1. 1 R D Pillsbury Sherbrooke Consulting, Inc. OPERA Analyses of the In-vessel Coils for the IDR In-Vessel Coil System Intermediate Design Review – 26 - 28 July, 2010

2. Contents What’s New Comparison of CDR and IDR IVCs Nomenclature Normal Operating Force – EOB Assumptions for the OPERA Analyses OPERA Model Forces on IVCs During Normal Operation Typical Eddy Current Patterns Induced Currents During Disruptions Forces on IVCs During Disruptions Issues and Resolutions Summary Backup –Comparison of IVC DC Forces At Maximum Current to Spatial Variation –Impact of Plasma Disruption Model on Currents in IVCs –Impact of Toroidal Flux Driver of Poloidal Currents in VV –Induced Currents in the Vacuum Vessel During a Disruption –2007 Plasma Disruption Scenarios –Comparison of 2007 and 2010 MD_UP Disruption Scenario –Plasma Models –Impact of Blanket on IVC Induced Currents (Modified Alternate Design) –Impact of Blanket on IVC Disruption Forces (Modified Alternate Design) In-Vessel Coil System Intermediate Design Review – 26 - 28 July, 2010 2

3. What’s New Positions of the IVCs have changed slightly – except for VS_UP which has moved a significant distance – see next figure. Maximum VS current stayed at 60 kA (240 kA-t). ELM Coils went from 4 turns at 23.5 kA to 6 turns at 15 kA (94 kA-t versus 90 kA-t). The conductor has changed significantly – R/l (Ohm/m) has about doubled – implications for the IVC current decay during the slow drift phases of the disruptions. IVC Feeder routing has changed. New disruption scenarios have been posted. In-Vessel Coil System Intermediate Design Review – 26 - 28 July, 2010 3

4. 4 Comparing CDR (purple) and IDR(red) The most significant difference is the position of the upper VS coil The other coils have only minor perturbations.

5. IVC Force Nomenclature In-Vessel Coil System Intermediate Design Review – 26 - 28 July, 2010 5 There are 36 20-node bricks in a sector. Forces are output at 2 points per VS and 10 - 12 points per ELM. Summation reduces these to 1 point per VS and 8 per ELM. Forces are provided in Cartesian coordinates and in local coordinates U – radial – into or outward from the VV, V – bursting, W - shear

6. PF and ELM Coil Currents In-Vessel Coil System Intermediate Design Review – 26 - 28 July, 2010 6

7. 7 Maximum Leg Force Magnitudes During Normal Operation (EOB) COIL LegCDR |F| (N) IDR |F| (N) VS_UP 1,087,207 381,519 VS_DN 1,295,501 1,152,627 ELM_DN_BOT 378,852 340,856 2 ELM_DN_LFT 298,633 258,377 2 ELM_DN_RHT 304,296 262,099 2 ELM_DN_TOP 423,028 393,116 2 ELM_MD_BOT 327,356 294,637 5 ELM_MD_LFT 785,900 697,772 5 ELM_MD_RHT 788,347 700,642 6 ELM_MD_TOP 332,249 306,742 6 ELM_UP_BOT 424,960 385,279 7 ELM_UP_LFT 256,980 250,991 7 ELM_UP_RHT 252,753 247,446 7 ELM_UP_TOP 333,599 298,618 7

8. In-Vessel Coil System Intermediate Design Review – 26 - 28 July, 2010 8 Maximum Leg Force Magnitudes During Normal Operation (EOB)

9. Assumptions in OPERA Modeling of Plasma Disruptions 1/9 th rotational symmetry of all coils and structure is assumed. Poloidal ribs are included. Blanket modules, support beam, divertor rail, and divertor are omitted. All conducting structures have an electrical conductivity of 1350 Siemens/mm. PF and TF Coils at fixed currents at End-of-Burn. Plasma disruption events are 2007 models. Plasma modeled by 25 - 30 coaxial solenoids with currents “turning on” and “turning off” to simulate motion and current decay. One run w/ 100 solenoids. For comparison w/ CDR no toroidal flux drive. One case run w/. IVCs are shorted at the start of the plasma disruption events. IVC structure and feeders are not included in the eddy current model. Induced currents in the IVC Feeders do not contribute to VV eddy currents. Maximum IVC current for normal operation 60 kA (VS) & 15 kA (ELM) In-Vessel Coil System Intermediate Design Review – 26 - 28 July, 2010 9

10. OPERA 3D Models In-Vessel Coil System Intermediate Design Review – 26 - 28 July, 2010 10 VS ELM CDRIDR

11. OPERA 3D Models In-Vessel Coil System Intermediate Design Review – 26 - 28 July, 2010 11

12. Induced Current in IVCs During the Three Disruption Scenarios In-Vessel Coil System Intermediate Design Review – 26 - 28 July, 2010 12 VDE-DNMDVDE- UP IVCs start at their current maxima and are shorted at time t=0 VS Coils are connected in a saddle (anti-series) configuration.

13. Currents Induced in the VS During a VDE- DN Disruption – 36 ms Linear Decay – CDR & IDR In-Vessel Coil System Intermediate Design Review – 26 - 28 July, 2010 13

14. Eddy Currents in the Vacuum Vessel – Vertical Disruption Down (36 ms linear Current Decay) In-Vessel Coil System Intermediate Design Review – 26 - 28 July, 2010 14

15. Eddy Currents in the Vacuum Vessel – Major Disruption Up (36 ms linear Current Decay) In-Vessel Coil System Intermediate Design Review – 26 - 28 July, 2010 15

16. Typical Eddy Currents in the Structure In-Vessel Coil System Intermediate Design Review – 26 - 28 July, 2010 16

17. Typical Eddy Currents in the Structure In-Vessel Coil System Intermediate Design Review – 26 - 28 July, 2010 17

18. Maximum Forces on the IVC For EOB and Across Three Disruption Scenarios In-Vessel Coil System Intermediate Design Review – 26 - 28 July, 2010 18

19. Summary IVC geometry is close to the CDR except for VS_UP DC Leg forces are similar to the CDR except for VS_UP IDR vessel currents induced by 2007 disruption events have not changed appreciably from the CDR The increased IVC resistance impacts the peak currents and forces during the disruption events ELM coil forces appear to be driven by the scenario (normal operation) and the VS driven by the disruption. In-Vessel Coil System Intermediate Design Review – 26 - 28 July, 2010 19

20. Issues and Resolution Plan In-Vessel Coil System Intermediate Design Review – 26 - 28 July, 2010 20 IssueResolution Pre/Post October Modeling of Blanket, Divertor, Support Beam, etc. Update model post-IDR. Generate new OPERA FEA modelPre Appropriate PD ScenariosGenerate new PD models and rerun OPERAPre Feeder ForcesGenerate new model from CATIA files. Use OPERA to calculate forces. Pre Due DiligenceFEA mesh/time step/plasma model sensitivityPre Appropriate Initial Conditions/ Model of IVCs During a Disruption Seek guidance from other groupsPre Assess impact of different PF currents and off-normal events Two fold approach. (1) Quasi-static analyses (no induced eddy currents in the cold-structure). (2) New disruption scenarios or use existing scenarios with different PF currents. Pre

21. Backup In-Vessel Coil System Intermediate Design Review – 26 - 28 July, 2010 21

22. ELM COIL CURRENTS In-Vessel Coil System Intermediate Design Review – 26 - 28 July, 2010 22 Flux Density vs. Toroidal Position at Plasma Boundary ELM Coil current versus toroidal angle

23. Comparison of EOB Forces from Spatial Variation of ELM Coil Currents with Maximum Possible In-Vessel Coil System Intermediate Design Review – 26 - 28 July, 2010 23

24. Comparison of EOB Forces from Spatial Variation of ELM Coil Currents with Maximum Possible In-Vessel Coil System Intermediate Design Review – 26 - 28 July, 2010 24

25. COMPARISON OF 25 and 100 Element Models of the MD_UP (36 ms linear decay) In-Vessel Coil System Intermediate Design Review – 26 - 28 July, 2010 25

26. Impact of Toroidal Flux Drive on VV Currents In-Vessel Coil System Intermediate Design Review – 26 - 28 July, 2010 26

27. 2007 VDE-UP Linear Decay In-Vessel Coil System Intermediate Design Review – 26 - 28 July, 2010 27

28. 2007 VDE-DN Linear Decay In-Vessel Coil System Intermediate Design Review – 26 - 28 July, 2010 28

29. 2007 Major Disruption – Linear Decay In-Vessel Coil System Intermediate Design Review – 26 - 28 July, 2010 29

30. Comparison of 2007 and 2010 Disruptions (MD_UP 36 ms linear decay) In-Vessel Coil System Intermediate Design Review – 26 - 28 July, 2010 30

31. 2007 Plasma Model of a VDE - UP with linear current decay Rc (mm)Zc(mm)a(mm)I (MA)t(ms) 6232.7 567.011994.5015.00000.0 6231.6 582.111996.5015.000010.0 6208.6 901.852016.3015.0590625.0 6105.41211.901915.5015.0650715.0 6026.51540.601804.8015.0470775.0 5949.21878.701697.3015.0500825.0 5760.52000.101675.6015.8150827.5 5729.42095.001643.7015.0310830.5 5701.52188.701608.9014.2620832.4 5658.42297.301567.8013.4800834.3 5625.52418.901530.3012.6930836.2 5585.52543.401485.6011.9180838.0 5519.72661.601441.4011.1030840.0 5487.82782.801402.4010.3040841.9 5433.82881.001354.00 95.115843.8 5416.12989.301297.80 87.580845.7 5364.23107.601229.20 79.800847.6 5328.43208.301154.00 72.276849.4 5283.83314.601091.00 64.598851.2 5252.43412.301002.00 57.008853.0 5198.43527.80914.010 49.234854.9 5153.23665.40810.669 41.442856.8 5116.63765.30707.70 33.752858.6 5041.83919.90546.40 25.928860.5 4974.44070.00373.2818.190862.3 4921.64220.40582.6510.657864.1 4800.94452.50319.582.9215866.0 In-Vessel Coil System Intermediate Design Review – 26 - 28 July, 2010 31

32. Plasma Model of a VDE - DN with linear current decay Rc (mm)Zc(mm)a(mm)I (MA)t(ms) 6232.7567.011994.515.0000.0 6234.6548.171992.015.00010.0 6230.0227.301923.314.930490.0 6203.8-105.421850.114.764580.0 6121.7-444.541760.814.787620.0 6057.6-806.311605.514.642645.0 5863.0-1088.41498.115.460651.7 5860.0-1081.31507.616.247653.0 5866.2-1078.71502.115.488654.6 5763.9-1395.61386.014.889656.4 5714.3-1514.01330.314.107658.2 5684.6-1621.51277.413.332660.1 5631.7-1711.51219.612.550662.0 5602.2-1797.21183.911.797663.8 5572.2-1886.41133.311.044665.6 5539.8-1972.21087.810.275667.4 5496.5-2094.11031.09.5102669.3 5482.7-2156.2976.368.7259671.2 5437.7-2257.0906.847.9468673.0 5414.7-2378.3825.487.1945674.9 5370.8-2495.8716.906.4198676.7 5356.8-2637.8636.775.6392678.5 5305.4-2772.4523.254.8663680.4 5257.4-2864.9416.044.0985682.1 5230.6-2988.6334.423.3317684.1 5176.5-3198.6742.542.5449686.0 5070.0-3311.0628.671.7935687.8 4995.3-3537.0478.851.0349689.6 4996.3-3860.2271.490.323691.3 5506.7-4419.255.260.022565693.1 In-Vessel Coil System Intermediate Design Review – 26 - 28 July, 2010 32

33. 2007 Plasma Model of a MD with linear current decay Rc (mm)Zc(mm)a(mm)I (MA)t(ms) 6232.7567.071994.5150 6232.7567.071994.5151 5907.4579.781916.415.0648.2 5903.7563.341921.815.849.1 5850.7524.091861.715.08613.7 5825.8535.561824.514.30115.5 5810.5539.961786.713.52517.4 5788.9546.621747.812.73219.3 5763.5577.361704.911.97221.1 5742.2658.051676.811.19423 5688.5982.721653.910.42324.9 5651.51301.11592.69.930126.1 5591.71613.71522.19.361427.5 5544.81941.31444.68.689129.1 5461.22254.31361.18.035830.6 5380.12553.31264.37.283132.4 5327.22719.51172.86.494134.3 5277.12914.61062.75.714336.2 5200.63096.7943.64.932938.1 5156.63234811.54.158839.9 5076.93433.2669.463.382141.8 5017.13647.2488.632.593943.7 4934.33854.6266.581.804445.5 4843.64063.2632.471.042447.4 4735.64340.4346.010.285249.2 In-Vessel Coil System Intermediate Design Review – 26 - 28 July, 2010 33

34. In-Vessel Coil System Intermediate Design Review – 26 - 28 July, 2010 34 Comparison of IVC Induced Currents for the Alternate Design w/ and w/o the Blanket – VDE UP

35. In-Vessel Coil System Intermediate Design Review – 26 - 28 July, 2010 35