reducing artificially the D2/Q4/Q5 aperture in LSS1 & LSS5. • Sticking to b* =25 cm, and depending on the reply to the above question,… (1) the LSS could be kept unchanged and the triplet aperture could range in between ~110 mm (no aperture margin in the triplet) ~120 mm (no matching found for 130 mm aperture triplet and n1LSS ~7), with a preference for 120 mm and a gradient pushed up to ~125 T/m, i.e. 156 T/m for the short sample limit. (2) D2/Q4/Q5 have to be moved w/o b.s. rotation (but perhaps in some Q5’s)and the triplet aperture could range in between ~110 mm (no aperture margin in the triplet) 130 mm (strength limitation in the LSS, essentially Q7), with a preference for 120 mm. (3) D2/Q4/Q5 have to be moved, b.s. rotation have to be performed (essentially Q5),additional tertiaries will be needed in front of Q5and the triplet aperture could range in between ~110 mm  130 mm. S. Fartoukh, LIUWG 28/05/2008

  34. Conclusions (2/2) • The long-standing problem (>10 years old) of theoff-momentum b-beating and vert. dispersion correctionis now solved … on paper. • But 600Aneeds to be granted in half of the MSD families to go down to b*=2527 cm depending on the triplet aperture/gradient (~21-22 cm for Nb3Sn triplets). • The aperture gain by the correction of the spurious H & V dispersion offers the possibility to open the next generation collimators from n1=6 to n1~8 (keeping 1s clearance above the secondaries for machine protection devices). • But everything is based on a new LHC injection optics for the 8 LHC sectors and the 8 LHC IR’s, which needs to be assessed @ 450 GeV in terms of settings (e.g. Iinj >3% Inom), MA, DA, collimation, machine protection,… • If no show-stopper are found, this new optics will certainly improve the performance of the nominal LHC. • Then a lot of things to be checked in parallel or a posteriori. • Detailed triplet layout (BPMS, 1 or 2 MQX types to keep bmax < 12-12.5 km, CO correctability for one MCBX per plane and per triplet on the non-IP side of Q3, …). • Triplet aperture vs beam-screen shape (rect-ellipse, octagonal,..) • An then, of course, DA, beam-beam and collimation studies @ 7 TeV. S. Fartoukh, LIUWG 28/05/2008