The HiLumi LHC Design Study is included in the High Luminosity LHC project and is partly funded by the European Commission within the Framework Programme 7 Capacities Specific Programme, Grant Agreement Triplet corrector layout Massimo Giovannozzi – CERN Acknowledgements: R. De Maria, S. Fartoukh

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

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

Introduction - I Situation in nominal LHC: Situation in nominal LHC: Non-linear corrector package provides compensation for non-linear errors in the IR (triplets, D1, D2). 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. 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 strength situation for the nominal machine Overview of the optical conditions Overview of the optical conditions

Introduction - III Strategy to set the correctors’ strength (see S. Fartoukh, LHC Project Note 349): minimisation of driving terms. Strategy to set the correctors’ strength (see S. Fartoukh, LHC Project Note 349): minimisation of driving terms. Selection of the driving terms to be corrected: Selection of the driving terms to be corrected: b3: c(b3; 1, 2) and c(b3; 2, 1) b3: c(b3; 1, 2) and c(b3; 2, 1) a3: c(a3; 0, 3) and c(a3; 3, 0) a3: c(a3; 0, 3) and c(a3; 3, 0) b4: c(b4; 4, 0) and c(b4; 0, 4) b4: c(b4; 4, 0) and c(b4; 0, 4) a4: c(a4; 3, 1) and c(a4; 1, 3) a4: c(a4; 3, 1) and c(a4; 1, 3) b6: c(b6; 0, 6) and c(b6; 6, 0) 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: Other facts: From numerical simulations it is found that non-linear correctors should not be used above 1 m of beta*. From numerical simulations it is found that non-linear correctors should not be used above 1 m of beta*. About 2  difference depending on the use of the non-linear triplets’ correctors.

Introduction - IV Other facts: 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). 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. 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… To be noted that these correctors provide additional sources of tune spread…

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

New layout of correctors - I The proposed lattice for HL-LHC foresees a number of non-linear correctors: 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. 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. The D1 magnet is now superconducting. Almost no drift left between corrector package and D1. 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. Strategy to set the correctors’ strength similar to that for the nominal machine. Selection of the driving terms to be corrected: Selection of the driving terms to be corrected: a5: c(a5; 0, 5) and c(a5; 5, 0) a5: c(a5; 0, 5) and c(a5; 5, 0) b5: c(b5; 5, 0) and c(b5; 0, 5) b5: c(b5; 5, 0) and c(b5; 0, 5) a6: c(a6; 5, 1) and c(a6; 1, 5) a6: c(a6; 5, 1) and c(a6; 1, 5) Feed down effects are not included in the correction strategy.

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

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

Outline Introduction Introduction New layout of correctors New layout of correctors Impact of non-linear correctors on dynamic aperture Impact of non-linear correctors on dynamic aperture Strength specification of correctors Strength specification of correctors Summary and outlook 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. 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. Data from IR1/5, left and right side of IRs have been combined. Error tables used: Error tables used: Triplets: June 2012 table provided by WP3 (E. Todesco). 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. 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: Error tables used: To note the difference between b6 and a6… To note the difference between b6 and a6… MQXDDXD1 MeanUncertaintyRandomMeanUncertaintyRandomMeanUncertaintyRandom b b b b a a a a

Strength specification of correctors - III Main results: Main results: The impact of the difference between b6 and a6…

Strength specification of correctors - IV Additionally, the required strength can be estimated (upper bound) by taking the integrated strength of the errors from triplets and D1. Additionally, the required strength can be estimated (upper bound) by taking the integrated strength of the errors from triplets and D1. In summary (results are given in terms of unnormalised K n L): In summary (results are given in terms of unnormalised K n L): Estimates using DX or D1 error tables Upper bound for DX or D1 error tables Tentative proposal

Summary and outlook Comments on the proposed non-linear correction system in the triplets: Comments on the proposed non-linear correction system in the triplets: Globally (very) effective to improve the dynamic aperture. Globally (very) effective to improve the dynamic aperture. Proposed possible strength specification for each corrector. 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. Feed down effects to be reviewed? Maybe they should be included in the strategy to set the strength of the correctors.

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