D esign of 16 T Cos θ bending dipole

1. Design of 16 T Cosθ bending dipole Riccardo Umberto Valente G.Bellomo, B.CAIFFI, P.Fabbricatore, S.Farinon, s.MARIOTTO, A.Pampaloni, A. M. RICCI, M. Sorbi, M. Statera

2. Overview Electromagnetic design • Design requirements • Ironyokeoptimization • Asymmetric coil configuration • 3D coil-ends design Mechanical design • Cold mass parameters • Mechanicalcostraints • Contactpressure & Von Misesstressesanalysis EuroCirCol meeting FCC 16T cos-theta dipole

3. Review of the first draft of the FCC CDR (May ‘18) Field quality requirements: • Collision: • Max variation due to iron saturation: , To reduce mutual influence of the two apertures (): • Inter-beam distance: from 204 mm to 250 mm • Iron yoke diameter: from 600 mm to 660 mm To keep the magnet compatible to LHC tunnel • Cold mass diameter: from 740 mm to 800 mm EuroCirCol meeting FCC 16T cos-theta dipole

4. Symmetric configuration - rectangular window Interbeamdistance 250 mm Δb2= 35 units Yokediameter 660 mm EuroCirCol Annual meeting 2018 FCC 16T cos-theta dipole

5. Symmetric coil configuration - Iron yoke to reduce Δb2 110 mm 40 mm 56.6 mm 45° Δb2 =from 35 units to 7 units b2 offset = -35 units 47.4 mm Interbeamdistance: 250 mm EuroCirCol meeting FCC 16T cos-theta dipole

6. Symmetric coil configuration - problems • There’s no chance of an improvement in b2 modifying only the iron shape • Bladder & keys technology requires flat interfaces between iron and steel pads Solution Breaking left-right symmetry in each cos-theta aperture Flatinterfaces EuroCirCol meeting FCC 16T cos-theta dipole

7. Asymmetric configuration - coil arrangement Left-right symmetrybroken Wedge: 0.86 mm Wedge: 0.74 mm EuroCirCol meeting FCC 16T cos-theta dipole

8. Asymmetric configuration – field quality Δb2 = 5.5 units Δb3 = 2.2 units EuroCirCol meeting FCC 16T cos-theta dipole

9. 3D coil ends – field quality Computation method: the integrated harmonics of an arbitrary short model has been projected on , using the following formula End of yoke EuroCirCol meeting FCC 16T cos-theta dipole Courtesy of A.M. Ricci

10. Coil end – 3D peak field • The analysis of peak field and field quality shows that the longer the coil end is the better it is. • 3D mechanics must be checked. EuroCirCol meeting FCC 16T cos-theta dipole Courtesy of A.M. Ricci

11. Mechanical design – cold mass • An iron wall with a pole shape was introduced between the two apertures to reduce range • The pole has been re-disigned in order to accomodate a common loading plate for all the 4 layers to garatuee a uniformcontact pressure • The thickness of the aluminum shell was reduced from 70 mm to 50 mm and an additional pre-compressed steel shell20 mm thick was added. Outer steelshell 20 mm thick Aluminum ring 50 mm thick Ironyoke Ø 660 mm Asymmetric coils Steel pad Titaniumloadingplate EuroCirCol meeting FCC 16T cos-theta dipole

12. Mechanical design - constraints • No detachment between coil and pole • Stress in conductor • Room temperature (RT), < 150 Mpa • Cryo temperature (1.9 K), < 200 Mpa • Stress in mechanicalstructurebelowyieldstrenght (seeTab.) Lorentzforces In cos-theta configuration, Lorentz forces push the coil: • Outward in the radial direction • Toward the midplanein the azimuthal direction EuroCirCol meeting FCC 16T cos-theta dipole

13. Contact pressure & VM stresses on conductor gap 2 µm Assembly Cool down Energization EuroCirCol meeting FCC 16T cos-theta dipole

14. VM stresses on mechanicalstructure - assembly Steel shell Titanium pole VM stresses the color scale isnormalized on maximum acceptable VM stresses (seeTab.) Aluminum ring Ironyoke Steel pad localized hot spots under the keys, whereplasticizationoccurs EuroCirCol meeting FCC 16T cos-theta dipole

15. VM stresses on mechanicalstructure – cool down Steel shell Titanium pole VM stresses the color scale isnormalized on maximum acceptable VM stresses (seeTab.) Aluminum ring Ironyoke Steel pad Stressesbelow the threshold EuroCirCol meeting FCC 16T cos-theta dipole

16. VM stresses on mechanicalstructure – energization Steel shell Titanium pole VM stresses the color scale isnormalized on maximum acceptable VM stresses (seeTab.) Aluminum ring Ironyoke Steel pad Stressesbelow the threshold EuroCirCol meeting FCC 16T cos-theta dipole

17. Conclusions • An ironinsertwith a particular pole shapeisintroducedbetween the apertures to reduce the range, during the allcurrenttrasient • An asymmetric coil configurationhasbeenoptimized to compensate the cross-talkingbetween the apertures, according to the copperwedgedistancelimit of 0.7 mm • The fieldqualitysatisfiesanyconstraints, in factboth and are within 5.5 unitsat injection and not far from zero atcollisionenergy • The bore field of 16 T isachieved keeping the work point on Load Line below the limit of 86% asrequired • 3D coil endsdesign satisfiesfieldquality and peakfieldconstraits, evenifmechanics must be checked • The VM stresses on conductorsare alwaysbelow the limitsduringassembly, cool down and energization • Thereisalwayscontact pressure between coils and pole, apart from verylocalizedregionafter the energization • The stress on mechanicalstructureisalwaysbelow the threshold, apart from verylocalized hot spots under the keyswhereplasticregimoccurs EuroCirCol meeting FCC 16T cos-theta dipole

18. Thankyou for the attention