1. Analysis of TF Load Paths and Vacuum Vessel Loading H. M. Fan Jan. 22, 2009

2. Upper PF1A Lower PF2 Upper PF1B Lower PF1B Upper PF1C Lower PF5 Upper PF3 Lower PF4 Upper PF2 Lower PF3 Upper PF5 Lower PF1C Upper PF4 Lower PF1A OH Outer TF coil Inner TF coil TF and PF Coils

3. Outer TF Coil Supports Tension only tie rod Flexible TF coil Ring bar Al block assembly Flexible TF coil Al block assembly Outer TF leg is supported by umbrella structure, tie rod, ring bar and vacuum vessel The ring bars and tie rods may reduce the in- plane and out-of-plane forces at the umbrella structure

4. CoilTurnsFillMin Curr Max Curr Usage Worst Case Current (kA)(kA-Turn)(kA)(kA-Turn) (kA) OH5150.6283-24.0-12348.024.012348.0-24 PF1a280.7000-4.0-112.028.0784.0128 PF1b100.7000-8.0-80.012.0120.0112 PF1c100.7000-12.0-120.020.0200.0120 PF2a140.74090.0 20.0280.0120 PF2b140.74090.0 20.0280.0120 PF3a150.6928-16.0-240.08.0120.0-16 PF3b150.6928-16.0-240.08.0120.0-16 PF4b80.7525-20.0-160.08.064.0-20 PF4c90.6723-20.0-180.08.072.0-20 PF5a120.7689-32.0-384.00.0 -32 PF5b120.7689-32.0-384.00.0 -32 PFAB1480.5613-48.01.048.011 PFAB2480.5613-48.01.048.011 Max. and Min. Upgraded PF Coil Currents

5. TF=71.16, OH=-20, PF1a=-11.35, PF2=-16.93, PF3=-18.83, PF4=-10.73, PL=1000 TF=130, OH=-24, PF1a=-4, PF1b=-8, PF1c=-10, PF2=0, PF3=-16, PF4=-20, PF5=-32, PL=0 F  = 12177 lbs Reactions of Outer TF Leg w/wo Upgrade Fz = 42664 lbs F  = 48793 lbs Fr = 42628 lbs 50347 lbs 32615 lbs 0 lbs 32615 lbs 0 lbs 6285 lbs Fz = 11617 lbs Fr = 13969 lbs 2130 lbs 6285 lbs 0 lbs 6285 lbs 0 lbs Note: For the upgrade coil currents, forces in the ring becomes compression. compressiontension No PF5

6. Radial Displacement of Ring Bar Decides the Ring Force – For Currents without Upgrade At ring, the radial displacement is 0.114 mm

7. At ring, the radial displacement is -0.613 mm Radial Displacement of Ring Bar Decides the Ring Force – For Currents with Upgrade

8. ItemForce Without current upgrade Upgrade A - with tension- only tie rods Upgrade A - w/o rings and tie rods Upgrade A - w/o rings Upgrade A - move ring 7” toward midheight Upgrade B - tension and comp. tie rods Reactions atFrlb-13,969-42,628-66,248-30,638-46,778-47,352 Al block FF lb-12,177-48,793-80,169-52,817-52,228-45,929 Fzlb-11,617-42,664-22,504-55,081-41,558-38,548 Ratios ofFrlb1.003.054.742.193.353.39 Reactions FF lb1.004.016.584.344.293.77 Fzlb1.003.671.944.743.583.32 Reactions atFrlb-1,199-28,354 -24,685-33,008-1,827 tie-rods FF lb-1,678-39,672 -34,539-41,661-43,354 Fzlb-530-12,530 -10,909-511-807 Totallb2,13050,347N/A43,83353,15543,400 Axial forcesFrlb00 00 at ring bar FF lb6,285-32,615 -50,14625,946 Fzlb00 00 Totallb6,28532,615N/A 50,14625,946 Negative force mean compression Force is mainly in vessel plane Structural Responses to Ring and Tie Rod Variations Note – The results above are responses of upper Aluminum block, ring bar and tie rod.

9. PF2aFzlb00 PF2bFzlb00 PF2 total lb00 PF3aFzlb80,904 PF3bFzlb-13,248 PF3 total lb67,655 PF4cFzlb83,602 PF4bFzlb10,130 PF4 total lb93,732 PF5aFzlb161,783 PF5bFzlb-193,781 PF5 total lb-31,999 Vertical Reactions of PF2 to PF5 Coils

10. Vacuum Vessel Model 90° cyclically symmetric model All ports with covers Not include TF coils, but the TF loadings were applied on the umbrella structure and the vacuum vessel Not include PF coils, but the PF loadings were applied on the PF support brackets Weight of TF and PF coils are also included.

11. Dead LoadsVacuum Loads Max. stress in support leg Max. stress Von Mises Stress Plots excluding Umbrella Structure

12. EM Loads EM, Vacuum and Dead loads Max. stress

13. Summary of Vacuum Vessel for Upgraded Loads Loads Dmax. (m) Max. Seqv (Pa) Dmax. (in) Max. Seqv (ksi) Max. stress location EM0.004005.94E+080.15786.16 near mid- height Vacuum0.000537.47E+070.02110.84 NB port DL0.000332.68E+070.0133.89 near leg support EM, Vac., DL0.004195.81E+080.16584.28 near mid- height Max. stress was found at the edge of port opening

14. Summary EM load is the most crucial load case in the vacuum vessel design. Because of symmetry in the EM load, ring bar can be used to reduce the in-plane load caused by the outer TF legs. Tie rod can minimize the deformation of the ring bar and take the out-of- plane loading without causing bending moment in the vacuum vessel. Provide struts between upper and lower PF4 and PF5 coils will effectively restrain the PF vertical force to the vacuum vessel. The highest stress was found at the welded joint area between vacuum vessel and port, the allowable stress for welding should also be checked. In the FEA model, the cross-sectional area of ring bar and tie rod is 4.0 in 2 and 1.0 in 2, respectively. Other design considerations may include but not limit to: 1.Modify dimension and location of the ring bar and tie rod 2.Improve the outer TF leg stiffness 3.Reinforce the vacuum vessel 4.And ………..