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 284404.

Triplet corrector layout

Massimo Giovannozzi – CERN

Acknowledgements: R. De Maria, S. Fartoukh

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

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Beta

-fun

ction

s (m

) BetaX BetaY

Introduction - III• 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:

• 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.

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DA

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Angle (degrees)

injection optics beta*=3.5 mbeta*=2 m beta*=1.1 mbeta*=0.8 m beta*=3.5 m; triplet correctors ONbeta*=2 m; triplet correctors ON beta*=1.1 m; triplet correctors ONbeta*=0.8;triplet correctors ON

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.

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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.

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min

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Angle (degrees)

corr ON; MQX err at 100% corr OFF; MQX err at 100%corr ON; MQX err at 50% corr OFF; MQX err at 50%

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…

MQXD DX D1Mean Uncertainty Random Mean Uncertainty Random Mean Uncertainty Random

b3 0 0.712 0.712 0 1.000 0.400 -0.9 0.727 0.727b4 0 0.512 0.512 0 0.200 0.100 0 0.126 0.126b5 0 0.368 0.368 0 0.500 0.100 0 0.365 0.365b6 0 1.44 1.024 0 0.050 0.020 0 0.060 0.060a3 0 0.712 0.712 0 1.000 0.300 0 0.282 0.282a4 0 0.512 0.512 0 0.300 0.400 0 0.444 0.444a5 0 0.368 0.368 0 0.100 0.050 0 0.152 0.152a6 0 0.96 0.264 0 0.100 0.050 0 0.176 0.176

Strength specification of correctors - III•Main results:

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trib

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K3 L (T/m)

MCSX MCSSX

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K4 L (T/m2)

MCOX MCOSX

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K5 L (T/m3)

MCDX MCDSX

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K6 L (T/m4)

MCTX MCTSX

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.

• In summary (results are given in terms of unnormalised Kn L):DX D1 Bound DX Ratio Bound D1 Ratio Proposed Increase (%)

MCSX (T/m) 17 18 35 2.0 38 2.2 20 13MCSSX (T/m) 15 15 34 2.3 32 2.1 20 33

MCOX (T/m2) 812 816 1460 1.8 1500 1.8 900 10

MCOSX (T/m2) 573 580 1337 2.3 1333 2.3 700 21

MCDX (T/m3) 47188 47881 82444 1.7 88185 1.8 50000 4

MCDSX (T/m3) 31986 32247 75643 2.4 79250 2.5 35000 9

MCTX (T/m4) 2.E+07 2.E+07 3.E+07 1.8 3.E+07 1.8 2E+07 32

MCTSX (T/m4) 3.E+06 3.E+06 1.E+07 4.7 1.E+07 4.4 4E+06 32

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:• 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.

Thank you for your attention