A Summary of Optics Studies

A Summary of Optics Studies Triplet layout and matching sections R. de Maria (LIUWG-3) E. Todesco (LIUWG-12) S. Fartoukh (LIUWG-2, LIUWG-15) J. Johnstone (LIUWG-13) Chromatic aberrations S. Fartoukh (LIUWG-15) Conclusions R. Ostojic, IRP1 CD Review, 31 July 2008

Triplet layouts – possible solutions R. de Maria, LIUWG-3

Triplet layouts – performance aspects Issues with Compact and Modular layouts: • Number of long range beam-beam encounters • Considerable aperture problems in the matching section • Increased strength of Q6 quadrupole • Increased chromatic aberrations • Improved DA (without beam-beam). • Challenging magnet design for given transverse dimensions and cable inventory R. de Maria, LIUWG-3

Symmetric triplet – Nb-Ti quad gradient E. Todesco, LIUWG-12

Symmetric triplet – parametric study • Assumptions: • Q1=Q3, Q2A=Q2B • all interconnect distances = 1.3 m • Approximate matching to Q4 in its present position • Magnetic length - free parameter E. Todesco, LIUWG-12

Symmetric triplet – performance reach Length vs. aperture: 42 m – 140 mm 40 m – 130 mm 38 m – 120 mm 36 m – 110 mm IIP = 850 Dn11 IIP = 1400 Chromatic correction vs triplet length: IIP = 850 (Q’ and b’ correction) -> b* = 0.26 m (36 m) b* = 0.28 m (42 m) IIP = 1400 (Q’ correction) -> b* = 0.15 m (36 m) b* = 0.17 m (42 m) E. Todesco, LIUWG-12

Matching sections - nominal IR optics • The reciprocal focal distance P is a very important indicator: • quite independent on b* (up to b* ~1m) but very dependant on the detailed triplet layout. • LSS aperture: low P means lower b and increased aperture in the LSS. • optics matching to the arcs: too low Palways makes the matching difficult. 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 b_Q4=1500m b_Q5=900m S. Fartoukh, LIUWG-15

IR optics with 110 mm/135 T/m 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 P (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. • 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. S. Fartoukh, LIUWG-15

Summary of IR optics with 110 mm/135 T/m • Optics with standard P-value (case Ia) are excluded by the LSS aperture unless LSS magnets (D2/Q4/Q5) are displaced. • Optics with strongly decreased P-value (case Ib) solve the LSS aperture problem but are at the limit of matchability for MQX gradient lower than ~135 T/m. • Realistic Case Ib-bis with 110 mm D1/MQX aperture could be an economical solution to envisage (i.e. with nominal LSS). No additional margin in the triplet n1 ~ 6.77 for b*=25 cm (Case Ib with 110 mm aperture assumed for MQX) S. Fartoukh, LIUWG-15

IR optics with 120 mm/125 T/m (1) • Case IIa: • Triplet matched with P=450 m, and displaced TAN, D2, Q4 and Q5. • No problem of strength and matching to the arcs.  Injection optics easy to find.  Sufficient aperture expected in the LSS. • Case IIb: • Triplet matched with nominal LSS and P further reduced to P=345 m.  Matching problems: Q7 ~ 200 T/m, Q4/Q5 ~ 0. • The natural IR phase cannot be reached limiting the injection b* (for a squeeze at constant IR phase).  Sufficient aperture expected in the LSS. S. Fartoukh, LIUWG-15

IR optics with 120 mm/125 T/m (2) n1=11 n1=8.5 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 beam screen rotation S. Fartoukh, LIUWG-15

Summary of optics with 120 mm/125 T/m • Case IIb (nominal LSS, Preduced by a factor 3 w.r.t. nom.) is not recommended due to difficult matching 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 P, with a good matching and no limitation for the injection b* (except the usual limitations in 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 additional triplet aperture margin (Dn1~0.51 w.r.t. n1=7) is not usable if the TAN-Y chambers are not modified. S. Fartoukh, LIUWG-15

Summary of optics with 130 mm/115 T/m • No solution found without moving Q4 and sufficiently low P-value to get n1 > 7 in the LSS. • Tricky but possible solution with P~400 m found by moving LSS magnets. However, the DS quadrupole strength is insufficient and the LSS aperture (mainly Q5) approaches n1=7. Q5.L Q5.R • Matched with P~400 m, only Q4 displaced, and b* =27 cm (at the limit for the correction of chromatic aberrations) • LSS quad strengths are large: 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) TAN..R TAN..L 10 mm additional margin for 130 mm aperture triplet/D1 S. Fartoukh, LIUWG-15

Conclusions - I • A symmetric triplet is favoured with respect to modular designs, in spite of lower aperture margin. • With reduction of b* from 0.5 to 0.25 m, the magnets and other equipment in the LSS beam-line (TAN) become limiting factors, both in terms of aperture and strength. • The P-value of the triplet determines the optics flexibility. Any value of P can be obtained by adjusting the layout of the triplet and the individual strength of the quadrupoles. • Values of P in the range 300-500 m are required (as compared to ~1000 m for the nominal LHC). The lower the P – the larger the aperture margin in the LSS, but the lower the matching flexibility. • Moving LSS magnets towards the arc improves the aperture in the LSS and allows longer triplets. The longest triplet (<40 m) is defined by the strength limitation of DS magnets and aperture of Q5. • Further conditions on the matching are given by the optics for chromatic correction.

Chromatic aberrations - preliminaries Linear chromaticity • Nominal LHC: IIP ~ 350 • Upgrade: IIP ~ 800  850 • Q’ IP ~ -65, i.e. ~ DQ’nat induced by the 8 LHC sectors. Q’’ and Db(d)/b(0) (linear off-momentum b-beating) • Db(d)/b(0) can reach ~100% for d=10-3. This has considerable consequences, in particular as it compromises the collimation system. The acceptable value is ~10%, as in the nominal LHC. • By phasing IR1 and IR5, Db(d)/b(0) can be cancelled in half of the ring but is then maximized in the other half for the nominal LHC tunes (0.31/.32). • Using the sextupole families, the contribution of the triplet to Db(d)/b(0) and Q’’ can be compensated. However, depending on the sextupoles settings significant Q’’’ and non-linear off-momentum beta-beating can be generated. S. Fartoukh, LIUWG-15

Chromatic corrections – strategies (1) IR phasing (p/2 between IR1 and IR5 and correction of the IR2/3/7/8 b1-b2 phase splits). W ~ 0 in IR7 and in the new triplets W ~ 1000 in IR3 Bucket: d = 0.36×10-3 Mom. collimator: d = 1.5×10-3 Min. momentum window: d = 10-3 IP1 IP3 IP5 IP7 IP1 Optics IIa-Beam1 Wx,y (s) Qx,y(d) • Db(d)/b(0)minimized in IR7 but maximized in IR3 (strong reduction of collimation efficiency). • Q’ corrected to 2 units: 40%- 68% of Imax (600A) needed in SF-SD. • No Q’’, but huge Q’’’ (the phase advance from IP1 to IP5 is no longer p/2 for non-zero d) which is the indication of large non-linear off-momentum b-beat. S. Fartoukh, LIUWG-15

Chromatic corrections – strategies (2) Use of sextupole families in the flip-flop mode in sectors adjacent to IP1 and IP5, and in the normal mode in other sectors. • Combination of schemes tried but unsuccessful due to strength limit of SD family and zero crossing during squeeze. • 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 to avoid zero-xing of RSF/D during squeeze. S. Fartoukh, LIUWG-15

Chromatic corrections – strategies (3) Two b’-sectors per triplet with specific conditions for the arc cell and IR phase advances. • SD families just strong enough (600 A required). • No zero-crossing during the squeeze. • Non-interleaved scheme (strong SD or SF spaced by ~p), small high order effects expected S. Fartoukh, LIUWG-15

Chromatic corrections – strategies (4) Two b’-sectors per triplet with specific conditions for the arc cell and IR phase advances – final result. Q(d) linear after MO correction (~200/450A needed in OF/OD) Db(d)/b(0) [%] in IP1 Db(d)/b(0) [%] in IP3 Db(d)/b(0) < 5-10% over the full range. Db(d)/b(0) [%] in IP5 Db(d)/b(0) [%] in IP7 Qx,y (d) with MO S. Fartoukh, LIUWG-15

Chromatic corrections – strategies (5) Two b’-sectors per triplet with specific conditions for the arc cell and IR phase advances – consequences. • Injection optics has to be changed, with a tune split of 3. • Arc tune-shift quadrupoles are used (DS now extends up to Q22) with some impact on the aperture @ 450 GeV. • Adjustment of phase across L/R side of IP required. • Residual Q’’ expected, 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-15

Correction of parasitic dispersion 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 a H and 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 allows the same optics in IR1 & IR5 with the nominal H&V alternated crossing scheme. • An increase in aperture of ~3.55 mm, i.e.Dn1~1-1.5 can be obtained. • … but with a non-zero nominal CO in the arcs, orthogonal fine tuning knobs must be defined S. Fartoukh, LIUWG-15

Conclusions - II • A complete optics solution for the LHC in collision and injection has been found that allows full compensation of the off-momentum b-beating. Due to the limited strength of the SD families, the lowest b* that can be compensated is ~27 cm in IP1 and IP5. • The new LHC phasing conditions also allow compensation of the parasitic dispersion at the IPs, with the gain of Dn11.5s in the triplets, and minimizes dispersion perturbations in IR3 and IR7. • The proposed solution requires a change of the LHC tune split from 5 to 3, and extension of the DS functionality up to Q22. Considerable effort is required to completely validate the new optics at injection and during squeeze. • Apart from the phase advance across the full IR, a specific phase relation between the IP and the insertion entry is required. The range of b* values for which these conditions can be met depend on the P-value of the triplet and the position of the LSS.

A Summary of Optics Studies