1. Susana Izquierdo Bermudez

2. Contents 1. Introduction 2. Coil cross section 3. Magnet parameters at operation conditions 1. Peak field 2. Physical and magnetic lengths 4. Load line and margin 5. Field quality (FQ): 1. Geometric & Iron saturation 2. Persistent currents 3. Eddy currents 4. 3D effects 5. Coil deformation during powering 6. Manufacturing tolerances 7. Magnetic shimming 1. Coil shimming 2. Passive shimming with ferromagnetic material 6. Summary 2

3. Introduction Field quality of the triplets is critical at nominal current 3 Magnetic design optimized for high field At low field, we are almost transparent to the beam

4. Coil Cross Section 4 HQ MQXF The cable width/aperture (w/r) is approximately maintained Aperture from 120 mm to 150 mm Cable from 15 to 18 mm width Similar stress with +30% forces Same coil lay-out: 4-blocks, 2-layer with same angle Optimized stress distribution Strand increase from 0.778 mm to 0.85 mm Same filament size from 108/127 to 132/169 Maximum # of strands: 40 Similar peak field  Lower J overall Positive side effect for quench protection (from 580 to 490 A/mm 2 )

5. Coil Cross Section 5 Criteria for the selection Maximize gradient and # of turns (protection) Distribute e.m. forces and minimize stress [F. Borgnolutti] Magnetic design optimization of a 150 mm aperture Nb3Sn low-beta quadrupole for the HiLumi LHC. IEEE Trans. Appl. Sup., vol. 24, no. 3, 2014. All harmonics below 1 units at R ref = 50 mm Field harmonics computed assuming the conductor is aligned in the outer diameter Units at R ref = 50 mm Conductors aligned in the winding mandrel Conductors aligned in the outer diameter b6 b10 b14

6. Magnet parameters 6 Parameters U NITS Operational temperature1.9K Clear aperture diameter150mm Nominal gradient140T/m Nominal current17.46kA Nominal peak field on the coil12.1T Stored energy at I nom 1.32MJ/m Differential inductance at I nom 8.22mH/m Superconductor current density (j sc )1635A/mm 2 Engineering current density (j eng )770A/mm 2 Overall current density at (j overall )490A/mm 2 Forces x2.74MN/m Forces y-3.91MN/m Yoke Pad B [T] The magnetic structure is made out of two parts, the “pad” and the “yoke”. Details will be addressed [M. Juchno].

7. Field in the coil 3D magnetic optimization to reduce the peak field enhancement at the ends: 7 1. Conductors placing at the ends 2. Reduction of the magnetic extension of the yoke Design solution: 6 blocks in the ends Peak field enhancement in the outer layer is reduced by 0.3 T by splitting block 4 in 2 Block 1 is divided to minimize the integrated harmonics Design solution: Only magnetic pad is shortened Peak field in the ends is lower than in the straight section More uniform stress distribution in the coil Lower reduction on the magnetic length HQ design ΔB p = -0.1 T ΔB p = -0.3 T ΔB p = 0.3 T Δl mag = 0 mm Δl mag = -18 mm Δl mag = -23 mm Block 1 Block 2 Block 3 Block 4

8. Field in the coil 8 Pole tip Straight part Arc length of the conductor Pole tip Straight part 050100150200250 0 20 40 layer jump length [mm] y [mm] B [T] 9 10 11 12 Layer jump Dimensions defined by scaling the hard way bending radius in HQ with the cable width. The field in the layer jump is lower than in the straight section The overall layer jump length is 270 mm and the bending radius is 800 mm.

9. Magnetic and Physical Lengths 9 Magnetic Pad Magnetic Length Coil length Magnetic Yoke ParametersUnitsSQXF LQXF LARP LQXF CERN Magnetic length at RTmm119840126820.5 Magnetic length at 1.9 Kmm1194.440006800 Coil length at RT (from conductor to conductor) mm131341276935.5 Overall coil length at RT (including splice extension) mm151043247132.5 Magnetic yoke extension at RTmm155043647172.5 Magnetic pad extension at RTmm97537896597.5 Gradient = 140 T/m at RT Magnetic Length: (assuming longitudinal thermal contraction = 3 mm/m ) LQXF CERN = 6.8 m LQXF LARP = 4.0 m

10. Load line and margin 10 Self field corr. (ITER barrel) 0.429 T/kA 5% cabling degradation Operational grad.: 140 T/m I op : 17.5 kA B peak_op : 12.1 T 81% of I ss at 1.9 K G ss : 171 T/m I ss : 21.6 kA B peak_ss : 14.7 T Stored energy: 1.3 MJ/m Inductance: 8.2 mH/m Say something about error Impact of higher I max strand – +10% increase in critical current  about +3% in I ss

11. Temperature margin 11 PIT/RRP????

12. FQ: Iron saturation Dependence of field quality on operational current due to iron saturation effect: All field quality optimized at top field (7 TeV) Optimization at 6.5 TeV instead of 7 TeV new guideline (November 14) 12

13. FQ: Persistent Currents 13 Estimates using magnetization measurements of actual QXF 169 wires performed at Ohio State University Harmonics are provided for second up-ramp following a pre- cycle corresponding to the one used for strand measurements Measured magnetization (OSU)Calculated b 6 (after pre-cycle) Stop plot at 17.4 kA [X. Wang]

14. FQ: Persistent Currents 14 Effect of ±20% magnetization on b 6, b 10 included – Nominal b 6 value of -10 units can be adjusted using current reset level during pre-cycle – Dynamic aperture simulations accept b 6 up to 20 units at injection Present value of magnetization average and spread are compatible with field quality requirements For future study: assessment of the variability in wire magnetization and resulting uncertainty Persistent current harmonics b6b6 b 10 NominalD(+20%M)NominalD(+20%M) 1.0 kA (injection)-10.0-2.43.4 +0.8 17.5 kA (high field) -0.97-0.12-0.10.0 [X. Wang]

15. FQ: Eddy Currents 15 Pros: Snap back reduction Suppression of ramp-rate dependence of field quality Increased reproducibility Cons: Less quench back for protection Stability (current sharing among layers) Stainless Steel Core 12 mm x 0.025 mm to control the cross-over resistance R c (~65 % coverage) [E. W. Collings] Effects of Core Type, Placement, and Width, on the Estimated Interstrand Coupling Properties of QXF-Type Nb3Sn Rutherford Cables. vol. 25, 2015. PLOT Reff vs coverage

16. FQ: 3D effects 16 Layer jump Splice b6b10b14a2a6 2D0.32-0.40-0.660.00 3D-SQXF8.06-0.54-0.70-8.900.60 3D-LQXF – 4 m2.65-0.44-0.67-2.670.18 3D-LQXF – 6.8 m1.69-0.42-0.67-1.570.10 main field in the straight section Yoke Extension Integrated field harmonics Integral over the magnet yoke extension:

17. FQ: 3D effects Plans for the next iteration: Minimize the length of the splice region and NbTi leads extension Partial compensation optimizing the block position in the lead end Partial compensation in the straight section 17 NbTi leads 210 mm Δb6 3D-SQXF4.13 3D-LQXF – 4 m1.23 3D-LQXF – 6.8 m0.73 Yoke Extension The contribution of the NbTi leads should be also taken into account: b6b10b14a2a6 2D0.32-0.40-0.660.00 3D-SQXF12.19-0.15-0.70-8.900.60 3D-LQXF – 4 m3.87-0.32-0.67-2.670.18 3D-LQXF – 6.8 m2.42-0.40-0.67-1.570.10 NbTi leads contribution: Total integrated field harmonics (including NbTi leads)

18. FQ: 3D effects 18 Partial compensation of the splice and leads contribution by optimizing the block position in the lead end: Original block position Shifted block position b6 original b6 shifted 2D0.32 3D-LQXF – 4 m3.92.3 3D-LQXF – 6.8 m2.41.5 The rest, will be compensated with the magnet cross section (see section 7.1) Remark: Total integrated field harmonics including 210 mm NbTi leads

19. FQ: Coil deformation during powering 19 Powering max.0.471 mm min. 0.239 mm Cool down max.0.508 mm min. 0.360 mm Loading at RT max.0.066 mm min. 0.041 mm [M. Juchno] Cross section is optimized for the warm coil in relax state, assuming the conductors are aligned in the outer diameter. In operation conditions, we expect 0.7 % more gradient and +0.93 units of b 6. Most of the contribution is coming from cool down. Warm coil in relax state Are we going to account for this in the next cross section iteration?

20. FQ: Manufacturing tolerances 20 Random displacement of coil blocks (normal distribution with zero central values and σ = d) r2r2 φ2φ2 α2α2 To define the “random” component in the field quality tables, the amplitude of the allowed multipoles have been increased based on the experience from LHC [ref] RANDOM COMPONET OrderNormalSkew 30.820.80 40.570.65 50.420.43 61.100.31 70.19 80.130.11 90.070.08

21. FQ: Magnetic shimming 21 Two main aspects to worry about: The size of b 6, as it is very sensitive and we should be able to apply fast correction actions during manufacturing if a problem is detected: coil shimming. The size of non allowed multipoles (a 3, b 3, a 4, b 4 ) This parameter is difficult to estimate. This parameter is difficult to estimate (you need an homogeneous set of few magnets) First data HQ shows we are a factor two-three off Similar results on the first MQXC Nb-Ti magnet (no it is not specific to Nb3Sn technology) Good result considering we are on a short model, first iteration Plan B: passive shimming with ferromagnetic material

22. FQ: Coil shimming 22 Tuning capabilities Using a 100 µm shim we are able to correct up to -2.3/+1.3 units on b 6. Only the shim in the mid-plane of the inner layer is giving a significant contribution to b 10 (-0.3 units). The rest of the harmonics are not affected. Pole Mid-plane IL = inner layer OL = outer layer 100 µm shim

23. FQ: Coil shimming Plan for next cross section iteration Cross section will be optimized using a nominal shim 100 µm thick An additional shim of 100 µm can be used to fine tune the field quality, 23 Nominal 100 µm shim Additional 100 µm shim Impact of including an additional 100 µm shim Impact of removing the nominal 100 µm shim Work in progress

24. FQ: Ferromagnetic shims 24 Three families of shims: Rods in the collars. Not interesting because the iron strongly saturates, they are transparent. Shims in the bladder slots, very interesting. Shims in the yoke slots. They are too far from the coil to act. [P. Hagen]

25. FQ: Ferromagnetic shims 25 [P. Hagen] Different shim configuration in the bladders slots allow us to correct up to ±5 units of b 3 and a 3 ±3 units of b 4 ±1 units of a 4 Fine tuning is possible: Changing the size of the shim Varying the permeability of the shims along the Z-axis Example of the impact of one shim placed in the bladder slot

26. Summary 26

28. 28 V1 SPC1 IL Cu Oct-2014 V2 SPC1 OL Cu Oct-2014 V3 SPC2 and SQXF1 Cu Jan 2014 April 2014 V4 SQXF2 Bad Nb3Sn June 2014 V5 SQXF3 Nb3Sn End July 2014 WP3 meeting Review End Parts Design Increase de Harmonic Order of the baseline ellipse (more roundish) Pole converged to BEND design Change angle last block IL Minor changes: Radius on the edges Flexible features Modify spacing among cables last block IL 20132014 October NovemberDecemberJanuaryFebruaryMarchAprilMayJuneJulyAug 42434445 46474849505152123456789101112131415161718192021222324252627282930313233 SPC1SPC2PreparationSQXF1ILOL SQXF2SQXF3 71.5˚  67.3˚ 68.5˚  71˚ Shorter coils with plastic end spacers to optimize ends SQXF coils Mechanical Optimization (delayed ~ 1 month)

29. Remark: analysis done in MQXF_V0 cross section, strand self field not included 29 Impact of block subdivision in peak field INNER LAYEROUTER LAYER Block 1ABlock 1BBlock 2Block 3Block 4ABlock 4B 3D peak field 4 Blocks10.4311.858.5311.96 6 Blocks9.7010.4311.857.349.9811.63 2D peak field10.4111.826.7811.17 Configuration Magnetic yoke z = [0-700] mm Magnetic pad z = [0-500] mm Non-magnetic pad z = [500-700] mm

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