A Summary of Optics Studies

R. Ostojic, IRP1 CD Review, 31 July

2008

A Summary of Optics Studies

1. Triplet layout and matching sections R. de Maria (LIUWG-3) E. Todesco (LIUWG-12) S. Fartoukh (LIUWG-2, LIUWG-15) J. Johnstone (LIUWG-13)

2. Chromatic aberrations S. Fartoukh (LIUWG-15)

3. Conclusions

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

0

50

100

150

200

70 90 110 130 150 170 190 210 230

Magnet aperture f (mm)

Gra

dien

t (T

/m)

80% of Nb-Ti at 1.9 K

E. Todesco, LIUWG-12

0

5

10

15

20 25 30 35 40 45 50 55 60Total quadrupole length (m)

Qua

drup

ole

leng

th (

m)

Q1-Q3

Q2a-b

Baseline

Linear(Q1-Q3)Linear(Q2a-b)

50

100

150

200

250

20 25 30 35 40 45 50 55 60Total quadrupole length (m)

Gra

dien

t (T

/m) Baseline

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

Symmetric triplet – performance reach

0.10

0.15

0.20

0.25

0.30

0.35

0.40

25 30 35 40 45Total quadrupole length (m)

b* (

m)

Off-mom. beta beating correction

Aperture required (10 s)

Aperture required (13 s)

Length vs. aperture:

42 m – 140 mm

40 m – 130 mm

38 m – 120 mm

36 m – 110 mm


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)

IIP = 850

IIP = 1400

n11

Matching sections - nominal IR optics

S. Fartoukh, LIUWG-15

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 P always makes the matching difficult.

bmax=4400m

bQ4=1500m

bQ5=900m

Triplet “reciprocal focal distance”:

1/P ~ (bexit ~ 1/1000 m-1

with bexit ~ 2km and exit = b’exit /2~ 2at the Q3 exit and entrance

IR optics with 110 mm/135 T/m


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 strongly reduced 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.

b crossing-pointwell in between D1 and D2 as for the nom. optics

b crossing-pointpushed against D2 new b-b wires location to be defined.

Case Case Ia Case Ib

Grad.[T/m] 132.74 136.41

Lq1=Lq3 [m] 8.70 8.50

Lq2 [m] 7.40 7.30

L* [m] 23.0 23.0

D(q1-q2a) [m] 2.50 2.70

D(q2a-q2b) [m] 1.00 1.00

D(q2b-q3) [m] 3.00 2.90

Beta_max [m] 11910 11810

Beta_Q4 [m] 3750 2125

Beta_Q5 [m] 2220 1340

Phase advance across the IR

~nominal

~2.6/2.6

~nominal~2.6/2.6

Summary of IR optics with 110 mm/135 T/m


No additional margin in the tripletn1 ~ 6.77 for b*=25 cm

(Case Ib with 110 mm aperture assumed for MQX)

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).

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.

Case Case IIa Case IIb

Grad.[T/m] 125.78 126.82

Lq1=Lq3 [m] 9.09 9.00

Lq2 [m] 7.75 7.70

L* [m] 23.0 23.0

D(q1-q2a) [m] 2.60 2.60

D(q2a-q2b) [m] 1.00 1.00

D(q2b-q3) [m] 2.68 2.80

D2/Q4 disp. [m] 16.0 0.0

Q5 disp. [m] 10.5 0.0

Beta_max [m] 12400 12380

Beta_Q4 [m] 2515 2320

Beta_Q5 [m] 1475 1470

IR phase ~ 2.6/2.6


IR optics with 120 mm/125 T/m (2)


Case IIa-beam1IR5 (H-Xing)

Q5D2/Q4TANQ3/D1

TCT.(in-going beam

in between TAN & D2)

n1=8.5

n1=11

Case IIa-beam1IR5 (H-Xing)

After b.s. rotation in Q5.L, D2.R, Q4.R & Q5.R

W/o beam screen rotation

Summary of optics with 120 mm/125 T/m


Case IIb (nominal LSS, P reduced 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 band apparently non-smooth squeeze sequence.

Case IIa is 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 (n1~0.51 w.r.t. n1=7) is not usable if the TAN-Y chambers are not modified.

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.

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)

Q5.L Q5.R

10 mm additional marginfor 130 mm aperture triplet/D1

TAN..L TAN..R

Summary of optics with 130 mm/115 T/m


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. ~ Q’nat induced by the 8 LHC sectors.

Q’’ and bb) (linear off-momentum b-beating) bb) can reach ~100% for =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, bb) 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 bb) and Q’’ can be compensated. However, depending on the sextupoles settings significant Q’’’ and non-linear off-momentum beta-beating can be generated.


Chromatic corrections – strategies (1)


IP3IP1 IP5 IP7 IP1

Optics IIa-Beam1

W ~ 1000 in IR3W ~ 0 in IR7 and in the new triplets

Wx,y (s)Qx,y

Bu

cket:

×

Min

. mom

entu

m w

ind

ow:

Mom

. collimator:

×

IR phasing 2 between IR1 and IR5 and correction of the IR2/3/7/8 b1-b2 phase splits).

bb 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

/2 for non-zero ) which is the indication of large non-linear off-momentum b-beat.


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’()-wave and the correction of the MQX contribution to Q’ needs to be done in the same sectors to get rid of Q’’’, b’’(), and to avoid zero-xing of RSF/D during squeeze.



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 ~),

small high order effects expected



bbin IP1

bbin IP5

bbin IP7

bbin IP3

Qx,y () with MO

b()/b(0) < 5-10%over the full range.

Q() linear afterMO correction

(~200/450A needed in OF/OD)

Two b’-sectors per triplet with specific conditions for the arc cell and IR phase advances – final result.



IR phase

x / [2]

and overall tune

V6.500 New optics

Beam1 Beam2 Beam1 Beam2

IR2 2.974 / 2.798 2.991 / 2.844 3.020 / 2.875 3.020 / 2.875

IR3 2.248 / 1.943 2.249 / 2.007 2.220 / 1.990 2.220 / 1.990

IR4 2.143 / 1.870 2.143 / 1.870 2.050 / 1.875 2.050 / 1.875

IR6 2.015 / 1.780 2.015 / 1.780 2.270 / 1.625 2.270 / 1.625

IR7 2.377 / 1.968 2.483 / 2.050 2.456 / 1.963 2.456 / 1.963

IR8 3.183 / 2.974 3.059 / 2.782 3.050 / 2.875 3.050 / 2.875

IR1&IR5 2.633 / 2.649 2.633 / 2.649 2.658 / 2.644 2.658 / 2.644

IR1 & IR5 left Never specified 1.044 / 1.754 1.614 / 0.890

IR1 & IR5 right Never specified 1.614 / 0.890 1.044 / 1.754

Qx/Qy 64.31/59.32 63.31/60.32

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.

Correction of parasitic dispersion


• 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 ~3.55 mm, i.e. n1~1-1.5 can be obtained.•… but with a non-zero nominal CO in the arcs, orthogonal fine tuning knobs must be defined

H- Xing in IR5

V- Xing in IR1

Closed H-orbit bumpsin sectors 45 & 56

Closed V-orbit bumpsin sectors 12 & 81

Dx & Dy back to 020 cm in the triplets of IR1 & IR5

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 n11.5 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.

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A Summary of Optics Studies

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