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Amplitude Detuning from misaligned Triplets and IR multipolar Correctors Joschua Dilly Humboldt Universit at zu Berlin, CERN 18.02.2020 Outline Setup Motivation Misaligning Correctors Misaligning Triplets

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SLIDE 1

Amplitude Detuning from misaligned Triplets and IR multipolar Correctors

Joschua Dilly Humboldt Universit¨ at zu Berlin, CERN 18.02.2020

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SLIDE 2

Outline

  • Setup

– Motivation – Misaligning Correctors – Misaligning Triplets – Simulation and Measurement details

  • Results

– Corrector Misalignments – Triplet Misalignments – Conclusion

18.02.20 Joschua Dilly Amp.Det. from Misalignments 1

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SLIDE 3

Outline

  • Setup

– Motivation – Misaligning Correctors – Misaligning Triplets – Simulation and Measurement details

  • Results

– Corrector Misalignments – Triplet Misalignments – Conclusion

18.02.20 Joschua Dilly Amp.Det. from Misalignments 1

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Motivation

With the advent of the HL-LHC, new triplets with larger aperture and new corrector packages1, for corrections of high-order non-linear magnetic field errors, will be installed in the low β Interaction Points (IP1 & IP5), which will require precise orbit control. The goal of this study is, to investigate the influence of the expected remaining orbit deviations2 in the triplets and the associated non-linear corrector packages on Amplitude Detuning. A preliminary study showed large detuning, which turned out to be a bug, but triggered this more extensive study.

  • 1O. Br¨

uning et al - LHC Report 504: Dynamic aperture studies for the LHC separation dipoles, 2004. https://cds.cern.ch/record/742967

  • 2D. Gamba et al - IP ORBIT CORRECTION UPDATE FOR HL-LHC, IPAC, 2018.

http://cds.cern.ch/record/2648556

18.02.20 Joschua Dilly Amp.Det. from Misalignments 2

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SLIDE 5

Misaligning Correctors

LHC HL-LHC

Figure: Schematic representation of half of the IR region in the accelerator. setup LHC/HL-LHC Sequence 60 WISE error realizations: octupole, (skew-)decapole and

(skew-)dodecapole to MQX and MBX

calculate triplet corrections for the MCX 50 misalignment realizations for MCX, uniformly

distributed ∈ [−1 mm, 1 mm] ⇒ check Amplitude Detuning

18.02.20 Joschua Dilly Amp.Det. from Misalignments 3

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Misaligning Correctors

LHC HL-LHC

Figure: Schematic representation of half of the IR region in the accelerator. setup LHC/HL-LHC Sequence 60 WISE error realizations: octupole, (skew-)decapole and

(skew-)dodecapole to MQX and MBX

calculate triplet corrections for the MCX 50 misalignment realizations for MCX, uniformly

distributed ∈ [−1 mm, 1 mm] ⇒ check Amplitude Detuning

18.02.20 Joschua Dilly Amp.Det. from Misalignments 3

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SLIDE 7

Misaligning Triplets

LHC HL-LHC

Figure: Schematic representation of half of the IR region in the accelerator. setup LHC/HL-LHC Sequence 60 WISE error realizations: octupole, (skew-)decapole and

(skew-)dodecapole MQX and MBX

calculate triplet corrections for the MCX 50 misalignment realizations for Q1-Q3,

truncated-gaussian distributed σ = 0.4 mm (0.8 mm Q3), cut at 2.5 σ ⇒ check Amplitude Detuning

18.02.20 Joschua Dilly Amp.Det. from Misalignments 4

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SLIDE 8

Misaligning Triplets

LHC HL-LHC

Figure: Schematic representation of half of the IR region in the accelerator. setup LHC/HL-LHC Sequence 60 WISE error realizations: octupole, (skew-)decapole and

(skew-)dodecapole MQX and MBX

calculate triplet corrections for the MCX 50 misalignment realizations for Q1-Q3,

truncated-gaussian distributed σ = 0.4 mm (0.8 mm Q3), cut at 2.5 σ ⇒ check Amplitude Detuning

18.02.20 Joschua Dilly Amp.Det. from Misalignments 4

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SLIDE 9

Setup

Simulation Measurements1 LHC HL-LHC (v1.3) LHC Energy 6.5 TeV 7.0 TeV 6.5 TeV β∗ 30 cm round optics Orbit flat orbit Qx, Qy 0.31, 0.32 MO Power

  • ff (see later)
  • ff

b4 corrected yes

1in MD3311 http://cds.cern.ch/record/2692810

18.02.20 Joschua Dilly Amp.Det. from Misalignments 5

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Calculate Detuning

Feeddown: K5 → K4 = dx · K5 K5S → K4 = −dy · K5S K6 → K4 = 1 2

  • dx2 − dy2

· K6 K6S → K4 = −dx · dy · K6S Detuning: ∂Qx ∂2Jx = K4 32π β2

x

∂Qx ∂2Jy = − K4 16π βxβy ∂Qy ∂2Jy = K4 32π β2

y

Kn(S): Integrated (skew) magnetic field strength, with n = 4 ⇒ octupole etc. dx, dy: Beam offset from element center Jx,y: Action

18.02.20 Joschua Dilly Amp.Det. from Misalignments 6

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Outline

  • Setup

– Motivation – Misaligning Correctors – Misaligning Triplets – Simulation and Measurement details

  • Results

– Corrector Misalignments – Triplet Misalignments – Conclusion

18.02.20 Joschua Dilly Amp.Det. from Misalignments 6

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Subsection 1 Corrector Misalignments

18.02.20 Joschua Dilly Amp.Det. from Misalignments 6

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Misalign LHC Correctors

2 4 6 8 ∂Qx/∂2Jx

  • 103m−1

50 100 Samples

Sim.: (6.9 ± 0.5) ·103m−1 −σ +σ Meas.: (0.8 ± 0.5) ·103m−1

Simulation before misalignments Fit Gauss measured

3 1

Shown: result for Beam 1 direct horizontal term Simulation ”offset” from zero due to amplitude detuning

from arc-sextupoles

Gaussian detuning distribution (from uniform misalignments)

⇒ compare for both beams and all detuning components

18.02.20 Joschua Dilly Amp.Det. from Misalignments 7

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Misalign LHC Correctors

Qx/ (2Jx) Qy/ (2Jy) Qx/ (2Jy) 15 10 5 5 10 Detuning [103 m

1]

B1 before misalignment B1 misaligned B1 measured B2 before misalignment B2 misaligned B2 measured

amplitude detuning spread from misalignments is small

compared to expected detuning without misaligments

also smaller or of similar order as measured amplitude

detuning

contribution only from feeddown from b6 as, this is the only

corrector

18.02.20 Joschua Dilly Amp.Det. from Misalignments 8

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Misalign HL-LHC Correctors

∂Qx/∂(2Jx) ∂Qy/∂(2Jy) ∂Qx/∂(2Jy) −15 −10 −5 5 10 Detuning [103 m−1] B1 before misalignment B1 misaligned B1 measured B2 before misalignment B2 misaligned B2 measured

amplitude detuning spread from misalignments is small

compared to expected detuning without misalignments

also smaller or of similar order as measured amplitude

detuning

contribution from feeddown from b5, a5, b6, and a6 (see

appendix)

18.02.20 Joschua Dilly Amp.Det. from Misalignments 9

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Subsection 2 Triplet Misalignments

18.02.20 Joschua Dilly Amp.Det. from Misalignments 9

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Misalign LHC Triplets

Qx/ (2Jx) Qy/ (2Jy) Qx/ (2Jy) 15 10 5 5 10 Detuning [103 m

1]

B1 before misalignment B1 misaligned B1 measured B2 before misalignment B2 misaligned B2 measured

amplitude detuning spread from misalignments is of equal

  • rder compared to expected detuning without

misalignments, but not problematic

large spread compared to HL-LHC; reasons under

investigation (possibly: cancellation due to shorter magnets / independent misalignments, differences in error-tables)

18.02.20 Joschua Dilly Amp.Det. from Misalignments 10

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Misalign HL-LHC Triplets

Qx/ (2Jx) Qy/ (2Jy) Qx/ (2Jy) 15 10 5 5 10 Detuning [103 m

1]

B1 before misalignment B1 misaligned B1 measured B2 before misalignment B2 misaligned B2 measured

amplitude detuning spread from misalignments is small

compared to expected detuning without misalignments

also spread smaller or of similar order as measured amplitude

detuning

18.02.20 Joschua Dilly Amp.Det. from Misalignments 11

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Misalign Triplets

... and compare to powered MO’s

LHC

Qx/ (2Jx) Qy/ (2Jy) Qx/ (2Jy) 50 50 100 Detuning [103 m

1]

B1 before misalignment B1 misaligned B1 Sim. w/ MO 300 A B2 before misalignment B2 misaligned B2 Sim. w/ MO 300 A

HL-LHC

Qx/ (2Jx) Qy/ (2Jy) Qx/ (2Jy) 50 50 100 Detuning [103 m

1]

B1 before misalignment B1 misaligned B1 Sim. w/ MO 300 A B2 before misalignment B2 misaligned B2 Sim. w/ MO 300 A

MO powering of

300 A causes amplitude detuning to increase from ∼ 5 · 103m−1 up to ∼ 100 · 103m−1 in the direct terms.

18.02.20 Joschua Dilly Amp.Det. from Misalignments 12

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Conclusion

Expected amplitude detuning spread is larger from

investigated triplet misalignment than from corrector misalignments in the LHC.

Expected amplitude detuning spread is marginally larger

from investigated corrector misalignments than from triplet misalignments in the HL-LHC.

The investigated misalignments, with spreads of ± 1 mm in

the MCX and ± 0.4 mm(0.8 mm) in the MQX do not cause problematic amplitude detuning in either machine.

Amplitude detuning is negligible when comparing to

expected detuning from MO powering.

Expected detuning from triplet-misalignments is smaller for

HL-LHC than for LHC for the same β∗ = 30 cm.

18.02.20 Joschua Dilly Amp.Det. from Misalignments 13

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Thank you for your attention!

18.02.20 Joschua Dilly Amp.Det. from Misalignments 14

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Outline

  • Setup

– Motivation – Misaligning Correctors – Misaligning Triplets – Simulation and Measurement details

  • Results

– Corrector Misalignments – Triplet Misalignments – Conclusion

18.02.20 Joschua Dilly Amp.Det. from Misalignments 14

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  • Amp. Det. References

Table: Reference Values Summary

[103 m−1] MD3311 w/ Errors MO-Powering 0 A 300 A 570 A 0 A w/o Sextupoles Beam 1 ∂Qx /∂2Jx LHC 0.8 ± 0.5 6.9 ± 0.0 6.6 95.2 174.8 0.1 HL-LHC – 5.4 ± 0.4 5.3 103.0 191.0 0.2 ∂Qy /∂2Jy LHC 8 ± 28 4.8 ± 0.0 4. 91.7 170.2 0.1 HL-LHC – 4.5 ± 0.4 4.6 102.7 191.0 0.2 ∂Qx /∂2Jy LHC

  • 3 ± 1
  • 8.7 ± 0.1
  • 7.9
  • 67.9
  • 121.8

0.0 HL-LHC –

  • 12 ± 2.5
  • 12.4
  • 73.2
  • 127.9

0.1 Beam 2 ∂Qx /∂2Jx LHC

  • 7.5 ± 0.5

2.1 ± 0.0 1.9 88.8 166.9 0.1 HL-LHC – 4.1 ± 0.4 4.2 102.2 190.4 0.2 ∂Qy /∂2Jy LHC

  • 2 ± 1

3.2 ± 0.0 3.0 91.8 171.8 0.1 HL-LHC – 5.9 ± 0.4 5.9 103.7 191.8 0.2 ∂Qx /∂2Jy LHC 6 ± 1

  • 11.6 ± 0.1
  • 12.5
  • 72.4
  • 126.3

0.0 HL-LHC –

  • 13.3 ± 2.2
  • 13.7
  • 74.6
  • 129.4

0.1

18.02.20 Joschua Dilly Amp.Det. from Misalignments 15

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Corrector Misalignment Feeddown

Table: Corrector misalignment summary - feeddown from field components to first order amplitude detuning [103 m−1] Sum Decapole Skew Decapole Dodecapole Skew Dodecapole Beam 1 ∂Qx /∂2Jx LHC 0.00 ± 0.53 – – 0.00 ± 0.53 – HL-LHC 0.01 ± 0.69 0.00 ± 0.43 0.01 ± 0.55 0.00 ± 0.05 0.00 ± 0.02 ∂Qy /∂2Jy LHC 0.00 ± 0.52 – – 0.00 ± 0.52 – HL-LHC 0.00 ± 0.70 0.00 ± 0.48 0.00 ± 0.52 0.00 ± 0.05 0.00 ± 0.02 ∂Qx /∂2Jy LHC 0.00 ± 0.68 – – 0.00 ± 0.68 – HL-LHC

  • 0.01 ± 0.77

0.00 ± 0.51 0.00 ± 0.59 0.00 ± 0.05 0.00 ± 0.02 Beam 2 ∂Qx /∂2Jx LHC 0.00 ± 0.52 – – 0.00 ± 0.52 – HL-LHC 0.00 ± 0.70 0.00 ± 0.48 0.00 ± 0.52 0.00 ± 0.05 0.00 ± 0.02 ∂Qy /∂2Jy LHC 0.00 ± 0.53 – – 0.00 ± 0.53 – HL-LHC

  • 0.01 ± 0.69

0.00 ± 0.43

  • 0.01 ± 0.55

0.00 ± 0.05 0.00 ± 0.02 ∂Qx /∂2Jy LHC 0.00 ± 0.68 – – 0.00 ± 0.68 – HL-LHC 0.01 ± 0.77 0.00 ± 0.51 0.01 ± 0.59 0.00 ± 0.05 0.00 ± 0.02

18.02.20 Joschua Dilly Amp.Det. from Misalignments 16

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Misalign LHC Correctors

−15 −10 −5 5 10 ∂Qx/∂2Jx

  • 103m−1

50 100 Samples

Sim.: (6.9 ± 0.5) ·103m−1 −σ +σ Meas.: (0.8 ± 0.5) ·103m−1

Simulation before misalignments Fit Gauss measured −15 −10 −5 5 10 ∂Qy/∂2Jy

  • 103m−1

50 100 Samples

Sim.: (4.8 ± 0.5) ·103m−1 −σ +σ Meas.: (-3.0 ± 1.0) ·103m−1

−15 −10 −5 5 10 ∂Qx/∂2Jy

  • 103m−1

50 100 Samples

Sim.: (-8.7 ± 0.7) ·103m−1 −σ +σ Meas.: (8.0 ± 28.0) ·103m−1

Figure: Beam 1

−15 −10 −5 5 10 ∂Qx/∂2Jx

  • 103m−1

50 100 Samples

Sim.: (2.1 ± 0.5) ·103m−1 −σ +σ Meas.: (-7.5 ± 0.5) ·103m−1

Simulation before misalignments Fit Gauss measured −15 −10 −5 5 10 ∂Qy/∂2Jy

  • 103m−1

50 100 Samples

Sim.: (3.2 ± 0.5) ·103m−1 −σ +σ Meas.: (6.0 ± 1.0) ·103m−1

−15 −10 −5 5 10 ∂Qx/∂2Jy

  • 103m−1

50 100 Samples

Sim.: (-11.6 ± 0.7) ·103m−1 −σ +σ Meas.: (-2.0 ± 1.0) ·103m−1

Figure: Beam 2

18.02.20 Joschua Dilly Amp.Det. from Misalignments 17

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Misalign LHC Correctors

−2 −1 1 2 ∂Qx/∂2Jx

  • 103m−1

50 100 Samples

Sum: (0.00 ± 0.53) ·103m−1 K6L: (0.00 ± 0.53) ·103m−1

Sum K6L −2 −1 1 2 ∂Qy/∂2Jy

  • 103m−1

50 100 Samples

Sum: (-0.00 ± 0.52) ·103m−1 K6L: (-0.00 ± 0.52) ·103m−1

−2 −1 1 2 ∂Qx/∂2Jy

  • 103m−1

50 100 Samples

Sum: (-0.00 ± 0.68) ·103m−1 K6L: (-0.00 ± 0.68) ·103m−1

Figure: Beam 1

−2 −1 1 2 ∂Qx/∂2Jx

  • 103m−1

50 100 Samples

Sum: (0.00 ± 0.52) ·103m−1 K6L: (0.00 ± 0.52) ·103m−1

Sum K6L −2 −1 1 2 ∂Qy/∂2Jy

  • 103m−1

50 100 Samples

Sum: (-0.00 ± 0.53) ·103m−1 K6L: (-0.00 ± 0.53) ·103m−1

−2 −1 1 2 ∂Qx/∂2Jy

  • 103m−1

50 100 Samples

Sum: (0.00 ± 0.68) ·103m−1 K6L: (0.00 ± 0.68) ·103m−1

Figure: Beam 2

18.02.20 Joschua Dilly Amp.Det. from Misalignments 18

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SLIDE 27

Misalign HL-LHC Correctors

−15 −10 −5 5 10 ∂Qx/∂2Jx

  • 103m−1

100 Samples

Sim.: (5.4 ± 0.7) ·103m−1 −σ +σ Meas.: (0.8 ± 0.5) ·103m−1

Simulation before misalignments Fit Gauss measured −15 −10 −5 5 10 ∂Qy/∂2Jy

  • 103m−1

100 Samples

Sim.: (4.5 ± 0.7) ·103m−1 −σ +σ Meas.: (-3.0 ± 1.0) ·103m−1

−15 −10 −5 5 10 ∂Qx/∂2Jy

  • 103m−1

100 Samples

Sim.: (-12.1 ± 0.8) ·103m−1 −σ +σ Meas.: (8.0 ± 28.0) ·103m−1

Figure: Beam 1

−15 −10 −5 5 10 ∂Qx/∂2Jx

  • 103m−1

100 Samples

Sim.: (4.1 ± 0.7) ·103m−1 −σ +σ Meas.: (-7.5 ± 0.5) ·103m−1

Simulation before misalignments Fit Gauss measured −15 −10 −5 5 10 ∂Qy/∂2Jy

  • 103m−1

100 Samples

Sim.: (5.9 ± 0.7) ·103m−1 −σ +σ Meas.: (6.0 ± 1.0) ·103m−1

−15 −10 −5 5 10 ∂Qx/∂2Jy

  • 103m−1

100 Samples

Sim.: (-13.2 ± 0.8) ·103m−1 −σ +σ Meas.: (-2.0 ± 1.0) ·103m−1

Figure: Beam 2

18.02.20 Joschua Dilly Amp.Det. from Misalignments 19

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SLIDE 28

Misalign HL-LHC Correctors

−3 −2 −1 1 2 3 ∂Qx/∂2Jx

  • 103m−1

1000 2000 Samples

Sum: (0.01 ± 0.69) ·103m−1 K5L: (-0.00 ± 0.43) ·103m−1 K5SL: (0.01 ± 0.55) ·103m−1 K6L: (-0.00 ± 0.05) ·103m−1 K6SL: (-0.00 ± 0.02) ·103m−1

Sum K5L K5SL K6L K6SL −3 −2 −1 1 2 3 ∂Qy/∂2Jy

  • 103m−1

1000 2000 Samples

Sum: (0.00 ± 0.70) ·103m−1 K5L: (0.00 ± 0.48) ·103m−1 K5SL: (0.00 ± 0.52) ·103m−1 K6L: (0.00 ± 0.05) ·103m−1 K6SL: (-0.00 ± 0.02) ·103m−1

−3 −2 −1 1 2 3 ∂Qx/∂2Jy

  • 103m−1

1000 2000 Samples

Sum: (-0.01 ± 0.77) ·103m−1 K5L: (0.00 ± 0.51) ·103m−1 K5SL: (-0.01 ± 0.59) ·103m−1 K6L: (-0.00 ± 0.05) ·103m−1 K6SL: (0.00 ± 0.02) ·103m−1

Figure: Beam 1

−3 −2 −1 1 2 3 ∂Qx/∂2Jx

  • 103m−1

1000 2000 Samples

Sum: (-0.00 ± 0.70) ·103m−1 K5L: (-0.00 ± 0.48) ·103m−1 K5SL: (-0.00 ± 0.52) ·103m−1 K6L: (-0.00 ± 0.05) ·103m−1 K6SL: (0.00 ± 0.02) ·103m−1

Sum K5L K5SL K6L K6SL −3 −2 −1 1 2 3 ∂Qy/∂2Jy

  • 103m−1

1000 2000 Samples

Sum: (-0.01 ± 0.69) ·103m−1 K5L: (0.00 ± 0.43) ·103m−1 K5SL: (-0.01 ± 0.55) ·103m−1 K6L: (0.00 ± 0.05) ·103m−1 K6SL: (0.00 ± 0.02) ·103m−1

−3 −2 −1 1 2 3 ∂Qx/∂2Jy

  • 103m−1

1000 2000 Samples

Sum: (0.01 ± 0.77) ·103m−1 K5L: (-0.00 ± 0.51) ·103m−1 K5SL: (0.01 ± 0.59) ·103m−1 K6L: (0.00 ± 0.05) ·103m−1 K6SL: (-0.00 ± 0.02) ·103m−1

Figure: Beam 2

18.02.20 Joschua Dilly Amp.Det. from Misalignments 20

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SLIDE 29

Triplet Misalignment Feeddown

Table: Triplet misalignment summary - feeddown from field components to first order amplitude detuning [103 m−1] Sum Decapole Skew Decapole Dodecapole Skew Dodecapole Beam 1 ∂Qx /∂2Jx LHC 0.03 ± 2.90 0.00 ± 2.59 0.03 ± 1.02 0.00 ± 0.68 0.00 ± 0.47 HL-LHC

  • 0.01 ± 0.62

0.00 ± 0.42

  • 0.01 ± 0.44

0.00 ± 0.07 0.00 ± 0.03 ∂Qy /∂2Jy LHC

  • 0.05 ± 3.07
  • 0.03 ± 1.44
  • 0.03 ± 2.61

0.00 ± 0.74 0.00 ± 0.15 HL-LHC 0.00 ± 0.61 0.00 ± 0.42

  • 0.01 ± 0.44

0.00 ± 0.07 0.00 ± 0.02 ∂Qx /∂2Jy LHC 0.02 ± 3.06 0.03 ± 2.25 0.00 ± 1.78 0.00 ± 1.04 0.00 ± 0.38 HL-LHC 0.00 ± 0.73 0.00 ± 0.50 0.01 ± 0.51 0.00 ± 0.09 0.00 ± 0.03 Beam 2 ∂Qx /∂2Jx LHC

  • 0.05 ± 3.07
  • 0.03 ± 1.44
  • 0.03 ± 2.60

0.00 ± 0.74 0.00 ± 0.15 HL-LHC 0.00 ± 0.61 0.00 ± 0.42

  • 0.01 ± 0.44

0.00 ± 0.07 0.00 ± 0.02 ∂Qy /∂2Jy LHC 0.03 ± 2.91 0.00 ± 2.59 0.03 ± 1.02 0.00 ± 0.68 0.00 ± 0.47 HL-LHC

  • 0.01 ± 0.62

0.00 ± 0.42

  • 0.01 ± 0.44

0.00 ± 0.07 0.00 ± 0.03 ∂Qx /∂2Jy LHC 0.02 ± 3.06 0.03 ± 2.25 0.00 ± 1.78 0.00 ± 1.04 0.00 ± 0.38 HL-LHC 0.00 ± 0.73 0.00 ± 0.50 0.01 ± 0.51 0.00 ± 0.09 0.00 ± 0.03

18.02.20 Joschua Dilly Amp.Det. from Misalignments 21

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SLIDE 30

Misalign LHC Triplets

−15 −10 −5 5 10 ∂Qx/∂2Jx

  • 103m−1

50 100 Samples

Sim.: (6.9 ± 2.9) ·103m−1 −σ +σ Meas.: (0.8 ± 0.5) ·103m−1

Simulation before misalignments Fit Gauss measured −15 −10 −5 5 10 ∂Qy/∂2Jy

  • 103m−1

50 100 Samples

Sim.: (4.7 ± 3.1) ·103m−1 −σ +σ Meas.: (-3.0 ± 1.0) ·103m−1

−15 −10 −5 5 10 ∂Qx/∂2Jy

  • 103m−1

50 100 Samples

Sim.: (-8.6 ± 3.1) ·103m−1 −σ +σ Meas.: (8.0 ± 28.0) ·103m−1

Figure: Beam 1

−15 −10 −5 5 10 ∂Qx/∂2Jx

  • 103m−1

50 100 Samples

Sim.: (2.1 ± 3.1) ·103m−1 −σ +σ Meas.: (-7.5 ± 0.5) ·103m−1

Simulation before misalignments Fit Gauss measured −15 −10 −5 5 10 ∂Qy/∂2Jy

  • 103m−1

50 100 Samples

Sim.: (3.2 ± 2.9) ·103m−1 −σ +σ Meas.: (6.0 ± 1.0) ·103m−1

−15 −10 −5 5 10 ∂Qx/∂2Jy

  • 103m−1

50 100 Samples

Sim.: (-11.6 ± 3.1) ·103m−1 −σ +σ Meas.: (-2.0 ± 1.0) ·103m−1

Figure: Beam 2

18.02.20 Joschua Dilly Amp.Det. from Misalignments 22

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SLIDE 31

Misalign LHC Triplets

−10 −5 5 10 ∂Qx/∂2Jx

  • 103m−1

1000 2000 Samples

Sum: (0.03 ± 2.90) ·103m−1 K5L: (-0.00 ± 2.59) ·103m−1 K5SL: (0.03 ± 1.02) ·103m−1 K6L: (-0.00 ± 0.68) ·103m−1 K6SL: (0.00 ± 0.47) ·103m−1

Sum K5L K5SL K6L K6SL −10 −5 5 10 ∂Qy/∂2Jy

  • 103m−1

1000 2000 Samples

Sum: (-0.05 ± 3.07) ·103m−1 K5L: (-0.03 ± 1.44) ·103m−1 K5SL: (-0.03 ± 2.61) ·103m−1 K6L: (0.00 ± 0.74) ·103m−1 K6SL: (0.00 ± 0.15) ·103m−1

−10 −5 5 10 ∂Qx/∂2Jy

  • 103m−1

1000 2000 Samples

Sum: (0.02 ± 3.06) ·103m−1 K5L: (0.03 ± 2.25) ·103m−1 K5SL: (-0.00 ± 1.78) ·103m−1 K6L: (0.00 ± 1.04) ·103m−1 K6SL: (-0.00 ± 0.38) ·103m−1

Figure: Beam 1

−10 −5 5 10 ∂Qx/∂2Jx

  • 103m−1

1000 2000 Samples

Sum: (-0.05 ± 3.07) ·103m−1 K5L: (-0.03 ± 1.44) ·103m−1 K5SL: (-0.03 ± 2.60) ·103m−1 K6L: (0.00 ± 0.74) ·103m−1 K6SL: (0.00 ± 0.15) ·103m−1

Sum K5L K5SL K6L K6SL −10 −5 5 10 ∂Qy/∂2Jy

  • 103m−1

1000 2000 Samples

Sum: (0.03 ± 2.91) ·103m−1 K5L: (-0.00 ± 2.59) ·103m−1 K5SL: (0.03 ± 1.02) ·103m−1 K6L: (-0.00 ± 0.68) ·103m−1 K6SL: (0.00 ± 0.47) ·103m−1

−10 −5 5 10 ∂Qx/∂2Jy

  • 103m−1

1000 2000 Samples

Sum: (0.02 ± 3.06) ·103m−1 K5L: (0.03 ± 2.25) ·103m−1 K5SL: (-0.00 ± 1.78) ·103m−1 K6L: (0.00 ± 1.04) ·103m−1 K6SL: (-0.00 ± 0.38) ·103m−1

Figure: Beam 2

18.02.20 Joschua Dilly Amp.Det. from Misalignments 23

slide-32
SLIDE 32

Misalign HL-LHC Triplets

−15 −10 −5 5 10 ∂Qx/∂2Jx

  • 103m−1

50 100 Samples

Sim.: (5.4 ± 0.6) ·103m−1 −σ +σ Meas.: (0.8 ± 0.5) ·103m−1

Simulation before misalignments Fit Gauss measured −15 −10 −5 5 10 ∂Qy/∂2Jy

  • 103m−1

50 100 Samples

Sim.: (4.5 ± 0.6) ·103m−1 −σ +σ Meas.: (-3.0 ± 1.0) ·103m−1

−15 −10 −5 5 10 ∂Qx/∂2Jy

  • 103m−1

50 100 Samples

Sim.: (-12.1 ± 0.7) ·103m−1 −σ +σ Meas.: (8.0 ± 28.0) ·103m−1

Figure: Beam 1

−15 −10 −5 5 10 ∂Qx/∂2Jx

  • 103m−1

50 100 Samples

Sim.: (4.1 ± 0.6) ·103m−1 −σ +σ Meas.: (-7.5 ± 0.5) ·103m−1

Simulation before misalignments Fit Gauss measured −15 −10 −5 5 10 ∂Qy/∂2Jy

  • 103m−1

50 100 Samples

Sim.: (5.9 ± 0.6) ·103m−1 −σ +σ Meas.: (6.0 ± 1.0) ·103m−1

−15 −10 −5 5 10 ∂Qx/∂2Jy

  • 103m−1

50 100 Samples

Sim.: (-13.2 ± 0.7) ·103m−1 −σ +σ Meas.: (-2.0 ± 1.0) ·103m−1

Figure: Beam 2

18.02.20 Joschua Dilly Amp.Det. from Misalignments 24

slide-33
SLIDE 33

Misalign HL-LHC Triplets

−2 −1 1 2 ∂Qx/∂2Jx

  • 103m−1

1000 2000 Samples

Sum: (-0.01 ± 0.62) ·103m−1 K5L: (0.00 ± 0.42) ·103m−1 K5SL: (-0.01 ± 0.44) ·103m−1 K6L: (-0.00 ± 0.07) ·103m−1 K6SL: (-0.00 ± 0.03) ·103m−1

Sum K5L K5SL K6L K6SL −2 −1 1 2 ∂Qy/∂2Jy

  • 103m−1

1000 2000 Samples

Sum: (-0.00 ± 0.61) ·103m−1 K5L: (0.00 ± 0.42) ·103m−1 K5SL: (-0.01 ± 0.44) ·103m−1 K6L: (0.00 ± 0.07) ·103m−1 K6SL: (0.00 ± 0.02) ·103m−1

−2 −1 1 2 ∂Qx/∂2Jy

  • 103m−1

1000 2000 Samples

Sum: (0.00 ± 0.73) ·103m−1 K5L: (-0.00 ± 0.50) ·103m−1 K5SL: (0.01 ± 0.51) ·103m−1 K6L: (-0.00 ± 0.09) ·103m−1 K6SL: (0.00 ± 0.03) ·103m−1

Figure: Beam 1

−2 −1 1 2 ∂Qx/∂2Jx

  • 103m−1

1000 2000 Samples

Sum: (-0.00 ± 0.61) ·103m−1 K5L: (0.00 ± 0.42) ·103m−1 K5SL: (-0.01 ± 0.44) ·103m−1 K6L: (0.00 ± 0.07) ·103m−1 K6SL: (0.00 ± 0.02) ·103m−1

Sum K5L K5SL K6L K6SL −2 −1 1 2 ∂Qy/∂2Jy

  • 103m−1

1000 2000 Samples

Sum: (-0.01 ± 0.62) ·103m−1 K5L: (0.00 ± 0.42) ·103m−1 K5SL: (-0.01 ± 0.44) ·103m−1 K6L: (-0.00 ± 0.07) ·103m−1 K6SL: (-0.00 ± 0.03) ·103m−1

−2 −1 1 2 ∂Qx/∂2Jy

  • 103m−1

1000 2000 Samples

Sum: (0.00 ± 0.73) ·103m−1 K5L: (-0.00 ± 0.50) ·103m−1 K5SL: (0.01 ± 0.51) ·103m−1 K6L: (-0.00 ± 0.09) ·103m−1 K6SL: (0.00 ± 0.03) ·103m−1

Figure: Beam 2

18.02.20 Joschua Dilly Amp.Det. from Misalignments 25

slide-34
SLIDE 34

Misalign Triplets

... and compare to highly powered MO’s

LHC

Qx/ (2Jx) Qy/ (2Jy) Qx/ (2Jy) 100 50 50 100 150 Detuning [103 m

1]

B1 before misalignment B1 misaligned B1 Sim. w/ MO 570 A B2 before misalignment B2 misaligned B2 Sim. w/ MO 570 A

HL-LHC

Qx/ (2Jx) Qy/ (2Jy) Qx/ (2Jy) 100 100 200 Detuning [103 m

1]

B1 before misalignment B1 misaligned B1 Sim. w/ MO 570 A B2 before misalignment B2 misaligned B2 Sim. w/ MO 570 A

MO powering of

570 A causes amplitude detuning to increase from ∼ 5 · 103m−1 up to ∼ 170 · 103m−1 in the direct terms.

18.02.20 Joschua Dilly Amp.Det. from Misalignments 26