Coil Concept and Design for NCSX
S. P. Hirshman, June 3, 1999
on behalf of the NCSX coil team
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
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
C82 Coil Reference Design: Critical Goals
• Physics– Maintain QA-ness (NC transport) and kink
stability at < = 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)
c82 Coil Design Process
PlasmaBoundary
NESCOIL
SVD Scan: Min (jmax)
Plasma-Coil Sep.(18 cm.)
Choose Candidate Coil Contours
Genetic Algorithm: Select Optimum Subset of Coils
Engineering Constraints jmax, coil-coil separtion
Reconstruction
“Fine Tuning”
Coil Designers MUST Serve Two Masters
PHYSICS ENGINEERING
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
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
Emergence of c82 Candidate Coil Designs
(all designs: <a> = 42 cm, 18 cm. plasma-coil separation, B = 1.2 T)
C82 Case Description Coils Per Jmax Berr -% Surface Deviation Kink Eigenvalue QA-ness measureID Period (kA/cm**2) (ave., max) cm (av., max) (/Target value) (chi-sq/chi-sqTarget)
RECONSTRUCTION INFO --> 121 Equal Current 26 14.7 .95, 7.0 .47, 2.1 9 1.5 (s=.5), 1.0 (s=.8)
A. Brooks: Hand Tuning
4064 Lo-Jmax 20 11.9 1.2, 6.3 3.3, 8.9 (--------)EF-10% adjusted VF 1.0, 3.8 5 2.0 (s=.5), 1.3 (s=.8)
4321 Target Jmax 20 15.8 .95, 5.0 .73, 2.6 6 1.5 (s=.5), 1.1 (s=.8)
Latest GA Lo-# coils 16 14.4 1.1, 4.8"Miner" Miracle (further reduction anticipated)
C82 26-coil/period Design
Coil Cutting Developments
• Rapid Singular Value Decomposition– (SVD) scanning for Valanju minima of 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
Jmax reduction comparison c82 vs. c93
c82.f88 svd scan (Berr target)Best at 121: Berr=0.6%, Jmax=.83
0.8316
0.2
0.4
0.6
0.8
1
1.2
100 110 120 130 140
number of svd weights kept out of 144
0.8
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2<Berr>
jMax
c93.f1010 svd scan (Berr target)Best at 196: Berr=0.22%, Jmax=.81
0.2
0.25
0.3
0.35
180 190 200 210 220
number of svd weights kept out of 220
0.8
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2<Berr>
jMax
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
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
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
Restoration of Kink Stability (cont’d)
• Physics identified significance of matching indentation and “wings” at v=– 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
Genetic Algorithm: Cutting Discrete Coils for c82
• GA: an efficient way to find an optimized subset of coils– pick Ncoil coils out of Ncontour contours (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)
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...
Genetic Algorithm for Coil SelectionDiscrete 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.
Toroidal angle / (2)
Poloidal angle / (2)
Genetic Algorithm for Coil Selection (initial zero weighting on Jmax)
Generation = 0001
Berror = .0090
Jmax = (coils too close to estimate…)
Genetic Algorithm for Coil Selection (lowest Berror state with coils)
Generation = 0236
Berror = .0041
Jmax =
Genetic Algorithm for Coil Selection (weight on Jmax turned on)
Generation = 1003
Berror = .0120
Jmax = est.
Genetic Algorithm for Coil Selection
Generation = 1025
Berror = .0079
Jmax = est.
Genetic Algorithm for Coil Selection
Generation = 1127
Berror = .0122
Jmax = 18.69
Genetic Algorithm for Coil Selection
Generation = 1105
Berror = .0119
Jmax = 18.37
Genetic Algorithm for Coil Selection
Generation = 1318
Berror = .0095
Jmax = 20.68
Genetic Algorithm for Coil Selection
Generation = 2795
Berror = .0090
Jmax = 20.47
Genetic Algorithm for Coil Selection (first big decrease in Jmax)
Generation = 3043
Berror = .0120
Jmax = 11.78
Genetic Algorithm for Coil Selection
Generation = 4001
Berror = .0123
Jmax = 11.86
Genetic Algorithm for Coil Selection
Generation = 4064
Berror = .0123
Jmax = 11.85
Genetic Algorithm for Coil Selection(decreased weighting of Jmax)
Generation = 4074
Berror = .0095
Jmax = 15.78
Genetic Algorithm for Coil Selection (final moderate jmax state)
Generation = 4321
Berror = .0094
Jmax = 15.75
Reconstruction for Low jmax c82(EF-10, VF correction):
kink restabilization likely
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
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
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
Vacuum Field Line Plots from fixed boundary
Vacuum Field Line Plots from d18.3.121.16 coil set with re-optimized currents
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.)
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
Coil Designers SUCCESSFULLY Serve Two
Masters
PHYSICS ENGINEERING