1. Joint Institute for Nuclear Research Further optimization of the solenoid design A.Efremov, E.Koshurnikov, Yu.Lobanov, A.Makarov, A.Vodopianov GSI, Darmstadt, 05.03.2008

2. 2 Coil and yoke dimensions Barrel part 1490 mm < r < 2300 mm 60 mm + 11×30 mm + 60 mm steel; 12 gaps of 30 mm Upstream door Upper radius: -1970 mm < z < -1585 mm Lower radius: -1970 mm < z < -1734 mm Downstream door 2465 mm < z < 2865 mm 5×60 mm steel; 4 gaps of 25 mm Cryostat -1190 mm < z < 1900 mm Gaps between the coil and cryostat ends: 170 mm (upstream) and 155 mm (downstream) In ZEUS: both gaps are 150 mm

3. 3 Solenoid cross-section Side view

4. 4 Solenoid cross-section Top view

5. 5 Coil parameters Coil axial dimensions-1020 mm < z < 1745 mm Cable cross-section (without insulation) 3.4 mm × 24.6 mm Design current density54 A/mm 2 Subcoil turns in each of 2 layers225, 116, 211 Operation current5.1 kA Axial magnetic force (coil rated position) +99 kN Field inhomogeneity (coil rated position) ΔB/B < 1.8% Radial component integral (coil rated position) |I up | < 1.72 mm

6. 6 Magnetic flux density distribution The flux density in the upstream door is B < 1.7 T and the flux density near it in the downstream direction is B < 1 T.

7. 7 Magnetic flux density distribution

8. 8 Field homogeneity B 0 = 2T |δ| < 1.78%

9. 9 Radial component integral |I up | < 1.72 mm

10. 10 Dependence of parameters on the coil position ΔZ [mm]Fz [kN]ΔB/B [%] [mm] 0+99-1.78 ÷ 1.61-1.72 ÷ 1.39 -10+51-1.96 ÷ 1.66-1.52 ÷ 2.00 +10+148-1.60 ÷ 1.55-1.98 ÷ 0.75 Coil configuration is defined using our computer code

11. 11 Barrel part of the solenoid

12. 12 Impact of the cable passages across the barrel part of solenoid 800 x 60 mm 2 at the octagon corners both at the upstream and downstream barrel ends Axisymmetric model: use of effective magnetic permeability fill factor: S total and S steel – cross-sections of barrel beam and its steel part in the plane crossing the gaps perpendicular to Z The calculations are not sensitive to the place of the gap on this plane

13. 13 Impact of the cable passages across the barrel part of solenoid

14. 14 Impact of the cable passages across the barrel part of solenoid Gaps squareFz [kN]ΔB/B [%] [mm] No gaps+99-1.78 ÷ 1.61-1.721 ÷ 1.390 Gaps +10%+99-1.70 ÷ 1.71-1.716 ÷ 1.412 Gaps+100-1.69 ÷ 1.72-1.718 ÷ 1.418 Gaps -10%+101-1.68 ÷ 1.73-1.720 ÷ 1.423 The passages have small influence on the homogeneity and field integral in central region

15. 15 Solenoid front view

16. 16 Solenoid cross-section

17. 17 Stress-strain analysis downstream door, inner (first) plate Fixation schemeAxial displacement [m] ΔZ < 0.05 mm

18. 18 0 1 Stress-strain analysis downstream door (second plate) Axial displacement [m]

19. 19 Stress-strain analysis downstream door (second plate) Number of welded spacers Maximal bending deflection [mm] No spacers8.1 1 spacer1.1 3 spacers<0.2 Fixation scheme

20. 20 Stress-strain analysis downstream door (second plate) Equivalent stress (Von Mises) σ < 25 MPa Allowable value: [σ] = 140 MPa 3 welded spacers

21. 21 Stress-strain analysis upstream door The door consists of 8 steel plates of 30 mm thickness consolidated in a package Equivalent stress (Von Mises) σ < 3 MPa

22. 22 1 0 Stress-strain analysis upstream door Maximal axial displacement ΔZ < 0.5 mm

23. 23 Beam deformation in the cross-section Yoke barrel gravity load G = 2000 kN Maximal value of the deformation: u y = 1.5 mm, u x = ± 1 mm gravity load and Px = 0.25 G, Py = 0.18 G (seismic load) Maximal value of the deformation: u y = 1.6 mm, u x = 2 mm Maximal stress σ max = 35 MPaMaximal stress σ max = 50 MPa With outer frames

24. 24 Solenoid coil Al cylinder subcoil 1subcoil 2subcoil 3 subcoil solid Al Al with slits (for shear stress reduction) 25 mm

25. 25 Solenoid coil Shear stress at the subcoil end face  < 5 MPa 1 0 subcoil solid Al

26. 26 Solenoid general view

27. 27 Solenoid general view

28. 28 Solenoid general view

29. 29 Solenoid details

30. 30 Solenoid details

31. 31 Solenoid details

32. 32

33. 33 Yoke beam construction (old dimensions)

34. 34 Mechanical analysis Design criteria for the solenoid structural parts produced from metal alloys are chosen in accordance with “Codes of design to calculate the strength of equipment and pipe-lines of nuclear power plants” PNAE-G-002-86 and “Codes of strength calculations for high pressure vessels” (GOST 1429-89). Design criteria for the yoke and support frames include building norms and codes for steel constructions (Russian) and Eurocodes 3. Allowable membrane stress in a solenoid structural part in the normal operation regime has to be chosen as follows: where safety coefficients (safety margins) for the coil are and for the yoke are Allowable bending stress in a structural part in the normal operation regime has to be chosen as follows:

35. 35 Beam deformation in the cross-section Yoke barrel gravity load G = 2000 kN Maximal value of the deformation: u y = 4.3 mm, u x = ± 2.5 mm gravity load and Px = 0.25 G, Py = 0.18 G (seismic load) Maximal value of the deformation: u y = 5.8 mm, u x = 9.6 mm Maximal stress σ max = 115 MPaMaximal stress σ max = 140 MPa Without outer frames