Quadrupole design study for the lhc phase I upgrade (3 rd iteration)

1. CERN, 24th July 2008 Quadrupole design study for the lhc phase I upgrade(3rd iteration) F. Borgnolutti Magnets, Cryostats and Superconductors Group Accelerator Technology Department, CERN Acknowledgments: E. Todesco, P. Fessia

2. content • Summarized of the previous work • Study of the dimension and location of the holes in the iron yoke for the He flow • Conclusion I • Preliminarily designs for a possible second cables distribution • Conclusion II & Future work

3. SUMMARIZED OF THE PREVIOUS WORK

4. Summarized of the previous work • We optimized quads with apertures of 110, 120 and 130mm • 2 layers, 3 and 4 blocks designs are considered • The cable performances are derived from the latest measurements performed at 1.9K on the spare cables of the LHC main dipole: • Cable 01 (inner layer): 14800 A @ 10T (slope of 4680 A/T) • Cable 02 (outer layer): 14650 A @ 9T (slope of 4050 A/T)

5. Summarized of the previous work • An analytical study showed that the short sample gradient we can expect (without iron yoke) is of: • 138 T/m for the 130mm aperture • 148 T/m for the 120mm aperture • 157 T/m for the 110mm aperture • An iron yoke placed at 37mm from the coil increases the short sample gradient by ~3-5% • Special grading • does not dramatically increase the short sample gradient • Uses more cable 01 which is the shorter cable length • Unit length of cable 01: 460 m • Unit length of cable 02: 780 m

6. Summarized of the previous work • Constrains: • Field quality • Multipoles b6, b10 and b14 < 1 unit (at Rref = 2/3 of the aperture radius) • Mechanical • Minimal angular thickness of the Pole nose of • 8.5º for the 110mm • 7.7º for the 120mm • 7.0º for the 130mm • Insulation at the mid-plane • 2 common sheet of 0.12mm • 2 additional sheet of 0.1mm at the outer layer • Inter-layer thickness of 0.5mm • Thickness of the copper wedge nose > 1 mm too small (to avoid cutting the insulation) nose S=16mm

7. Summarized of the previous work • First set of designs (without iron): 110mm (MQXC V13) 130mm (MQXC V2) 120mm (MQXC V3) 120mm (MQXC V8)

8. STUDY OF THE DIMENSION AND LOCATION OF THE HOLES IN THE IRON YOKE FOR THE He FLOW

9. IRON yoke geometry • Iron yoke dimensions • In all cases the collar thickness is of 37mm and the outer radius of the yoke is set at 275mm. Therefore the yoke thickness depends on the aperture diameter: • 110mm aperture yoke thickness of 152mm • 120mm aperture “ 147mm • 130mm aperture “ 142mm • Possible holes dimensions an positions in the yoke for He flow • Holes of 80mm • 4 holes located at the mid-planes • 4 holes located at the poles • It’s possible to move a bit the holes radialy while keeping at least 16mm of matter

10. IRON yoke geometry • Holes of 110mm • 4 holes located at the mid-planes • 4 holes located at the poles • The holes have to be centered in the yoke • Aperture of 110mm d=21mm (d=36mm for 80mm hole) • Aperture of 120mm d=18.5mm (d=33.5 for 80mm hole) • Aperture of 130mm d=16mm (d=31 for 80mm hole) 275 mm 110 mm 37 mm d

11. Iron yoke effect on magnetic field • Influence of the holes dimensions and positions in the iron yoke on the magnetic field: We study the 120mm MQXC V8 case • For the 80mm cases the reduction of the transfer function is of 1-1.5%, it is ~1% higher for the 110mm cases. • In all cases, the reduction of the transfer function is in between what we have for the MQXB (2%) and MQXA (5.2%)

12. Iron yoke effect on magnetic field Multipoles versus current • Δb6 is a bit smaller when the holes are located at the mid-plane • In both the 80mm and 110mm hole diameters cases, the Δb10 and Δb14 are less than 0.1 units. • Not any “not allowed” multipole appears because the four-fold symmetry is always respected

13. Iron yoke: choice of the hole diameter and position • From the integration point of view the best solution would be 4 holes of 110mm diameter located at the mid-plane • From the magnetic point of view: • the case of the 4 holes of 110mm diameter seems to be acceptable because the reduction of the transfer function is lower than what we have for the MQXA (5.2%) and the Δb6 is a bit lower than the other cases. • we expect to be able to improve the field quality by modifying the cross section (see following slides) or directly in the iron

14. MQXC cross sections and iron yoke • Due to the presence of the holes and due to the slight changes in the cross-section designs (due to the multipoles optimization) the short sample parameters have to be re-computed The presence of 110mm holes at the mid-plane only reduces the short sample gradient by 0.2-0.5% • Transfer function of the 4 MQXC cross-sections The reduction of the transfer function of the 4 MQXC cross- sections is in between what we have for the MQXA and MQXB

15. MQXC cross sections and iron yoke • Multipoles after optimizing the coil blocks position • We tried to optimize the cross-sections to cancel the multipoles b6, b10 and b14: We didn’t manage to further reduce b10 and b14 • Multipoles b10 and b14 are almost insensitive to the iron saturation. • We have to try to reduce the multipoles by playing with the iron yoke

16. Conclusion I • We studied a first set of three designs of 110, 120 and 130mm apertures which almost reach the maximal short sample gradient expected • We first set the field quality constrain to 1 unit, expecting to further reduce the multipoles after yoking (by re-optimizing the cross-section) • Yoking: we studied the effect of the holes in the iron needed for the He flow. It seems that the best option from the integration point of view (four 110mm holes at the mid-planes) is acceptable from the magnetic point of view • We found that the short sample gradient is only reduce by ~0.5% when four 110mm holes are inserted at the mid-planes. • We tried to re-optimized the cross-sections to cancel the multipoles b6, b10 and b14 but we didn’t manage to reduce b14 below 0.7 units and b10 below 0.3 units. However we have not tried to play on the iron shape yet…remains to be done

17. Preliminarily designs for a possible second cables distribution

18. MQXC: NEW cross-sections • We are looking for some other designs in order to improve the field quality • Below is a possible second set of MQXC quads. It is just some preliminarily results, lot of work remains to be done. Under study! … • We still consider an iron yoke with 110mm hole located at the mid-plane • The reduction of the transfer function is still smaller than for the MQXA (5.2%). For the 110mm design (MQXC V16) it is even smaller than the MQXB 130mm 120mm (MQXC V15) 110mm (MQXC V16)

19. MQXC: NEW cross-sections • All the multipoles are very closed to zero (at least below 0.1 unit) at nominal current (80% of the short sample), but the short sample gradient is 2-3% smaller than the previous MQXC design

20. CONCLUSION iI • We studied a new set of possible MQXC cross-sections: 110, 120 mm • We managed to get a good field quality (all multipoles below 0.1 unit) at nominal current • The short sample gradients are 2 to 3% smaller than the first set of designs FUTURE WORK • Trying to reduce the multipoles in the first set of MQXC designs by playing with the yoke • Designing other cross-sections with new cables distributions