Amplitude Detuning from Corrector Misalignments in the LHC and - - PowerPoint PPT Presentation

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Amplitude Detuning from Corrector Misalignments in the LHC and - - PowerPoint PPT Presentation

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Amplitude Detuning from Corrector Misalignments in the LHC and HL-LHC (Part II) Joschua Dilly O MC 30.10.2019 Nonlinear-Corrector Misalignments 1 Setup General Results Results split by IP Main Steps of Simulation O MC 30.10.2019

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SLIDE 1

Amplitude Detuning from Corrector Misalignments in the LHC and HL-LHC (Part II)

Joschua Dilly

OMC

30.10.2019 Nonlinear-Corrector Misalignments 1

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SLIDE 2

Setup General Results Results split by IP Main Steps of Simulation

OMC

30.10.2019 Nonlinear-Corrector Misalignments 2

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SLIDE 3

Setup

OMC

30.10.2019 Nonlinear-Corrector Misalignments 3

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SLIDE 4

Simulation Setup

  • Setup LHC/HL-LHC Sequence
  • Add Sextupole, Octupole, Decapole and Dodecapole errors

from 60 WISE to IP and close-to-IP MQ and MB

  • Calculate triplet corrections for the MCX
  • 50 uniformly distributed misalignments ∈ [−1 mm, 1 mm] per

seed ⇒ Check Amplitude Detuning

OMC

30.10.2019 Nonlinear-Corrector Misalignments 4

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SLIDE 5

Simulation Setup

  • Setup LHC/HL-LHC Sequence
  • Add Sextupole, Octupole, Decapole and Dodecapole errors

from 60 WISE to IP and close-to-IP MQ and MB

  • Calculate triplet corrections for the MCX
  • 50 uniformly distributed misalignments ∈ [−1 mm, 1 mm] per

seed ⇒ Check Amplitude Detuning

OMC

30.10.2019 Nonlinear-Corrector Misalignments 4

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SLIDE 6

Simulation Setup

  • Setup LHC/HL-LHC Sequence
  • Add Sextupole, Octupole, Decapole and Dodecapole errors

from 60 WISE to IP and close-to-IP MQ and MB

  • Calculate triplet corrections for the MCX
  • 50 uniformly distributed misalignments ∈ [−1 mm, 1 mm] per

seed ⇒ Check Amplitude Detuning

OMC

30.10.2019 Nonlinear-Corrector Misalignments 4

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SLIDE 7

Simulation Setup

  • Setup LHC/HL-LHC Sequence
  • Add Sextupole, Octupole, Decapole and Dodecapole errors

from 60 WISE to IP and close-to-IP MQ and MB

  • Calculate triplet corrections for the MCX
  • 50 uniformly distributed misalignments ∈ [−1 mm, 1 mm] per

seed ⇒ Check Amplitude Detuning

OMC

30.10.2019 Nonlinear-Corrector Misalignments 4

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SLIDE 8

Simulation Setup

  • Setup LHC/HL-LHC Sequence
  • Add Sextupole, Octupole, Decapole and Dodecapole errors

from 60 WISE to IP and close-to-IP MQ and MB

  • Calculate triplet corrections for the MCX
  • 50 uniformly distributed misalignments ∈ [−1 mm, 1 mm] per

seed ⇒ Check Amplitude Detuning

OMC

30.10.2019 Nonlinear-Corrector Misalignments 4

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SLIDE 9

Calculation

Feeddown: K K5

4

= dx · K5 (1) K K5S

4

= −dy · K5S (2) K K6

4

= 1 2

  • dx2 − dy 2

· K6 (3) K K6S

4

= −dx · dy · K6S (4) Detuning: ∂Qx ∂2Jx = K4 32π β2

x

(5) ∂Qx ∂2Jy = − K4 16π βxβy (6) ∂Qy ∂2Jy = K4 32π β2

y

(7)

OMC

30.10.2019 Nonlinear-Corrector Misalignments 5

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SLIDE 10

Simulation Setup

LHC HL-LHC β∗ [m] 0.30 0.20 Energy [TeV] 6.5 7.0 Orbit Flat Qx, Qy 0.31, 0.32

OMC

30.10.2019 Nonlinear-Corrector Misalignments 6

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SLIDE 11

Mistakes in the old Simulation Setup

  • Difference to aligned case was not calculated
  • MC*XF (IP1 and IP5) were not misaligned in HLLHC

OMC

30.10.2019 Nonlinear-Corrector Misalignments 7

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SLIDE 12

General Results

OMC

30.10.2019 Nonlinear-Corrector Misalignments 8

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SLIDE 13

Table: LHC simulation summary

[103 m−1] SODT DT SO S O SODT w/ CC Beam 1 ∂Qx /∂2Jx PTC

  • 0.02 ± 2.72

0.00 ± 0.53

  • 0.03 ± 2.68
  • 0.04 ± 0.05

0.08 ± 0.81 0.08 ± 0.99 FD 0.00 ± 0.53 0.00 ± 0.53 – – – 0.00 ± 0.53 ∂Qy /∂2Jy PTC

  • 0.02 ± 5.62

0.00 ± 0.52

  • 0.02 ± 5.60
  • 0.02 ± 0.05

0.15 ± 0.81 0.14 ± 1.01 FD 0.00 ± 0.52 0.00 ± 0.52 – – – 0.00 ± 0.52 ∂Qx /∂2Jy PTC 0.52 ± 8.13 0.00 ± 0.68 0.56 ± 8.10 0.06 ± 0.07 0.27 ± 1.16 0.29 ± 1.46 FD 0.00 ± 0.68 0.00 ± 0.68 – – – 0.00 ± 0.68 Beam 2 ∂Qx /∂2Jx PTC

  • 0.13 ± 6.02

0.00 ± 0.52

  • 0.12 ± 5.99
  • 0.05 ± 0.06

0.09 ± 0.50 0.08 ± 0.63 FD 0.00 ± 0.52 0.00 ± 0.52 – – – 0.00 ± 0.52 ∂Qy /∂2Jy PTC

  • 0.02 ± 5.62

0.00 ± 0.53 0.02 ± 2.86

  • 0.06 ± 0.06

0.16 ± 0.30 0.14 ± 0.57 FD 0.00 ± 0.53 0.00 ± 0.53 – – – 0.00 ± 0.53 ∂Qx /∂2Jy PTC 0.62 ± 8.96 0.00 ± 0.68 0.62 ± 8.92 0.11 ± 0.12 0.26 ± 1.03 0.29 ± 1.07 FD 0.00 ± 0.68 0.00 ± 0.68 – – – 0.00 ± 0.68 Simulation Parameters: S = Sextupole Errors, O = Octupole Errors, D = Decapole Errors, T = Dodecapole Errors, CC = Coupling Correction Methods: PTC = From PTC simulations, FD = From Feed-Down calculations

OMC

30.10.2019 Nonlinear-Corrector Misalignments 9

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SLIDE 14

Table: HL-LHC simulation summary

[103 m−1] SODT DT SO S O SODT w/ CC Beam 1 ∂Qx /∂2Jx PTC

  • 0.03 ± 1.57

0.02 ± 1.56

  • 0.06 ± 0.13
  • 0.07 ± 0.11

0.01 ± 0.06 – FD

  • 0.02 ± 1.57
  • 0.02 ± 1.56

– – – – ∂Qy /∂2Jy PTC

  • 0.05 ± 1.58

0.01 ± 1.58

  • 0.06 ± 0.12
  • 0.07 ± 0.11

0.01 ± 0.04 – FD

  • 0.01 ± 1.59
  • 0.01 ± 1.59

– – – – ∂Qx /∂2Jy PTC 0.02 ± 1.74

  • 0.02 ± 1.73

0.15 ± 0.26 0.13 ± 0.21 0.01 ± 0.14 – FD 0.00 ± 0.68 0.02 ± 1.74 – – – – Beam 2 ∂Qx /∂2Jx PTC

  • 0.07 ± 1.59
  • 0.01 ± 1.58
  • 0.07 ± 0.16
  • 0.07 ± 0.12

0.01 ± 0.11 – FD 0.01 ± 1.59 0.01 ± 1.59 – – – – ∂Qy /∂2Jy PTC

  • 0.08 ± 1.56
  • 0.02 ± 1.56
  • 0.07 ± 0.14
  • 0.08 ± 0.13

0.01 ± 0.04 – FD 0.02 ± 1.56 0.02 ± 1.56 – – – – ∂Qx /∂2Jy PTC 0.18 ± 1.76 0.02 ± 1.73 0.17 ± 0.25 0.15 ± 0.24 0.02 ± 0.06 – FD

  • 0.02 ± 1.73
  • 0.02 ± 1.74

– – – – Simulation Parameters: S = Sextupole Errors, O = Octupole Errors, D = Decapole Errors, T = Dodecapole Errors, CC = Coupling Correction Methods: PTC = From PTC simulations, FD = From Feed-Down calculations

OMC

30.10.2019 Nonlinear-Corrector Misalignments 10

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SLIDE 15

Amplitude Detuning LHC (SODT)

−20 −10 10 20 ∆∂Qx/∂2Jx

  • 103m−1

100 200 Samples

Beam 1: (-0.02 ± 2.72) ·103m−1 Beam 2: (-0.13 ± 6.02) ·103m−1

Beam 1 Beam 2 −20 −10 10 20 ∆∂Qy/∂2Jy

  • 103m−1

100 200 Samples

Beam 1: (-0.02 ± 5.62) ·103m−1 Beam 2: (0.01 ± 2.92) ·103m−1

−20 −10 10 20 ∆∂Qx/∂2Jy

  • 103m−1

100 200 Samples

Beam 1: (0.56 ± 8.13) ·103m−1 Beam 2: (0.62 ± 8.96) ·103m−1

PTC

−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

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

Beam 2 Feed-Down Calculations

  • almost centered around 0 m−1
  • σ up to 9 · 103 m−1
  • centered around 0 m−1
  • only contributions from b6
  • much lower σ than from PTC

OMC

30.10.2019 Nonlinear-Corrector Misalignments 11

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SLIDE 16

Amplitude Detuning LHC (DT)

−2.0 −1.5 −1.0 −0.5 0.0 0.5 1.0 1.5 2.0 ∆∂Qx/∂2Jx

  • 103m−1

50 100 Samples

Beam 1: (0.00 ± 0.53) ·103m−1 Beam 2: (0.00 ± 0.52) ·103m−1

Beam 1 Beam 2 −2.0 −1.5 −1.0 −0.5 0.0 0.5 1.0 1.5 2.0 ∆∂Qy/∂2Jy

  • 103m−1

50 100 Samples

Beam 1: (-0.00 ± 0.52) ·103m−1 Beam 2: (-0.00 ± 0.53) ·103m−1

−2.0 −1.5 −1.0 −0.5 0.0 0.5 1.0 1.5 2.0 ∆∂Qx/∂2Jy

  • 103m−1

50 100 Samples

Beam 1: (-0.00 ± 0.68) ·103m−1 Beam 2: (0.00 ± 0.68) ·103m−1

PTC

−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

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

Beam 2 Feed-Down Calculations

  • centered around 0 m−1
  • σ a third of HL-LHC
  • same σ as from PTC
  • very similar shapes PTC ↔ FDC

OMC

30.10.2019 Nonlinear-Corrector Misalignments 12

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SLIDE 17

Amplitude Detuning LHC (SO)

−20 −10 10 20 ∆∂Qx/∂2Jx

  • 103m−1

100 200 Samples

Beam 1: (-0.03 ± 2.68) ·103m−1 Beam 2: (-0.12 ± 5.99) ·103m−1

Beam 1 Beam 2 −20 −10 10 20 ∆∂Qy/∂2Jy

  • 103m−1

100 200 Samples

Beam 1: (-0.02 ± 5.60) ·103m−1 Beam 2: (0.02 ± 2.86) ·103m−1

−20 −10 10 20 ∆∂Qx/∂2Jy

  • 103m−1

100 200 Samples

Beam 1: (0.56 ± 8.10) ·103m−1 Beam 2: (0.62 ± 8.92) ·103m−1

PTC

−0.0010 −0.0005 0.0000 0.0005 0.0010 ∂Qx/∂2Jx

  • 103m−1

2000 Samples

Sum: (0.00 ± 0.00) ·103m−1

Sum −0.0010 −0.0005 0.0000 0.0005 0.0010 ∂Qy/∂2Jy

  • 103m−1

2000 Samples

Sum: (0.00 ± 0.00) ·103m−1

−0.0010 −0.0005 0.0000 0.0005 0.0010 ∂Qx/∂2Jy

  • 103m−1

2000 Samples

Sum: (0.00 ± 0.00) ·103m−1

Beam 1

−0.0010 −0.0005 0.0000 0.0005 0.0010 ∂Qx/∂2Jx

  • 103m−1

2000 Samples

Sum: (0.00 ± 0.00) ·103m−1

Sum −0.0010 −0.0005 0.0000 0.0005 0.0010 ∂Qy/∂2Jy

  • 103m−1

2000 Samples

Sum: (0.00 ± 0.00) ·103m−1

−0.0010 −0.0005 0.0000 0.0005 0.0010 ∂Qx/∂2Jy

  • 103m−1

2000 Samples

Sum: (0.00 ± 0.00) ·103m−1

Beam 2 Feed-Down Calculations

  • very similar to SODT case
  • σ very large
  • no contributions

OMC

30.10.2019 Nonlinear-Corrector Misalignments 13

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SLIDE 18

Amplitude Detuning LHC (S and O)

−0.2 0.0 0.2 0.4 0.6 ∆∂Qx/∂2Jx

  • 103m−1

200 400 Samples

Beam 1: (-0.04 ± 0.05) ·103m−1 Beam 2: (-0.05 ± 0.06) ·103m−1

Beam 1 Beam 2 −0.2 0.0 0.2 0.4 0.6 ∆∂Qy/∂2Jy

  • 103m−1

200 400 Samples

Beam 1: (-0.02 ± 0.05) ·103m−1 Beam 2: (-0.06 ± 0.06) ·103m−1

−0.2 0.0 0.2 0.4 0.6 ∆∂Qx/∂2Jy

  • 103m−1

200 400 Samples

Beam 1: (0.06 ± 0.07) ·103m−1 Beam 2: (0.11 ± 0.12) ·103m−1

PTC - Sextupole Errors

−3 −2 −1 1 2 3 4 5 ∆∂Qx/∂2Jx

  • 103m−1

200 400 Samples

Beam 1: (0.08 ± 0.81) ·103m−1 Beam 2: (0.09 ± 0.50) ·103m−1

Beam 1 Beam 2 −3 −2 −1 1 2 3 4 5 ∆∂Qy/∂2Jy

  • 103m−1

200 400 Samples

Beam 1: (0.15 ± 0.81) ·103m−1 Beam 2: (0.16 ± 0.30) ·103m−1

−3 −2 −1 1 2 3 4 5 ∆∂Qx/∂2Jy

  • 103m−1

200 400 Samples

Beam 1: (0.27 ± 1.16) ·103m−1 Beam 2: (0.26 ± 1.03) ·103m−1

PTC - Octupole Errors

  • one sided slope
  • together much smaller than SO
  • r SODT case.

OMC

30.10.2019 Nonlinear-Corrector Misalignments 14

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SLIDE 19

Amplitude Detuning LHC (SODT w/ CC)

−4 −2 2 4 ∆∂Qx/∂2Jx

  • 103m−1

100 200 Samples

Beam 1: (0.08 ± 0.99) ·103m−1 Beam 2: (0.08 ± 0.63) ·103m−1

Beam 1 Beam 2 −4 −2 2 4 ∆∂Qy/∂2Jy

  • 103m−1

100 200 Samples

Beam 1: (0.14 ± 1.01) ·103m−1 Beam 2: (0.14 ± 0.57) ·103m−1

−4 −2 2 4 ∆∂Qx/∂2Jy

  • 103m−1

100 200 Samples

Beam 1: (0.29 ± 1.46) ·103m−1 Beam 2: (0.29 ± 1.07) ·103m−1

PTC

−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

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

Beam 2 Feed-Down Calculations

  • coupling correction reduces AD

spread

  • still larger than from

Feed-Down Calculations

  • same as without coupling

correction

OMC

30.10.2019 Nonlinear-Corrector Misalignments 15

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SLIDE 20

Amplitude Detuning HL-LHC (SODT)

−6 −4 −2 2 4 6 ∆∂Qx/∂2Jx

  • 103m−1

100 Samples

Beam 1: (-0.03 ± 1.57) ·103m−1 Beam 2: (-0.07 ± 1.59) ·103m−1

Beam 1 Beam 2 −6 −4 −2 2 4 6 ∆∂Qy/∂2Jy

  • 103m−1

100 Samples

Beam 1: (-0.05 ± 1.58) ·103m−1 Beam 2: (-0.08 ± 1.56) ·103m−1

−6 −4 −2 2 4 6 ∆∂Qx/∂2Jy

  • 103m−1

100 Samples

Beam 1: (0.12 ± 1.75) ·103m−1 Beam 2: (0.18 ± 1.76) ·103m−1

PTC

−6 −4 −2 2 4 6 8 ∂Qx/∂2Jx

  • 103m−1

1000 2000 Samples

Sum: (-0.02 ± 1.57) ·103m−1 K5L: (0.01 ± 0.97) ·103m−1 K5SL: (-0.03 ± 1.25) ·103m−1 K6L: (-0.00 ± 0.10) ·103m−1 K6SL: (-0.00 ± 0.04) ·103m−1

Sum K5L K5SL K6L K6SL −6 −4 −2 2 4 6 8 ∂Qy/∂2Jy

  • 103m−1

1000 2000 Samples

Sum: (-0.01 ± 1.59) ·103m−1 K5L: (-0.00 ± 1.07) ·103m−1 K5SL: (-0.00 ± 1.17) ·103m−1 K6L: (0.00 ± 0.11) ·103m−1 K6SL: (-0.00 ± 0.04) ·103m−1

−6 −4 −2 2 4 6 8 ∂Qx/∂2Jy

  • 103m−1

1000 2000 Samples

Sum: (0.02 ± 1.74) ·103m−1 K5L: (-0.00 ± 1.14) ·103m−1 K5SL: (0.02 ± 1.33) ·103m−1 K6L: (-0.00 ± 0.12) ·103m−1 K6SL: (0.00 ± 0.04) ·103m−1

Beam 1

−8 −6 −4 −2 2 4 6 ∂Qx/∂2Jx

  • 103m−1

1000 2000 Samples

Sum: (0.01 ± 1.59) ·103m−1 K5L: (0.00 ± 1.07) ·103m−1 K5SL: (0.00 ± 1.17) ·103m−1 K6L: (-0.00 ± 0.11) ·103m−1 K6SL: (0.00 ± 0.04) ·103m−1

Sum K5L K5SL K6L K6SL −8 −6 −4 −2 2 4 6 ∂Qy/∂2Jy

  • 103m−1

1000 2000 Samples

Sum: (0.02 ± 1.56) ·103m−1 K5L: (-0.01 ± 0.96) ·103m−1 K5SL: (0.03 ± 1.24) ·103m−1 K6L: (0.00 ± 0.10) ·103m−1 K6SL: (0.00 ± 0.04) ·103m−1

−8 −6 −4 −2 2 4 6 ∂Qx/∂2Jy

  • 103m−1

1000 2000 Samples

Sum: (-0.02 ± 1.73) ·103m−1 K5L: (0.00 ± 1.14) ·103m−1 K5SL: (-0.02 ± 1.33) ·103m−1 K6L: (0.00 ± 0.12) ·103m−1 K6SL: (-0.00 ± 0.04) ·103m−1

Beam 2 Feed-Down Calculations

  • centered around 0 m−1
  • much lower σ than LHC

(9 vs. 1.7 ·10−3 m−1)

  • contributions from

a5, b5, a6, b6; strongest contribution from a5 and b5

  • σ similar to PTC!

OMC

30.10.2019 Nonlinear-Corrector Misalignments 16

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SLIDE 21

Results split by IP

OMC

30.10.2019 Nonlinear-Corrector Misalignments 17

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SLIDE 22

Amplitude Detuning LHC in IP1 and IP5

−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

−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

Beam 1 Beam 2

  • Very similar to all IPs

OMC

30.10.2019 Nonlinear-Corrector Misalignments 18

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SLIDE 23

Amplitude Detuning LHC in IP2 and IP8

−0.015 −0.010 −0.005 0.000 0.005 0.010 ∂Qx/∂2Jx

  • 103m−1

100 200 Samples

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

Sum K6L −0.015 −0.010 −0.005 0.000 0.005 0.010 ∂Qy/∂2Jy

  • 103m−1

100 200 Samples

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

−0.015 −0.010 −0.005 0.000 0.005 0.010 ∂Qx/∂2Jy

  • 103m−1

100 200 Samples

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

−0.010 −0.005 0.000 0.005 0.010 0.015 ∂Qx/∂2Jx

  • 103m−1

100 200 Samples

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

Sum K6L −0.010 −0.005 0.000 0.005 0.010 0.015 ∂Qy/∂2Jy

  • 103m−1

100 200 Samples

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

−0.010 −0.005 0.000 0.005 0.010 0.015 ∂Qx/∂2Jy

  • 103m−1

100 200 Samples

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

Beam 1 Beam 2

  • Two orders of magnitude lower than for IP1 and IP5

OMC

30.10.2019 Nonlinear-Corrector Misalignments 19

slide-24
SLIDE 24

Amplitude Detuning HL-LHC in IP1 and IP5

−6 −4 −2 2 4 6 8 ∂Qx/∂2Jx

  • 103m−1

1000 2000 Samples

Sum: (-0.02 ± 1.57) ·103m−1 K5L: (0.01 ± 0.97) ·103m−1 K5SL: (-0.03 ± 1.25) ·103m−1 K6L: (-0.00 ± 0.10) ·103m−1 K6SL: (-0.00 ± 0.04) ·103m−1

Sum K5L K5SL K6L K6SL −6 −4 −2 2 4 6 8 ∂Qy/∂2Jy

  • 103m−1

1000 2000 Samples

Sum: (-0.01 ± 1.59) ·103m−1 K5L: (-0.00 ± 1.07) ·103m−1 K5SL: (-0.00 ± 1.17) ·103m−1 K6L: (0.00 ± 0.11) ·103m−1 K6SL: (-0.00 ± 0.04) ·103m−1

−6 −4 −2 2 4 6 8 ∂Qx/∂2Jy

  • 103m−1

1000 2000 Samples

Sum: (0.02 ± 1.74) ·103m−1 K5L: (-0.00 ± 1.14) ·103m−1 K5SL: (0.02 ± 1.33) ·103m−1 K6L: (-0.00 ± 0.12) ·103m−1 K6SL: (0.00 ± 0.04) ·103m−1

−8 −6 −4 −2 2 4 6 ∂Qx/∂2Jx

  • 103m−1

1000 2000 Samples

Sum: (0.01 ± 1.59) ·103m−1 K5L: (0.00 ± 1.07) ·103m−1 K5SL: (0.00 ± 1.17) ·103m−1 K6L: (-0.00 ± 0.11) ·103m−1 K6SL: (0.00 ± 0.04) ·103m−1

Sum K5L K5SL K6L K6SL −8 −6 −4 −2 2 4 6 ∂Qy/∂2Jy

  • 103m−1

1000 2000 Samples

Sum: (0.02 ± 1.56) ·103m−1 K5L: (-0.01 ± 0.96) ·103m−1 K5SL: (0.03 ± 1.24) ·103m−1 K6L: (0.00 ± 0.10) ·103m−1 K6SL: (0.00 ± 0.04) ·103m−1

−8 −6 −4 −2 2 4 6 ∂Qx/∂2Jy

  • 103m−1

1000 2000 Samples

Sum: (-0.02 ± 1.73) ·103m−1 K5L: (0.00 ± 1.14) ·103m−1 K5SL: (-0.02 ± 1.33) ·103m−1 K6L: (0.00 ± 0.12) ·103m−1 K6SL: (-0.00 ± 0.04) ·103m−1

Beam 1 Beam 2

  • Very similar to all IPs

OMC

30.10.2019 Nonlinear-Corrector Misalignments 20

slide-25
SLIDE 25

Amplitude Detuning HL-LHC in IP2 and IP8

−0.010 −0.005 0.000 0.005 0.010 ∂Qx/∂2Jx

  • 103m−1

100 200 Samples

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

Sum K6L −0.010 −0.005 0.000 0.005 0.010 ∂Qy/∂2Jy

  • 103m−1

100 200 Samples

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

−0.010 −0.005 0.000 0.005 0.010 ∂Qx/∂2Jy

  • 103m−1

100 200 Samples

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

−0.010 −0.005 0.000 0.005 0.010 ∂Qx/∂2Jx

  • 103m−1

100 200 Samples

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

Sum K6L −0.010 −0.005 0.000 0.005 0.010 ∂Qy/∂2Jy

  • 103m−1

100 200 Samples

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

−0.010 −0.005 0.000 0.005 0.010 ∂Qx/∂2Jy

  • 103m−1

100 200 Samples

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

Beam 1 Beam 2

  • Two orders of magnitude lower than for IP1 and IP5

OMC

30.10.2019 Nonlinear-Corrector Misalignments 21

slide-26
SLIDE 26

Main Steps of Simulation

OMC

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slide-27
SLIDE 27

Simulation Steps

  • setup and slice Sequence according to masks
  • LHC: makethin
  • HL-LHC: install additional components, exec myslice
  • apply optics, deactivate all orbit, crossing
  • activate errors: a3 - b6
  • call WISE (60 seeds) → apply for MQW, MQX(F[AB] in HL-LHC)
  • run Triplet-D1-Correction script

⇒ match tune, output ptc twiss

  • 50 uniformly distributed misalignments ∈ [−1 mm, 1 mm] per seed
  • LHC: MC[SOT].*X\..*[1258]
  • HL-LHC: MC[SODT].*XF?\..*[1258]

⇒ match tune; output esave, ptc twiss (per misalignment)

OMC

30.10.2019 Nonlinear-Corrector Misalignments 23