L* and Triplet Length JAI FCC Team Jose Abelleira , Androula Alekou, - - PowerPoint PPT Presentation

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l and triplet length
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L* and Triplet Length JAI FCC Team Jose Abelleira , Androula Alekou, - - PowerPoint PPT Presentation

Jan 21, 2024 239 likes β€’440 views

L* and Triplet Length JAI FCC Team Jose Abelleira , Androula Alekou, Emilia Cruz, Leon van Riesen-Haupt , Andrei Seryi (JAI-OX), Laury Nevay (JAI-RHUL) 11 th October 2016 Chromaticity =

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L* and Triplet Length

JAI FCC Team Jose Abelleira, Androula Alekou, Emilia Cruz, Leon van Riesen-Haupt, Andrei Seryi (JAI-OX), Laury Nevay (JAI-RHUL) 11th October 2016

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L* and Triplet Length, 11th October 2016 2

  • 𝝐𝑹

𝝐𝜺 = 𝟐 πŸ“π† 𝜸 𝒕 𝒍 𝒕 𝒆𝒕

– Larger 𝜸 and longer quads cause higher chromaticity – Larger L* forces 𝜸 to be larger and needs stronger focusing – Higher chromaticity requires more correction and takes more space – Try and keep triplet as short as possible Chromaticity

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L* and Triplet Length, 11th October 2016 3

W functions for different L*

20000 40000 60000 80000 100000 500 1000 1500 2000 2500

Wx S (m) Wx 36 Wx 45 Wx 61

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L* and Triplet Length, 11th October 2016 4

W functions for different L*

20000 40000 60000 80000 100000 400 600 800 1000 1200 1400 1600 1800 2000 2200

Wy S (m) Wy 36 Wy 45 Wy 61

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L* and Triplet Length, 11th October 2016 5

  • Minimise the size of

the Focusing magnets

– Save space – Reduce chromaticity – Easier correction scheme – Cheaper

  • Current design

– ~ πŸ“πŸ 𝝉 beam stay clear – ~140 m long – 10 m gaps between magnets

Shortening inner triplet

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L* and Triplet Length, 11th October 2016 6

Figure of Merit

  • Fast thin lens figure of merit scan

– Analytically work out strengths needed – Work out space for quads – Work out aperture from length and strength – Estimate beam stay clear

  • Thick Lens PyMadX

– Scan smaller area determined by fast scan – Match accurately using MadX – Work out stay clear using aperture module

π’ŽπŸ’ π’ŽπŸ“ π’ŽπŸ‘ π‘΄βˆ— π’ŽπŸ 𝒆

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L* and Triplet Length, 11th October 2016 7

Set total length and fix required beam stay clear, Ξ²*, L*, gaps and shielding Use fast FOM to scan large range in strength and phase space

Determine sensible range 𝑕 Β± 0.005, π‘š4βˆ’2% + 8%

Use PyMadX for small scan of accurate beam stay clear using current shielding (12 Γ— 25 resolution) Find setup with largest beam stay clear

If beam stay clear larger than required

Plot ideal setup and output lengths + strengths

Python Script

If beam stay clear smaller than required Increase total length

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L* and Triplet Length, 11th October 2016 8

First attempt 70 m (12 𝝉, πœΈβˆ— = 𝟏. πŸ’, 3 m gaps)

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L* and Triplet Length, 11th October 2016 9

Chromaticity First attempt

20000 40000 60000 80000 100000 400 600 800 1000 1200 1400 1600

Wy S (m) Wy 45 Wy 45 New

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L* and Triplet Length, 11th October 2016 10

Use code to find shortest setup with good beam stay clear Use this setup for radiation studies of triplet Work out shielding required for this setup Change shielding accordingly

Optimising shielding

Set required Ξ²*, L* and use initial shielding Integrate and match into machine for further studies

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L* and Triplet Length, 11th October 2016 11

Model of the new triplet

Q1 Q2A Q2B Q3 Beam pipe

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L* and Triplet Length, 11th October 2016 12

Comparison with nominal apertures

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L* and Triplet Length, 11th October 2016 13

Energy deposition

  • Peak dose (3000 fb-1) for horizontal

crossing

Significant reduction in peak dose

  • Ilaria. Dose in nominal

triplet (FCC week 2016)

peak dose for Q2A

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L* and Triplet Length, 11th October 2016 14

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L* and Triplet Length, 11th October 2016 15

Aperture as a function of strength

  • So far assumed

constant maximum strength:

– 𝑠

π‘π‘žπ‘“π‘ π‘’π‘£π‘ π‘“ = πΆπ‘π΅π‘Œ 𝑕

=

11 T 𝑕

  • Received an

email by Daniel Schoerling about the cold bore

  • ap. R

w G (mm) (mm) (T/m) 50 25 193 60 28 166 70 33 149 80 35 133 90 38 120 100 40 110 110 43 102 120 45 94 130 48 88

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L* and Triplet Length, 11th October 2016 16

80 100 120 140 160 180 200 40 60 80 100 120 140

Accurate Aperture B/g Aperture

Apperture (mm) Gradient (T/m)

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L* and Triplet Length, 11th October 2016 17

4.4 4.6 4.8 5.0 5.2 5.4

  • 3.0
  • 2.8
  • 2.6
  • 2.4
  • 2.2
  • 2.0

Log(Aperture/m) Log(Gradient/T/m)

Equation y = a + b*x Weight No Weighting Residual Sum of Squares 5.6075E- 4 Pearson's r

  • 0.99967
  • Adj. R-Squar

0.99924 Value Standard Err Log(Aperture /m) Intercept 3.40813 0.05738 Slope

  • 1.2152

0.01188

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L* and Triplet Length, 11th October 2016 18

Model

  • In future uses of my code I can

update the aperture calculations

  • 𝐡 = π‘“π½π‘œπ‘’π‘“π‘ π‘‘π‘“π‘žπ‘’π‘•π»π‘ π‘π‘’π‘—π‘“π‘œπ‘’ = 29.96π‘•βˆ’1.215 m
  • Difference not significant to change

previous designs

  • Previous designs probably discarded

when iterating with Jose

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L* and Triplet Length, 11th October 2016 19

80 100 120 140 160 180 200 40 60 80 100 120 140

Accurate Aperture B/g Aperture Model

Apperture (mm) Gradient (T/m)