1. Field Quality Specifications for Triplet Quadrupoles of the LHC Lattice v.3.01 Option 4444 and Collimation Study Yunhai Cai Y. Jiao, Y. Nosochkov, M-H. Wang (SLAC) R. Assmann, R. Bruce, S. Fartoukh, M. Giovannozzi, R. De Maria, E. McIntosh, F. Schmidt (CERN) LARP CM18/HiLumi LHC Collaboration Meeting Fermilab, 7 – 9 May 2012

2. Outline 2 Dynamic aperture study for the proposed LHC high luminosity lattice as a function of the IP triplet multipole field errors. Specification of the field quality for the proposed large aperture triplet quadrupoles. Collimation study and benchmarking of beam loss map calculation. Lattice: LHC v.3.01, collision option “4444” with  *=15/15 cm at IP1 and IP5, Nb-Ti superconducting triplet quadrupoles with 120 mm coil diameter, beam energy of 7 TeV. Code: SixTrack.

3. Features of the High Luminosity Lattice 3 The LHC v.3.01 collision lattice has lower than nominal  * at IP1 (ATLAS) and IP5 (CMS) crossing points resulting in higher  -functions in the IP triplet quads. A dedicated large  - modulation in the adjacent arcs is used for local cancelation of the triplet chromaticity. Large aperture triplet quads (d c =120 mm) are proposed to accommodate larger beam size. Impact: Higher  -functions in the triplet and adjacent arcs amplify the effects of triplet errors and sextupole aberrations causing reduction of dynamic aperture. New tolerances on triplet field quality need to be specified for an acceptable dynamic aperture in collision.

4. Beta Functions: Nominal LHC versus v.3.01 “4444” 4 Nominal LHC  * = 55/55 cm v.3.01 “4444”  * = 15/15 cm  max ~ 4.5km  max ~ 21.5km Dedicated  modulation in arcs 81,12,45,56 for IR chromaticity correction IP5IP1

5. Interaction Region: Nominal LHC versus v.3.01 “4444” 5 L*=23 m L FFS =268m TripletSeparation dipoles D1/2Matching section Q4/5/6 Proposed large aperture Nb-Ti superconducting triplet quadrupoles Q1,Q2,Q3 with coil diameter of d c = 120 mm. Nominal LHC  * = 55/55 cm v.3.01 “4444”  * = 15/15 cm  max ~ 4.5km  max ~ 21.5km

6. Achromatic Telescopic System (ATS) for Correction of IP Triplet Non-linear Chromaticity at Low  * 6 Peak beta functions in the IP triplets increase as  max ~ 1/  * and yield higher triplet chromaticity at low  * which requires stronger correcting sextupoles. A dedicated beta modulation is created in the arcs adjacent to IP1 and IP5 in order to raise beta functions at the sextupoles (  sext ~ 1/  *) and increase their effect thus avoiding exceeding their field limit. In addition, these sextupoles are arranged in -I pairs to minimize their geometric aberrations and have a proper phase advance relative to the triplets for a local correction of non-linear triplet chromaticity. IP1 Arc 81 Arc 12  arc ~ 700 m  *=15/15cm v.3.01 “4444”

7. Multipole Field Scaling in a SC Quadrupole 7 where n=1 is for a dipole, etc. B ref is main quad field at r 0 Note: the a n,b n coefficients are defined in 10 -4 units. The a n and b n values in the multipole field tables represent Gaussian sigmas used to generate random errors. Furthermore, they are split in two components: the“uncertainty” term (deviation from systematic) and the “random” term. Scaling with reference radius r 0 does not change the multipole field B x,y and does not affect dynamic aperture. Nominal r 0 = 17 mm → new triplet quad r 0 = 50 mm. Scaling with coil diameter d c in a SC quad (P. Ferracin, et al, Phys. Rev. ST Accel. Beams 3, 122403 (2000)). Nominal d c = 70 mm → new triplet quad d c = 120 mm. Scaling with peak beta function in triplet  max to keep the triplet resonance driving terms constant (SLHC Project Report 0038 by S. Fartoukh). Nominal  max = 4.5 km → new  max = 21.5 km in lattice v.3.01 “4444”.

8. Multipole Field Correctors in the Triplet 8 a3, b3, a4, b4, b6 correctors IP The correctors compensate the resonance driving terms. Due to correction, the a3, b3, a4, b4, b6 coefficients are expected to be more relaxed. On the other side of IP the x-y beta functions are exchanged due to anti-symmetry, hence the correctors sample both x and y large betas

9. Measured Multipoles for the Nominal Triplet Quadrupoles with d c =70 mm at r 0 =17 mm 9 skewuncertaintyrms normaluncertaintyrms a10.0000 b10.0000 a20.0000 b20.0000 a30.52350.6354b30.41350.7873 a40.44320.3883b40.15520.1563 a50.08740.1423b50.11420.2171 a60.23060.2637b60.20980.3088 a70.02540.0411b70.03110.0374 a80.01400.0280b80.00600.0096 a90.01270.0078b90.00850.0116 a100.00940.0179b100.03030.0086 a110.00460.0028b110.00840.0106

10. Multipole Table “Target3” Scaled from the Measured Table to r 0 =50 mm and d c =120 mm 10 skewuncertaintyrms normaluncertaintyrms a10.0000 b10.0000 a20.0000 b20.0000 a30.52390.6359b30.41390.7879 a40.76110.6667b40.26640.2683 a50.25740.4191b50.33650.6396 a61.16551.3328b61.06031.5608 a70.22030.3564b70.27010.3244 a80.20870.4162b80.08890.1423 a90.32380.2003b90.21650.2971 a100.41370.7838b101.32560.3755 a110.34570.2116b110.63400.7965 a120.1863 b120.1863 a130.1164 b130.23280.1164 a140.43660.1455b140.58210.1455 Expected values for multipoles n = 12,13,14 are added from table “ITD1_errortable_v2” (SLHC Project Report 0040)

11. SixTrack Tracking Set-Up 11 60 random seeds for final tracking, 20 seeds for intermediate multipole scan 30 particle pairs per aperture step (2  11 angles 100,000 turns 7 TeV beam energy assumed beam emittance (normalized) 3.75 um initial  p/p = 2.7e-4 tune = 62.31, 60.32 triplet multipole correction, arc errors and corrections are included arc errors are always included arc errors only is benchmarked against our CERN colleague’s simulation

12. Dynamic Aperture for Multipole Table “Target3” 12 The line shows average aperture for 60 seeds and the error bars show the spread between the minimum and maximum aperture for 11 angles DA min = 5.07  Aperture is too small

13. Multipole Table “Target31” Scaled from Table “Target3” to  max = 21.5 km 13 skewuncertaintyrms normaluncertaintyrms a10.00000 b10.00000 a20.00000 b20.00000 a30.050160.06089b30.039630.07545 a40.033340.02920b40.011670.01175 a50.005160.00840b50.006740.01281 a60.010690.01223b60.009720.01431 a70.000920.00150b70.001130.00137 a80.000420.00080b80.000150.00027 a90.000290.00019b90.000190.00024 a100.000180.00030b100.000540.00018 a110.00007 b110.00015 a120.000016 b120.000016 a130.000004 b130.0000090.000004 a140.0000080.000003b140.0000100.000003

14. Dynamic Aperture for Multipole Table “Target31” 14 DA min = 14.94  The aperture exceeds the target. The multipole coefficients can be relaxed somewhat.

15. Option-1: Individual Scan of a n Random Values 15 Each multipole coefficient is scanned individually between “target3” and “target31” values while other multipoles are at “target31” values. Note the a3, a4 do not affect aperture due to the triplet multipole correctors

16. Option-1: Individual Scan of a n Uncertainty Values 16

17. Option-1: Individual Scan of b n Random Values 17 The aperture is not sensitive to b3, b4 due to the triplet multipole correctors, but the b6 still has impact on the aperture.

18. Option-1: Individual Scan of b n Uncertainty Values 18

19. Option-1: Final Multipole Scaling for Target Aperture 19 All coefficients are set to correspond to the same value of dynamic aperture in the individual scans (aperture cut). After a few iterations of the aperture cut, the target aperture can be reached. In this case, it corresponds to the aperture cut of 14.8 , i.e. quite close to the “target31” table. target aperture “target31”

20. Final Multipole Table “Target39” in Option-1 at r 0 =50 mm 20 skewuncertaintyrms normaluncertaintyrms a10.00000 b10.00000 a20.00000 b20.00000 a30.287010.34839b30.226750.43166 a40.397220.34797b40.139050.14002 a50.131290.02945b50.090180.07111 a60.414580.02698b60.535010.38921 a70.110630.02557b70.010310.01215 a80.104520.00820b80.027660.00557 a90.158170.01044b90.009110.00844 a100.094350.00924b100.018720.00674 a110.077560.00700b110.008200.00998 a120.055410.00354b120.004560.00363 a130.036790.00442b130.003960.00268 a140.018920.00364b140.006110.00364 In addition to the described option-1 procedure, in this table we limited the least sensitive coefficients to be not larger than the mid-value between “target3” and “target31” tables in order to help relaxing the other more sensitive coefficients. In this case, the aperture cut is 14.7  

21. 21 Comparison of “Target3”, “Target31” and “Target39” Tables (Normalized to “Target3” Values) 21

22. Dynamic Aperture for Multipole Table “Target39” 22 DA min = 12.35 

23. “target31” target aperture Option-2: The Coefficients Are Scaled with the Same Factor 23 As a starting point (named “target31_p3” table), all coefficients are set to a mid-value between “target3” and “target31” tables. Then the coefficients are scaled together in 10 steps from “target31” to “target31_p3” table. The target aperture was obtained when the setting is about 1 step from “target31” table. The last digit in the legend shows the step number from “target31” table

24. Final Multipole Table “Target31_p3_1” in Option-2 at r 0 =50 mm 24 skewuncertaintyrms normaluncertaintyrms a10.00000 b10.00000 a20.00000 b20.00000 a30.073870.08962b30.058370.11113 a40.069690.06109b40.024370.02453 a50.008790.02891b50.023240.04414 a60.068360.07837b60.062260.09155 a70.011900.01923b70.014650.01740 a80.010680.02174b80.004580.00725 a90.016690.01001b90.010970.01526 a100.020860.03934b100.066760.01907 a110.017140.01043b110.032040.04023 a120.00931 b120.00931 a130.00582 b130.011640.00582 a140.021830.00728b140.029100.00728 Compared to option-1, the option-2 results in more relaxed high order multipoles, but tighter low order multipoles 

25. Comparison of “Target3”, “Target31” and “Target31_p3_1” Tables (Normalized to “Target3” Values) 25

26. Dynamic Aperture for Multipole Table “Target31_p3_1” 26 DA min = 11.75 

27. Comparison of Dynamic Aperture 27 option-1 option-2

28. 28 Momentum Collimation Betatron Collimation C. Bracco “Phase 1” “Final” system: Layout is 100% frozen! LHC Collimation System

29. Loss map of beam-1 at  *=1.5 m with horizontal halo, sheet beam. This is a statistical result of 1000 random seeds with 64*100 particles per seed. This calculation is to benchmark against similar calculation by R. Bruce at CERN (see next page). Beam Loss Map for LHC Collimation System 29

30. Original Loss Map Calculation by Roderik Bruce at CERN 30

31. Summary 31 Dynamic aperture has been studied as a function of multipole field errors in the proposed 120 mm aperture triplet quadrupoles for the LHC lattice v.3.01, collision option “4444”. As a starting point, the study used the measured field for the nominal triplet quads which was then re-scaled for the new reference radius, larger quad coil diameter and higher triplet peak beta function. The target minimum dynamic aperture of 12-13  has been reached by scanning the triplet multipole field coefficients. Two versions of the triplet field specification table have been obtained using two methods for the multipole field scan. These tables are fairly close to the prediction based on the analytical scaling of the nominal triplet table. Calculation of beam loss maps has been successfully benchmarked against a similar calculation at CERN for the nominal lattice.