Coil Concept and Design for NCSX

1. Coil Concept and Design for NCSX S. P. Hirshman, June 3, 1999 on behalf of the NCSX coil team

2. NCSX Coil Team Members • Art Brooks, Don Monticello and Neil Pomphrey • Princeton Plasma Physics Laboratory • Coil cutting, plasma reconstruction (VMEC, PIES), Flexibility (Curopt) • William (“Buff”) Miner, Jr. and Prashant Valanju • Fusion Research Center • The University of Texas at Austin • SVD current optimization, GA coil cutting • Steve Hirshman • Oak Ridge National Laboratory • Logistical support

3. Coil Design Activity for NCSX • Identification of critical design goals • Physics, engineering constraints • Development of computation tools • Advanced algorithms (Gen.Alg., CurOpt) • Application to c82 preliminary design • status of target criteria and coil topology • Flexibility and start-up considerations

4. C82 Coil Reference Design: Critical Goals • Physics • Maintain QA-ness (NC transport) and kink stability at <b> = 4% for reconstructed surfaces • Engineering (maintain reconstructability) • limit jmax < 15 kA/cm2 at |B| = 1.2T (RBT = 1.65) • reduce number of coils (cost) • maximize coil-to-coil separation (machining)

5. c82 Coil Design Process NESCOIL SVD Scan: Min (jmax) Plasma-Coil Sep. (18 cm.) Plasma Boundary Choose Candidate Coil Contours Engineering Constraints jmax, coil-coil separtion Genetic Algorithm: Select Optimum Subset of Coils “Fine Tuning” Reconstruction

6. Coil Designers MUST Serve Two Masters ENGINEERING PHYSICS Coils MUST be kink stable! too kinky to build!

7. Progress Toward Candidate NCSX Coils • At Previous PAC • current sheet solutions - looked promising • discrete coils reconstructed for an impractically large number (> 30) per period • current density acceptable for c10 • plasma-coil minimum separation was NOT uniformly maintained by winding surface

8. NCSX Candidate Coils (cont’d) • Present Status: • finite coil designs (< 30 per period) for c82 • Designs exist with 16 - 20 coils (per period) • “Good” reconstruction of flux surfaces • jmax < 15 kA/cm2 (< 12 in some cases -> improved flat top, high |B|) • winding surface - plasma distance (18 cm) • improved kink-stability in reconstructions

9. Emergence of c82 Candidate Coil Designs (all designs: <a> = 42 cm, 18 cm. plasma-coil separation, B = 1.2 T)

10. C82 26-coil/period Design

11. Coil Cutting Developments • Rapid Singular Value Decomposition • (SVD) scanning for Valanju minimaof jmax • eliminate small eigenvalues resulting from Least Squares fit of B-field • NESCOIL current sheet: basis for discrete coils • Reconstruction recovery of kink stability • the Pomphrey tweak • Genetic Algorithm • application to cutting discrete coils

12. Jmax reduction comparison c82 vs. c93

13. Reconstruction with c82 Coils • Geometric reconstruction • NESCOIL -> coils -> VMEC (free-bdy) -> surfaces: assess displacement from target • Physics reconstruction • Calculate of kink stability, QA-ness • PIES reconstruction (in progress) • Existence of 3D flux surfaces • basis for stability/transport calculations

14. Geometric Reconstruction • c82 case 121 (26 coils/period) • started from lowest Valanju minimum • SVD weights retained = 121 • very low displacement error • reconstruction: looks “good” to the eye • jmax (14.7 kA/cm2) even lower than target requirement

15. Physics Reconstruction for c82 (121/26 coils) • Quasi-Axisymmetry is well-maintained • Kink is initially unstable • Restoration of Kink Stability • An example of synergy between the physics and the coil groups • the Pomphrey tweak

16. Restoration of Kink Stability (cont’d) • Physics identified significance of matching indentation and “wings” at v=p • Outboard pusher/puller coils were modestly re-energized (by 10%) to recover kink stability • Application suggests a viable experimental knob for “tweaking” the plasma configuration

20. Genetic Algorithm: Cutting Discrete Coils for c82 • GA: an efficient way to find an optimized subset of coils • pick Ncoilcoils out of Ncontourcontours (obtained from NESCOIL, where Ncoil << Ncontour) • contour selection based on minimizing physics and engineering criteria: • Berror, Jmax, minimum coil-to-coil separation • rapid 2D analysis tool (cf. 3D ONSET)

21. C82 Coil Cutting: A Slide Show • The following slide show demonstrates the GA application for coil-cutting • first, locate Berror minimum (may be global) • vary weights on Jmax • obtain optimized low and moderate current states • This “chromosome quartet” is composed in B. Miner...

22. Genetic Algorithm for Coil Selection Discrete Potential Contour Evolution Initial conditions: Current sheet Berror = .2% 98 coils generated from 60 contour levels. GA selects the “optimal” 20 coils per period which yield a joint minimum in Berror and Jmax. Poloidal angle / (2p) Toroidal angle / (2p)

23. Genetic Algorithm for Coil Selection (initial zero weighting on Jmax) Generation = 0001 Berror = .0090 Jmax = (coils too close to estimate…)

24. Genetic Algorithm for Coil Selection (lowest Berror state with coils) Generation = 0236 Berror = .0041 Jmax =

25. Genetic Algorithm for Coil Selection (weight on Jmax turned on) Generation = 1003 Berror = .0120 Jmax = est.

26. Genetic Algorithm for Coil Selection Generation = 1025 Berror = .0079 Jmax = est.

27. Genetic Algorithm for Coil Selection Generation = 1127 Berror = .0122 Jmax = 18.69

28. Genetic Algorithm for Coil Selection Generation = 1105 Berror = .0119 Jmax = 18.37

29. Genetic Algorithm for Coil Selection Generation = 1318 Berror = .0095 Jmax = 20.68

30. Genetic Algorithm for Coil Selection Generation = 2795 Berror = .0090 Jmax = 20.47

31. Genetic Algorithm for Coil Selection (first big decrease in Jmax) Generation = 3043 Berror = .0120 Jmax = 11.78

32. Genetic Algorithm for Coil Selection Generation = 4001 Berror = .0123 Jmax = 11.86

33. Genetic Algorithm for Coil Selection Generation = 4064 Berror = .0123 Jmax = 11.85

34. Genetic Algorithm for Coil Selection (decreased weighting of Jmax) Generation = 4074 Berror = .0095 Jmax = 15.78

35. Genetic Algorithm for Coil Selection (final moderate jmax state) Generation = 4321 Berror = .0094 Jmax = 15.75

36. Reconstruction for Low jmax c82(EF-10, VF correction):kink restabilization likely

37. NCSX Start-up:Coil Issues • Three “distinct” plasma states that coils must be capable of supporting • Vacuum start-up • zero current, zero beta • Start of flattop • full current, low beta • End of flattop • full current, full beta: reference design point

38. NCSX Flexibility:Coil Issues • Coils must have flexibility to produce • good vacuum surfaces • in spite of low iota, resonances => stochasticity • good surfaces at reference state • kink, QA-ness assessed assuming good surfaces • kink stability and confinement for a range of profiles (pressure, current) around the reference state

39. Tools for Start-up Assessment • In Vacuum • Cary-Hanson code (resonance suppression) • AVAC • In Vacuum or Finite Beta • Couple Curopt code (Brooks and Pomphrey) to output from PIES- get internal (plasma) |B|mn spectrum, not just on surface - and target specific resonances for suppression • Determine whether c82 coils have the re-quired flexibility to restore plasma volume

40. Vacuum Field Line Plots from fixed boundary

41. Vacuum Field Line Plots from d18.3.121.16 coil set with re-optimized currents

42. Tools for Robustness (flexibility) Assessment of c82 • Curopt code • couple with physics group to analyze stability, QA-ness of neighboring states as pressure, current profiles vary • compute currents in fixed c82 coils that most nearly generate these desired states • repeat standard reconstruction analysis • Free boundary VMEC analysis (Mike Z.)

43. Future Tasks for Coil Group • Finish c82 low J, low coil number calculations • Look at c93: even lower J possible => greater experimental flexibility • Work with physics, experimental teams to formulate flexibility, start-up implications for coils

44. Coil Designers SUCCESSFULLY Serve Two Masters ENGINEERING PHYSICS C82 COILS Low Jmax! kink stable at 4%