1. PEER Review of Coil Tolerances and Trim Coil Requirements plus Magnetic Material in Test Cell April 19, 2004 Art Brooks

2. Objective To demonstrate that the Tolerance Specification for the NCSX Coil systems in conjunction with the External Trim Coils provide reasonable assurance that the required Magnetic Field Quality can be attained.

3. Coil Tolerances Specifications The Coil Tolerance herein pertains to the location of the current center of the installed coils relative to the ideal/theoretical position: –Modular Coils +/- 1.5 mm (0.060 in) –PF Coils+/- 3.0 mm (0.120 in) –TF Coils+/- 3.0 mm (0.120 in) –Trim Coils+/- 3.0 mm (0.120 in) Tolerances are further allocated to limit tolerance buildup between various fabrication and assembly operations.

4. Trim Coil Current Specification 30 External Trim Coils are designed for 80 KAT max current – 8 turns at 10 KA Analysis of trim coil capability in suppressing islands assumes all 30 independent –Fewer independent circuits may be needed once coils are installed and field mapping reveals actual needs

5. Overview Coil Tolerances and Trim Coil Requirements are closely coupled. –Earlier work (Collected in the Field Error Source Assessment Notebook) showed that coil tolerances, while fairly tight from a fabrication and assembly point of view, could not alone assure required magnetic surface quality (less than 10% of magnetic flux lost to islands and stochastic regions) Trim Coils are needed even if Field Coils are manufactured and installed within spec. Trim Coils must also provide field correction from other potential sources of field error –Magnetic Material in Test Cell (Building Steel, NB magnets, etc) –Coil lead stems and turn transitions –Eddy Currents in structures, etc

6. Predicting Impact of Coil Tolerances Original work (Pre-PDR) added a differential field to an ideal field (VMEC LI383 Plasma) –Assumed Max (Design Limit) Currents in each coil –Systematic and Random Geometric Perturbations applied to Coils –VACISLD Code use to Estimate Island Size –TRACE Code use to verify island size by following field lines of net field in VMEC coordinates –SVD solution used to determine Trim Coil Currents needed to compensate Concerns: –Impact on boundary/volume unclear at high Trim Coil Currents –presence of zero shear near rational surface (6/9) near boundary Recent work looks at a vacuum configuration with iota crossing ½ near edge with small but non-zero shear –More appropriate for initial field line mapping –Less conservative – uses actual coil currents for a vacuum state

7. Review of Earlier Results and Methods Earlier Results Considered: –M45 Coils –LI383 Plasma –Used rated currents for coils (Worse Case) –Both Systematic and Random distribution of coil distortions and misalignment assumed. –Impact of Coil Location with respect to Plasma

8. Li383 Targeted Resonances Near 6/9 3/5 3/6 3/7 2/5 near axis not targeted

9. Island Width Evaluation used in VACISLD using VMEC data

10. Benchmark of Field Line Tracing of Perturbation Field* from Coils on VMEC Field PIES TraceBrtp *From 1 KA M5 Trim Coils

11. Impact of Tolerance Schemes on Modular, TF and PF

13. Update of Tolerance Study C08r00 Coils (aka M50_e04) M50_e04 Free Boundary VMEC Plasma Rated Coil Currents Coil Distortions Randomly Distributed 100 cases run Near Resonance, Near Zero Shear Islands smaller than M45/Li383 partly because of coil distance to plasma. M50 LI383

14. Suppressing Worse Case Islands from Random distribution of Coil Tolerances Large ½ Island Induced by coil tolerance Large ½ Island Suppressed, Max trim coil current = 20 KA* *Less Current Required if not targeting higher order modes

15. Impact on Placement of Individual Coils Each Individual Coils was displaced the full tolerance (1.5 mm Mod, 3.0 mm TF & PF) in each degree of freedom about a coordinate system located at its center Rated Currents were used Island Size relative to the M50_E04 S3 Plasma Configuration were calculated Results show sensitivity to positioning Can also be first step toward using positioning to improve fabrication tolerances

16. Islands Induced for Displacement of Individual Modular Coils

17. Islands Induced for Displacement of Individual Inboard PF Coils 1 - 3

18. Islands Induced for Displacement of Individual Outboard PF Coils 4 - 6

19. Islands Induced for Displacement of Individual TF Coils

20. Developing a Relevant Vacuum Configuration As Basis for Further Studies Need a Clean Vacuum Configuration (ie Full, Island Free) that crosses a significant resonance (ie iota=0.5) near edge using c08r00 coils Earlier efforts by A Georgievskij suggests adjusting TF and Vertical Fields to control iota Internal m=6 coils used to clean up 6,3 islands Field Line Tracing Compared to VMEC run –Good agreement suggest use of VACISLD and SVD to set external trim coil currents would be adequate.

21. Vacuum Field using S3 Coil Currents 3/6 Islands suppressed using Internal m=6 coils Vacuum Configuration for Assessing Impact of Coil Tolerances Overlay of VMEC Calculated iota=0.5 surface shows good agreement TF and PF Field Adjusted to control iota

22. Effect of TF and PF Field Changes on Vacuum Iota Profile

23. Tolerance Studies in Vacuum C08r00 Coils (aka M50_e04) Vacuum Free Boundary VMEC Plasma Consistent Vacuum State Coil Currents Coil Distortions Randomly Distributed 100 cases run Islands much larger than for S3 state primarily due to lower shear (0.075 vacuum vs 0.34 S3)

24. Suppressing Worse Case m=2 Islands from Random distribution of Coil Tolerances Large ½ Island Induced by coil tolerance Large ½ Island Suppressed, Max trim coil current = 13.5 KA No loss of LCFS

25. Determining Trim Coil Currents Needed to Suppress Induced Islands Current demands strongly impacted by resonances targeted –Low order modes require modest current –High order modes require excess current and will not be controllable by external trim coils Chart shows max current in external trim coil set needed to suppress assumed single field error of [B s /B  ] m,n = 1.e-4 –(for m=2,  ’=0.3,  s= 5% Flux) Significantly larger currents are required when suppressing multiple islands –Max Current grows to 20 KAT if targeting all blue, and to 60 KAT if 6,3 is included –Reducing Number of Independent Circuits (trim coils) may further increase currents.

26. Modeling Magnetic Material in Test Cell Chang Jun developed ANSYS model of the Test Cell Building Steel excited by PF Coils (main contributor to remote field). Portion of Building steel shown above. Air elements removed for clarity

27. Remote Field Magnetizes Building Steel which in turn produces Error Field at Plasma Field at Plasma ~ 10 Gauss, primarily vertical. If uncorrected, produces islands totaling ~5% of plasma flux. 2.5 KA in PF6 needed to compensate.

28. Additional Task Underway or Planned Evaluate impact of coil deformation under loads –Results to be extracted from Len Myatts structural model of Modular Coils – D Strickler, A Brooks Optimize final assembly position of Coils based on measured data following fabrication –D Strickler Evaluate impact of magnetic permeability deviations from spec (1.02) –C Jun Extract and Analyze filament models of Coils from ProE including all as designed turn transitions and lead stems. Do we need to combine all known sources of field errors to assess total impact?

29. Charge 1. Are the bases for the coil tolerance requirements complete? – Field errors from coil imperfections – Errors from fixed ferromagnetic material in building 2. Are the tolerance requirements well defined? – For mod coils – For TF and PF coils – For trim coils 3. Are the trim coil performance requirements (no., current, dI/dt, etc.) well defined? 4. Are additional analyses underway to investigate relaxation of tolerances, if needed, to address: – coil deflections from cooldown and magnetic loads – magnetic material in coil structures – coil position optimization 5. Are additional analyses planned to address final coil design, including actual crossover and lead geometry and location?