MCZ 041103 1

Equilibrium and Stability of

High- Plasmas in

Wendelstein 7-ASM.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 2004

Vilamoura, Portugal

3 November 2004

MCZ 041103 2

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

MCZ 041103 3

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 ≤ ext ≤ 0.6

Flexible coilset:• Modular coils produce helical field

• TF coils, to control rotational transform

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

W7-ASCompleted operation in 2002

MCZ 041103 4

0

1

2

3

4

0

5

10

15

20

250

1

2

0

1

2

3

4

0.1 0.2 0.3 0.4Time (s)

ne

(102

0 m

-3)

PNB

Prad

Mirnov B.

P

ow

er

(M

W)

(A.U

.) ≈ 3.4 % : Quiescent, Quasi-stationary ≈ 3.4 % : Quiescent, Quasi-stationary

B = 0.9 T, iotavac ≈ 0.5

Almost quiescent high- phase, MHD-activity in early medium- phase

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

IP = 0, but there can be local currents

Similar to High Density H-mode (HDH)

Similar >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 limit ~ 2%

54022

MCZ 041103 5

0

1

2

3

4

0 20 40 60 80 100 120

<> peak <> flat-top avg.

<>

(%

)

flat-top / E

> 3.2% maintained for > 100 E > 3.2% maintained for > 100 E

• Peak <> = 3.5%

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

• -peak -flat-top-avg very stationary plasmas

• No disruptions

• Duration and not limited by onset of observable MHD

• What limits the observed value?

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Reconstructed Self-Consistent EquilibriumReconstructed Self-Consistent Equilibrium

0

0.5

1

1.5

2

2.5

1.7 1.8 1.9 2 2.1 2.2Major Radius (m)

Pre

ssur

e (

104)

0

0.1

0.2

0.3

0.4

0.5

0.6

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 =3.4% plasma : lower central iota, flatter profile

p iota

54022

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Sensitive to Equilibrium Characteristics Sensitive to Equilibrium Characteristics

• Achieved maximum is sensitive to iota, control coil current, vertical field, toroidal mirror depth.• At low iota, maximum is close to classical equilibrium limit ~ a/2• Control coil excitation does not affect iota or ripple transport• Is limited by an equilibrium limit?

Divertor Control Coil Variation Iota Variation

53052-55

0 0.1 0.2

ICC / IM

0

1

2

3

<>

(%

)

0

1

2

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 = 1.8%

ICC/IM = 0.15 = 2.0%

ICC/IM = 0.15 = 2.7%

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

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

• At experimental maximum 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 LimitDegradation of Equilibrium May set Limit• PIES equilibrium calculations indicate that fraction of good surfaces drops with

• Drop occurs at higher for higher ICC / IM

• Experimental value correlates with loss of ~35% of minor radius to stochastic fields or islands

• Loss of flux surfaces to islands and stochastic regions should degrade confinement. May be mechanism causing variation of 0

20

40

60

80

100

0 1 2 3

ICC / IM = 0.15ICC / IM = 0

Exp.

Exp.

Fra

ctio

n o

f g

oo

d f

lux

surf

ace

s (%

)

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Pressure Driven Modes Observed, at Intermediate Pressure Driven Modes Observed, at Intermediate X-Ray Tomograms

Dominant mode m/n = 2/1.

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

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

Does not inhibit access to higher ! Linear stability threshold is not indicative of 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 degrades confinement

• Strong MHD activity only in narrow 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

2

3

0

0.5

1

1.5

2

2.5

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

0

1

2

0

10

20

30

0

1

2

3

4

0.1 0.2 0.3 0.4 0.5Time (s)

Mirnov B

PNB

Prad

.

P

ow

er

(M

W)

(A.U

.)

• Typical high- 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- phase, then spontaneous transition and rise to moderate .

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

I5 / IM = 1.4

56337

B=13.6%

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

= 0.5% = 1% = 1.5% = 2% = 2.5%

pp ppp

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

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

• Thomson pressure profile measurement is only available for = 1.6%. Measured pressure profile shape was scaled up/down to evaluate other values.

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

Exp.

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

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

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

stochastic magnetic field. May limit .

• 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

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Magnetic Diagnostics are Sensitive to CurrentMagnetic Diagnostics are Sensitive to Current

-5

0

5

10

15

Cur

rent

den

sity

(A

/cm

2)

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

1.7

-9

-8

-7

0 0.5 1 1.5 2

Relative Current Magnitude

(10-

5 W

)(1

0-4 W

)

Seg. 4

Seg. 3

measured

measured

simulated

simulated

Fit54022