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

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

  • 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

  • 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 ≤ 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

  • MCZ 041103 4

    0

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    05

    10

    15

    2025

    0

    1

    2

    0

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    4

    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

  • MCZ 041103 5

    0

    1

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    4

    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?

  • MCZ 041103 6

    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 (1

    04)

    0

    0.1

    0.2

    0.3

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    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 β=3.4% plasma : lower central iota, flatter profile

    p iota

    54022

  • MCZ 041103 7

    〈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

    1

    2

    3

    (%)

    0

    1

    2

    3

    0.3 0.4 0.5 0.6

    [%]

    Vacuum Rotational Tranform

    Axis shift �∆ ~ a/2

  • MCZ 041103 8

    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

  • MCZ 041103 9

    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

    40

    60

    80

    100

    0 1 2 3

    ICC / IM = 0.15ICC / IM = 0

    β (%)

    Exp.

    Exp.

    Frac

    tion

    of g

    ood

    flux

    surfa

    ces

    (%)

  • MCZ 041103 10

    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.

  • MCZ 041103 11

    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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    1.5

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    2.5

    0.3 0.4 0.5 0.6

    (%)

    Vacuum Rotational Transform

    Mirnov A

    mplitude (G

    )

  • MCZ 041103 12

    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%

  • MCZ 041103 13

    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.

  • MCZ 041103 14

    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

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    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

    1.7

    -9

    -8

    -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