Triplet corrector layout and strength specifications Riccardo De Maria, Stephane Fartoukh, Massimo Giovannozzi – CERN Acknowledgements: E. Todesco

Outline Introduction New layout of correctors Impact of non-linear correctors on dynamic aperture Strength specification of correctors Summary and outlook

Outline Introduction New layout of correctors Impact of non-linear correctors on dynamic aperture Strength specification of correctors Summary and outlook

Introduction - I Situation in nominal LHC: Non-linear corrector package provides compensation for non-linear errors in the IR (triplets, D1, D2). Location of the correctors changed between V6.4 and V6.5 to provide more favourable optical conditions.

Introduction - II Overview of the strength situation for the nominal machine Overview of the optical conditions

Introduction - III Strategy to set the nonlinear correctors’ strength (see S. Fartoukh, LHC Project Note 349): minimisation of driving terms. Selection of the driving terms to be corrected: b3: c(b3; 1, 2) and c(b3; 2, 1) a3: c(a3; 0, 3) and c(a3; 3, 0) b4: c(b4; 4, 0) and c(b4; 0, 4) a4: c(a4; 3, 1) and c(a4; 1, 3) b6: c(b6; 0, 6) and c(b6; 6, 0) The choice of the resonances is based on the proximity to the working point Feed down effects are not included in the correction strategy.

Introduction - IV Other facts: From numerical simulations it is found that non-linear correctors should not be used above 1 m of beta*. About 2 s difference depending on the use of the non-linear triplets’ correctors.

Introduction - IV Other facts: So far the non-linear correctors have not been used in operation due to difficulties with the temperature control (to be fixed during LS1). This year these correctors have been used for the first time during MDs in an attempt to correct the non-linear field errors in the IR. To be noted that these correctors provide additional sources of tune spread…

Outline Introduction New layout of correctors Impact of non-linear correctors on dynamic aperture Strength specification of correctors Summary and outlook

New layout of correctors - I The proposed lattice for HL-LHC foresees a number of non-linear correctors: In addition to those already installed in the LHC (i.e., b3, a3, b4, a4, b6) also b5, a5, and a6 are proposed. To note that: The D1 magnet is now superconducting. Almost no drift left between corrector package and D1.

New layout of correctors - II Strategy to set the correctors’ strength similar to that for the nominal machine. Selection of the driving terms to be corrected: a5: c(a5; 0, 5) and c(a5; 5, 0) b5: c(b5; 5, 0) and c(b5; 0, 5) a6: c(a6; 5, 1) and c(a6; 1, 5) Feed down effects are not included in the correction strategy.

New layout of correctors - III The HL-LHC layout foresee three types of h/v orbit correctors around the triplet: MCBX1 and MCBX2 on the left/right of Q2a/Q2b MCBX3, roughly double of MCBX1/2 in the corrector package MCBRD, 2-in1 in the non-ip side of D2 even stronger than MCBX3.

New layout of correctors - VI The triplet dipole correctors are used to: Contribute to the crossing and separation scheme, Compensate mechanical misalignments of the triplets. For the HL-LHC: The crossing angle and bumps are x2 larger than nominal The crab cavities impose that the crossing and separation bumps are closed in D2 implying correction of Beam1 and Beam 2 not independent and correctors with shorter lever arm. As results one needs stronger dipole correctors.

Outline Introduction New layout of correctors Impact of non-linear correctors on dynamic aperture Strength specification of correctors Summary and outlook

Impact of non-linear correctors on DA Clear positive impact on DA. No systematic check corrector by corrector.

Outline Introduction New layout of correctors Impact of non-linear correctors on dynamic aperture Strength specification of correctors Summary and outlook

Strength specification of correctors - I Checked the distribution of strengths for the usual 60 realisations of the multipole errors in triplets and D1. Data from IR1/5, left and right side of IRs have been combined. Error tables used: Triplets: June 2012 table provided by WP3 (E. Todesco). D1: November 2012 table provided by WP3 (E. Todesco). A cross-check with a table based on improved DX magnet (S. Fartoukh) has been made too.

Strength specification of correctors - II Error tables used: To note the difference between b6 and a6… Combinations used: MQXD + D1 MQXF + D1 D1 only MQXD MQXF DX D1 Mean Unc. Random b3 0.712 0.820 1.000 0.400 -0.9 0.727 b4 0.512 0.570 0.200 0.100 0.126 b5 0.368 0.420 0.500 0.365 b6 1.440 1.024 0.8 1.100 0.050 0.020 0.060 a2 0.000 20.000 0.679 a3 0.800 0.300 0.282 a4 0.650 0.444 a5 0.430 0.152 a6 0.960 0.264 0.310 0.176 To note the difference between b6 and a6 for the IT To test sensitivity to IT FQ table To test sensitivity to D1 FQ table

Strength specification of correctors - III MQXD+D1 MQXD+D1 Main results: MQXF+D1 MQXF+D1

Strength specification of correctors - IV MQXD+D1 MQXD+D1 Main results: The impact of the difference between b6 and a6… MQXF+D1 MQXF+D1 The impact of the difference between b6 and a6…

Strength specification of correctors - V MQXF+D1 MQXF+D1 D1 D1

Strength specification of correctors - VI MQXF+D1 MQXF+D1 Main results: The impact of the difference between b6 and a6… D1 D1

Strength specification of correctors - VII Main results: MQXF+D1 20 units of random a2 are added to MQXF error table (corresponding to up to 3 mrad of roll angle)

Strength specification of correctors - VII Summary of strengths: Contribution of D1 FQ to correctors strength: Sextupole, decapole: a factor of 3-4 smaller than IT contribution (not considering the final safety margin). Other components: negligible.

Strength specification of orbit correctors Orbit corrector strengths depend linearly with the crossing angle and parallel separation, but in a not obvious way on the optics configurations:

Strength specification of orbit correctors For misalignment errors (assuming uncorrelated +-0.5mm) there is a trade off between controlling the closed orbit and the maximum strength of correctors:

Strength specification of orbit correctors Summary of dipole correctors: MCBX1/2 [Tm] MCBX3 MCBRD Squeezed (15cm beta*, 590murad) 0.15 2.1 4.5 Only +-0.5mm of misalignments 1.3 2.5 1.0 Squeezed and +-0.5mm of misalignments 1.5 4.6 5.5 Non crossing plane and misalignments 3 Tunable range 1.6 3.1 5.2 Tunable range and misalignments 5.6 6.2 Extended tunable range 4 7.5 Extended tunable range and misalignments 10 8.5

Summary and outlook Comments on the proposed non-linear correction system in the triplets: Globally (very) effective to improve the dynamic aperture. Proposed possible strength specification for each corrector. Feed down effects to be reviewed? Maybe they should be included in the strategy to set the strength of the correctors. Comments for the dipole correctors: Can we make the correction scheme more efficient or rely more on mechanical re-alignments? Which optics flexibility do we need to support?

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