1. NSTX TF outer leg analysis Because the stress on umbrella structure is too high, there are some ideas to reduce it, like adding a case to enhance the stiffness of TF coil, adding a ring to constrain the expansion and adding tie bars to constrain the movement. (KA) Parameters: ss case ring Tie bar

2. NSTX Coil Model ss Al 6061 blocks are fixed, the reaction force is calculated to approximate the force to umbrella structure. Welded solid bar (5*5”), tube may be better. 1. Materials of case, ring and tie bar are all ss. 2. Different lengths, positions and orientations are calculated.

3. Result 1 (plasma curr=0A) r: radius direction; theta: out-of-plane direction; z: center stack direction case no case (plasma curr=0A) adding case (0.5" thick ss, 12" wide) Additionally, adding ring (0.5*12" in rect, welded) Additionally, adding tie bar (3*3” rect, pin connected) Total end reaction force (kN) (the ends of Al6061 blocks are fixed and reaction force is here) 297296275253 End reaction force r (kN)245.71246.08237.88215.33 End reaction force theta (kN) out-of-plane 166.49164.18137.52127.95 End reaction force z (kN)11.9568.51212.93734.467 coil stress Von Mises (Mpa)187169111103 S r (Mpa)15914394.692.4 S theta (Mpa) out-of-plane5044.630.733.2 S z (Mpa)89.28988.387.8 Old parameters: 1. ss case doesn’t help to reduce the force. 2. Rings and tie bars have some effect on force reduction. Then different positions of rings and different orientations of tie bars are further studied.

4. Result 2 (plasma curr=0A) r: radius direction; theta: out-of-plane direction; z: center stack direction Ring at height of PF4 link to vacuum vessel case no case (plasma curr=0A) adding case (0.5" thick ss, 12" wide) adding straight ring (0.5*12" in rect, welded) adding tie bar (3*3 in rect, pin connected) Total end reaction force (kN)297296260257 End reaction force r (kN)245.71246.08218.75218.71 End reaction force theta (kN)166.49164.18137.65130.58 End reaction force z (kN)11.9568.512129.67631.391 max coil stress Von Mises (Mpa)187169117103 S r (Mpa)15914310292.6 S theta (Mpa) out-of-plane5044.636.733.3 S z (Mpa)89.2898887.7 max shear stress between coil and case S r-theta (Mpa)35.826.4 S theta-z (Mpa)57.920.3 S r-z (Mpa): coil length direction 65.325.2 Old parameters:

5. r: radius direction; theta: out-of-plane direction; z: center stack direction Ring at height of PF3 link to vacuum vessel: bar1, 2 and 3 have different directions, see following pictures. case no case (plasma curr=0A) adding case (0.5" thick ss, 12" wide) adding straight ring (0.5*12" in rect, welded) adding bar1 (3*3 in rect, pin connected) adding bar2 (3*3 in rect, pin connected) adding bar3 (3*3 in rect, pin connected) Total end reaction force (kN) 297294269239249224 End reaction force r (kN)245.71245.96223.2212.98 225192.09 End reaction force theta (kN) 166.49161.03149.95105.98 105.95106.05 End reaction force z (kN)11.95610.310.15519.366 9.254444.565 max coil stress Von Mises (Mpa) 18716013786.3 86 S r (Mpa)15913711860.5 63.551.7 S theta (Mpa) out-of- plane 5043.837.625.9 25.8 S z (Mpa)89.28988.787.8 87.6 max shear stress between coil and case S r-theta (Mpa)8.526.328.4 1851.8 S theta-z (Mpa)16.626.716.7 18.616.7 S r-z (Mpa): coil length direction 43.5 45.433.329.929

6. Ring at height of PF3 with different tie bar orientations 0.1m (~4”) bar 1 bar 2 bar 3

7. Result 3 (plasma curr=0A) r: radius direction; theta: out-of-plane direction; z: center stack direction case no additional support (plasma curr=0A) middle ring 2 rings 2 rings and horizontal bar 1 middle ring and - 25º oriented bar welding bar Total end reaction force (kN) 297274237225212186 End reaction force r (kN)245.71-230.49-177.57-148.25-155.65-126.6 End reaction force theta (kN) Out-of-plane force 166.49-146.87-143.77-143.52-120.91-92.256 End reaction force z (kN)11.956-18.119-64.298-89.967-78.6-100.87 Total bar end reaction force (kN) 65.3777034 bending moment (N- m) bar end reaction force r (kN) -65.377-55.82215.883539.61 bar end reaction force theta (kN) 0.00-33.054-16.805-2415.1 bar end reaction force z (kN) 0-25.15824.543-1029.9 See following pages for these cases. Significant reduction in the force. Old parameters:

8. Coil deflection without additional support Coil deflection at this position is not very high and thus adding rings here will not help very much. Adding ring in the middle will change the deflection shape and then adding another ring to further constrain the coil.

9. Adding ring in the middle will change the deflection shape and then adding another ring to further constrain the coil. (2 nd and 3 rd column in the result 3 table) Adding ring in the middle (2 nd column in the result table) Coil deflection Adding 2 rings to constrain the coil (3rd column in the result table)

10. Adding 2 rings and some pinned bars to further constrain the coil. (4 th and 5 th column in the result 3 table Adding pinned bars to constrain the coil (4 th column in the result table) Adding pinned bars to constrain the coil (5th column in the result table) Horizontal bar 25º oriented bar

11. Result 4 (plasma curr=0A): similar to result 3 but with updated parameters r: radius direction; theta: out-of-plane direction; z: center stack direction min current (extreme negative current) case no case (plasma curr=0A) middle ring 2 rings 2 rings and straight bar welding bar Total end reaction force (kN) 411345325315210 End reaction force r (kN)-253.71-230.49-183.13-152.85-130.34 End reaction force theta (kN) Out-of-plane force -322.77-256.61-260.75-260.05-128.34 End reaction force z (kN)13.63-17.851-65.538-92.048-103.55 bar end reaction force (kN)67.51788 bending moment (N-m) bar end reaction force r (kN) -67.51716.682736.1 bar end reaction force theta (kN) 0.00-82.127-2494 bar end reaction force z (kN) 025.527-5212.8 See last page for the position of rings and bars. Significant reduction in the force. Updated parameters: TF=129.7,OH=-24,PF1a=-4, PF1b=-8, PF1c=-12, PF2a=0, PF2b=0, PF3a=-16, PF3b=-16, PF4b=-20, PF4c=-20, PF5a=-32, PF5b=-32,PFab1=-1, PFab2=-1,plasma=0 unit: KA

12. ss Al 6061 blocks are fixed Welded solid bar (5*5”), tube may be better. Coil deflection Fixing a section of the coil tightly will help to reduce the force at the Aluminum block, the closer the fixed point to the Aluminum block, the more reduction on the force. Welding bar