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

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 • 𝝐𝑹 𝝐𝜺 = 𝟐 𝟓𝝆 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 L* and Triplet Length, 11 th October 2016 2

W functions for different L* 2500 Wx 36 Wx 45 2000 Wx 61 1500 Wx 1000 500 0 0 20000 40000 60000 80000 100000 S (m) L* and Triplet Length, 11 th October 2016 3

W functions for different L* 2200 2000 Wy 36 1800 Wy 45 1600 Wy 61 1400 Wy 1200 1000 800 600 400 0 20000 40000 60000 80000 100000 S (m) L* and Triplet Length, 11 th October 2016 4

Shortening inner triplet • Minimise the size of the Focusing magnets – Save space – Reduce chromaticity – Easier correction scheme – Cheaper • Current design – ~ 𝟓𝟏 𝝉 beam stay clear – ~140 m long – 10 m gaps between magnets L* and Triplet Length, 11 th October 2016 5

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 – 𝒆 Estimate beam stay clear • Thick Lens PyMadX 𝒎 𝟓 𝒎 𝟐 𝒎 𝟑 𝒎 𝟒 – Scan smaller area determined by fast scan – 𝑴 ∗ Match accurately using MadX – Work out stay clear using aperture module L* and Triplet Length, 11 th October 2016 6

Python Script Set total length and fix required beam stay clear, β *, L*, gaps and shielding If beam stay clear smaller than required Use fast FOM to scan large range in strength and phase space Increase total length Determine sensible range 𝑕 ± 0.005 , 𝑚 4 −2% + 8% Use PyMadX for small scan of accurate beam stay clear using current shielding ( 12 × 25 resolution) Find setup with largest beam stay clear If beam stay clear larger than required Plot ideal setup and output lengths + strengths L* and Triplet Length, 11 th October 2016 7

First attempt 70 m (12 𝝉 , 𝜸 ∗ = 𝟏. 𝟒 , 3 m gaps) L* and Triplet Length, 11 th October 2016 8

Chromaticity First attempt Wy 45 Wy 45 New 1600 1400 1200 Wy 1000 800 600 400 0 20000 40000 60000 80000 100000 S (m) L* and Triplet Length, 11 th October 2016 9

Optimising shielding Set required β *, L* and Use code to Use this use initial shielding find shortest setup for setup with radiation good beam studies of stay clear triplet Work out Change shielding shielding Integrate and match into required for accordingly this setup machine for further studies L* and Triplet Length, 11 th October 2016 10

Model of the new triplet Q1 Q2A Q3 Q2B Beam pipe L* and Triplet Length, 11 th October 2016 11

Comparison with nominal apertures L* and Triplet Length, 11 th October 2016 12

Energy deposition • Peak dose (3000 fb -1 ) for horizontal crossing Significant reduction in peak dose peak dose for Q2A Ilaria. Dose in nominal triplet (FCC week 2016) L* and Triplet Length, 11 th October 2016 13

L* and Triplet Length, 11 th October 2016 14

Aperture as a function of strength • So far assumed constant ap. R w G maximum (mm) (mm) (T/m) strength: 50 25 193 – 𝑠 𝑏𝑞𝑓𝑠𝑢𝑣𝑠𝑓 = 60 28 166 70 33 149 𝐶 𝑁𝐵𝑌 11 T = 80 35 133 𝑕 𝑕 90 38 120 • Received an 100 40 110 email by Daniel 110 43 102 120 45 94 Schoerling 130 48 88 about the cold bore L* and Triplet Length, 11 th October 2016 15

140 Accurate Aperture 120 B/g Aperture Apperture (mm) 100 80 60 40 80 100 120 140 160 180 200 Gradient (T/m) L* and Triplet Length, 11 th October 2016 16

y = a + b*x Equation -2.0 No Weighting Weight Residual 5.6075E- Sum of 4 Squares -0.99967 Pearson's r -2.2 0.99924 Adj. R-Squar Value Standard Err Log(Aperture/m) Intercept 3.40813 0.05738 Log(Aperture -2.4 /m) Slope -1.2152 0.01188 -2.6 -2.8 -3.0 4.4 4.6 4.8 5.0 5.2 5.4 Log(Gradient/T/m) L* and Triplet Length, 11 th October 2016 17

Model • In future uses of my code I can update the aperture calculations • 𝐵 = 𝑓 𝐽𝑜𝑢𝑓𝑠𝑑𝑓𝑞𝑢 𝑕 𝐻𝑠𝑏𝑒𝑗𝑓𝑜𝑢 = 29.96𝑕 −1.215 m • Difference not significant to change previous designs • Previous designs probably discarded when iterating with Jose L* and Triplet Length, 11 th October 2016 18

140 Accurate Aperture 120 B/g Aperture Model Apperture (mm) 100 80 60 40 80 100 120 140 160 180 200 Gradient (T/m) L* and Triplet Length, 11 th October 2016 19