# Equilibrium and Stability of High-βPlasmas in Wendelstein 7-AS · •B = 0.9 T, iota vac ≈0.5...

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MCZ 041103 1

Equilibrium and Stability of High-β Plasmas in Wendelstein 7-AS

M.C. Zarnstorff1,A. Weller2, J. Geiger2, E. Fredrickson1, S. Hudson1, J.P. Knauer2, A. Reiman1,

A. Dinklage2, G.-Y. Fu1, L.P. Ku1, D. Monticello1, A. Werner2, the W7-AS Team and NBI-Group.

1Princeton Plasma Physics Laboratory2Max-Planck Institut für Plasmaphysik, Germany

IAEA Fusion Energy Conference 2004Vilamoura, Portugal

3 November 2004

MCZ 041103 2

Outline• β limits and sustainment in Wendelstein-7AS• Limiting mechanisms• Equilibrium & Stability properties• Conclusions

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W7-AS – a flexible experiment

5 field periods, R = 2 m, minor radius a ≤ 0.16 m, B ≤ 2.5 T, vacuum rotational transform 0.25 ≤ ιext ≤ 0.6

Flexible coilset:• Modular coils produce helical field

• TF coils, to control rotational transform ι

• Not shown: –divertor control coils–OH Transformer–Vertical field coils

W7-ASCompleted operation in 2002

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2025

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0.1 0.2 0.3 0.4Time (s)

n e

(102

0 m

-3)

P NB

P rad

Mirnov B.

(%)

Pow

er (

MW

)(A

.U.)

〈β〉 ≈ 3.4 % : Quiescent, Quasi-stationary〈β〉 ≈ 3.4 % : Quiescent, Quasi-stationary• B = 0.9 T, iotavac ≈ 0.5• Almost quiescent high- β phase, MHD-activity in early medium-βphase

• In general, β not limited by any detected MHD-activity.

• IP = 0, but there can be local currents

• Similar to High Density H-mode (HDH)

• Similar β>3.4% plasmas achieved with B = 0.9 – 1.1 T with either NBI-alone, or combined NBI + OXB ECH heating.

• Much higher than predicted βlimit ~ 2%

54022

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0

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0 20 40 60 80 100 120

peak flat-top avg.

(%)

τflat-top / τE

〈β〉 > 3.2% maintained for > 100 τE〈β〉 > 3.2% maintained for > 100 τE• Peak = 3.5%

• High-β maintained as long as heating maintained, up to power handling limit of PFCs.

• 〈β〉-peak ≈ 〈β〉-flat-top-avg⇒ very stationary plasmas

• No disruptions

• Duration and β not limited by onset of observable MHD

• What limits the observed βvalue?

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Reconstructed Self-Consistent EquilibriumReconstructed Self-Consistent Equilibrium

0

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2.5

1.7 1.8 1.9 2 2.1 2.2Major Radius (m)

Pre

ssur

e (1

04)

0

0.1

0.2

0.3

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0 0.2 0.4 0.6 0.8 1

Normalized minor radius

Rot

atio

nal T

rans

form

Fit

No current

• STELLOPT/VMEC design-optimization code adapted to be a free-boundary equilibrium reconstruction code: fit p & j profiles to match measurements

• Available data:– 45 point single-time Thompson scattering system– 19 magnetic measurements

• Reconstructed equilibrium of β=3.4% plasma : lower central iota, flatter profile

p iota

54022

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〈β〉 Sensitive to Equilibrium Characteristics〈β〉 Sensitive to Equilibrium Characteristics

• Achieved maximum β is sensitive to iota, control coil current, vertical field, toroidal mirror depth.

• At low iota, maximum β is close to classical equilibrium limit ∆ ~ a/2• Control coil excitation does not affect iota or ripple transport• Is β limited by an equilibrium limit?

Divertor Control Coil VariationIota Variation

53052-55

0 0.1 0.2ICC / IM

0

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2

3

(%)

0

1

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3

0.3 0.4 0.5 0.6

[%]

Vacuum Rotational Tranform

Axis shift �∆ ~ a/2

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Control Coil Variation Changes Flux Surface Topology

Control Coil Variation Changes Flux Surface Topology

ICC/IM = 0〈β〉 = 1.8%

ICC/IM = 0.15〈β〉 = 2.0%

ICC/IM = 0.15〈β〉 = 2.7%

• PIES equilibrium analysis using fixedpressure profile from equilibrium fit(not yet including current profile).

• Calculation: at ~ fixed β, ICC/IM=0.15gives better flux surfaces

• At experimental maximum β values -- 1.8% for ICC/IM =0-- 2.7% for ICC/IM = 0.15

calculate similar flux surface degradation

VMECboundary

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Degradation of Equilibrium May set β LimitDegradation of Equilibrium May set β Limit• PIES equilibrium calculations

indicate that fraction of good surfaces drops with β

• Drop occurs at higher β for higher ICC / IM

• Experimental β value correlateswith loss of ~35% of minor radius to stochastic fields or islands

• Loss of flux surfaces to islands and stochastic regions shoulddegrade confinement. May bemechanism causing variation of β. 0

20

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0 1 2 3

ICC / IM = 0.15ICC / IM = 0

β (%)

Exp.

Exp.

Frac

tion

of g

ood

flux

surfa

ces

(%)

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Pressure Driven Modes Observed, at Intermediate βPressure Driven Modes Observed, at Intermediate βX-Ray Tomograms

• Dominant mode m/n = 2/1.

• Modes disappear for β > 2.5% (due to inward shift of iota = ½?)

• Reasonable agreement with CAS3D and Terpsichore linear stability calcs.Predicted threshold β < 1%

• Does not inhibit access to higher β ! Linear stability threshold is not indicative of β limit.

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Low-mode Number MHD Is Very Sensitive to Edge Iota

Low-mode Number MHD Is Very Sensitive to Edge Iota

• Controlled iota scan,varying ITF / IM, fixed B, PNB

• Flattop phase

• Strong MHD clearly degradesconfinement

• Strong MHD activity only innarrow ranges of external

iota

• Equilibrium fitting indicates strong MHD occurs when edge iota ≈ 0.5 or 0.6 (m/n=2/1 or 5/3)

• Strong MHD easily avoided by ~4% change in TF current

Mirnov Ampl.(5-20kHz)

0

1

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0.3 0.4 0.5 0.6

(%)

Vacuum Rotational Transform

Mirnov A

mplitude (G

)

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High-n Instabilities Observed in Special SituationsHigh-n Instabilities Observed in Special Situations

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Mirnov B

PNB

Prad

.

(%)

Pow

er (

MW

)(A

.U.)

• Typical high-β plasmas are calculated to be ballooning stable. No high-n instabilities are observed.

• High-n instabilities are observed if Te drops below ~ 200eV. Probably a resistive instability.

• W7AS can vary the toroidal ripple or mirror ratio using ‘corner coils’ (I5)

• For I5 > IM, very unstable low-βphase, then spontaneous transition and rise to moderate β.

• In later β > 2% phase, plasma calculated to be in ballooning 2ndstability regime.How does it get there?

I5 / IM = 1.4

56337

δB=13.6%

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Unstable

StableStableStableStableStable

UnstableUnstable

UnstableUnstable

Access to 2nd Stability: Via Stable PathAccess to 2nd Stability: Via Stable Path

〈β〉 = 0.5% 〈β〉 = 1% 〈β〉 = 1.5% 〈β〉 = 2% 〈β〉 = 2.5%

ι′

p ′p′ p ′p ′p ′

• Local stability diagrams for infinite-n ballooning evaluated using technique of Hudson and Hegna. Plots shown for r/a = 0.7

• For 〈β〉 > 2%, plasma is calculated to be in second regime for r/a < 0.8

• Thomson pressure profile measurement is only available for 〈β〉 = 1.6%. Measured pressure profile shape was scaled up/down to evaluateother 〈β〉 values.

∴ 2nd stability to ballooning can be accessed on stable path, due toincrease of shear with β and deformation of stability boundary.

Exp.

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Conclusions• Quasi-stationary, quiescent plasmas with 〈β〉 up to 3.5% produced in W7-AS

for B = 0.9 – 1.1T, maintained for >100 τE

• Maximum β-value appears to be controlled by changes in confinement, not MHD activity– No disruptions observed– No stability limit observed. Maximum β not limited by MHD activity. – Maximum β much higher than linear stability threshold.– Maximum β correlated with calculated loss of ~35% of minor radius to

stochastic magnetic field. May limit β.

• Pressure driven MHD activity is observed in some cases– Usually saturates at ~harmless level. Why?– Strong when edge iota ≈ 0.5 or 0.6– Exists in narrow range of iota ⇒ easily avoided by adjusting coil currents.

• In increased mirror-ratio plasmas, calculations indicate second-stability for ballooning modes can be accessed via a stable path due to the evolution of the shear and stability boundary.

MCZ 041103 15

MCZ 041103 16

Magnetic Diagnostics are Sensitive to CurrentMagnetic Diagnostics are Sensitive to Current

-5

0

5

10

15

Cur

rent

den

sity

(A/c

m2)

Fit

Model: uniform Zeff

Model: hollow Zeff

0 0.2 0.4 0.6 0.8 1

Normalized minor radius• Small, but significant current inferred from equilibrium fit.

Estimated uncertainty of magnitude approx. ± 20% from Rogowski segments• Three moments used to fit current profile,

higher order moments used to force j(a)=0• Fitted current is larger (in outer region) than model calculations of net current

from beam + bootstrap + compensating Ohmic currents.

1.4

1.5

1.6

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-9

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-7

0 0.5 1 1.5 2Relative Current Magnitude

(10-

5 W

)(1

0-4

W)

Seg. 4

Seg. 3

measured

measured

simulated

simulated

Fit54022