1. HL-LHC Corrector Magnet 3D design status Giovanni Volpini on behalf of the LASA team CERN, February 25, 2014

2. Specification done, design in progress First tests, first experiences… To start when a 3D em “stable” design is issued To be done So far, looks OK Work status Magnets Design Problems waiting for us just round the (3D) corner… magnetic length cross-talk between magnets fringe field (“harmonics” at the magnet ends) forces between magnets Residual magnetization at I=0 and impact on the harmonics Cross check COMSOL results w/ Roxie (March 2014) Mechanical design (May 2014) Construction & test Wind & impregnate a dummy coil (June 2014) Design the test cryostat Giovanni Volpini, CERN 25 February 2014 2 Being addressed

3. Sextupole cross-section Giovanni Volpini, CERN 25 February 2014 3 yoke coil Sextupole bore

4. 3D design: geometry Giovanni Volpini, CERN 25 February 2014 4 rectangular, race track, coils; iron yoke extruded; option for a stray flux return yoke investigated in the COMSOL model COMSOL Roxie with flux return without flux return

5. Computations performed Using the two codes to cross-check & validate the results Linear iron (µ r = 4000) to validate a model & cross-check results “Roxie”- like saturating iron with filling factor 0.985 Six cases {40 mm, 50 mm, 60 mm} x {with RY, without RY (Air)} For each the following current have been considered {20 A, 50 A, 100 A, 150 A, 200 A, 300 A, 400 A} For each case, Longitudinal & Integrated A 3 /B 3, integrated harmonics, peak field on conductor Giovanni Volpini, CERN 25 February 2014 5

6. COMSOL vs Roxie Use two codes to cross-check & validate the results: COMSOL + Mathematica for harmonic analysis; Roxie 2D results: agreement within few parts/10 4 on fields; few % on relevant harmonics. Satisfactory for our purposes. WARNING: use of LSOLV in Roxie option leads to inaccurate results, with a discrepancy w.r.t. COMSOL as large as 3% on fields. 3D results: agreement within ~1% on fields; 10% on relevant harmonics. Acceptable but not exciting. Giovanni Volpini, CERN 25 February 2014 6

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8. Operating point & length, I Giovanni Volpini, CERN 25 February 2014 8 Design integrated strength 60 mT m Design operating current ratio vs. s.s. limit (40%) … vs integrated B 3 …vs peak field on coils We compute the Ic at the peak field at s.s. limit. Dividing the magnetomotive force at s.s. limit by Ic, we get the no. of turns required. Dividing the operating magnetomotive force by the no. turns, we get the operating current.

9. WITHOUT R.Y.WITH R.Y. Iron length[mm] 405060405060 Operating magnetomot. force [A turns] 311042231218290379192605620235 B peak at s.s. limit[T] 4.673.693.255.714.833.52 Wire Ic[A] 338.4411.1451.4276.5327.6425.4 Operating current[A] 135.4164.5180.6110.6131170 No. Turns required[-] 228136101343199119 Giovanni Volpini, CERN 25 February 2014 9 Operating point & length, II 2D design was made with 166 turns x 150 A, the operating point was around the 40% on the load line.

10. B 3 /A 3 component inside and outside Giovanni Volpini, CERN 25 February 2014 10 Iron length (w.o. flux return, if present) nominal “magnetic ½length” (60.5 mm) nominal spacing between magnets (100 mm) with flux return without flux return

11. a 9 component Giovanni Volpini, CERN 25 February 2014 11 WITHOUT R.Y.WITH R.Y. Iron length [mm]405060405060 I = 20 A 26.020.415.86.13.92.6 I = 150 A 26.821.817.74.33.63.1 In units 10 -4

12. summary For the sextupole, the overall 3D e.m. design seems compatible with the space constraints; Flux return at the magnet ends : for a given magnetomotive force and iron length, is less effective reduces the stray field reduces the integrated harmonics so it is probably OK: any drawback? hole shape Harmonics content not critical, numbers appear acceptable, Flux Return is also effective in reducing unwanted components. Giovanni Volpini, CERN 25 February 2014 12

13. open issues summary Questions to be answered as soon as possible… operating currents; outer iron diameter & shape; radiation hardness compliance, insulation & impregnation; field quality & fringe field; mechanical & electrical connection between magnets and LHe vessel to be defined, along with room for bus-bars etc.; …and, not to be forgotten: the MgB 2 solution (playground) other solutions (combined function magnet)? Giovanni Volpini, CERN 25 February 2014 13

14. Giovanni Volpini, CERN 25 February 2014 14 Exiting from Flatland may be a though experience… The End

15. Other slides Giovanni Volpini, CERN 25 February 2014 15

16. WITHOUT R.Y.WITH R.Y. Iron length[mm] 405060405060 Operating magnetomot. force [A turns] 3110422312182902605620235 B peak at s.s. limit[T] 3.923.082.763.502.98 Wire Ic[A] 391.8469.2504.0427.1479.8 Operating current[A] 196235252214240 No. Turns required[-] 160957312284 Giovanni Volpini, CERN 25 February 2014 16 Operating point @ 50% of s.s. 2D design was made with 166 turns x 150 A, it was around the 40% on the load line.

17. Infinite elements Giovanni Volpini, CERN 25 February 2014 17 Iron half length 50 mm With flux return With (red) Without (purple) infinite elements Impact Integrated strength < 0.1% Main component < 0.01 % Int b9 < 2 units

18. Giovanni Volpini, CERN 25 February 2014 18

19. magnet specs & operating features Name Orientation Order Aperture Int strenght at radius = 50 mm Magnetic length Operating current Wire diameter Outer radius (construction) Stored energy Inductance TOTAL [-][mm][Tm][m][A][mm] [J][H] MCQSXS21501.000.7893000.7230.030412.80.676 MCSXN/S31500.060.1081500.5150.01200.50.107 MCOXN/S41500.040.1081500.5150.0654.20.058 MCDXN/S51500.030.1221500.5150.0588.70.052 MCTXN61500.090.4561500.5150.02649.40.235 MCTSXS61500.0150.0761500.5150.0441.60.039 Giovanni Volpini, CERN 25 February 2014 19

20. 2D cross sections: 6-pole Yoke radius = 160 mm Recooler bore D 50 mm @ r = 190 mm, so it’s outside the yoke J eng (overall) ~ 260 A/mm² B peak iron = 3.7 T B peak coil = 2.0 T 03.12.2013 p 140 Giovanni Volpini, CERN 25 February 2014 20

21. 6- and 12-pole load lines B peak on coil B @ r=50mm Design current = 150 A 4.22 K I c 179 A @ 5 T, 4.22 K Sextupole Dodecapole 1.9 K Sextupole Dodecapole Giovanni Volpini, CERN 25 February 2014 21