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