Equilibrium and Stability of High-βPlasmas in Wendelstein 7-AS · •B = 0.9 T, iota vac ≈0.5...
Transcript of Equilibrium and Stability of High-βPlasmas in Wendelstein 7-AS · •B = 0.9 T, iota vac ≈0.5...
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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
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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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⟨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%
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⟨β⟩ > 3.2% maintained for > 100 τE⟨β⟩ > 3.2% maintained for > 100 τE
• Peak <β> = 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
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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
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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
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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
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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
<β>
Mirnov Ampl.(5-20kHz)
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High-n Instabilities Observed in Special SituationsHigh-n Instabilities Observed in Special Situations
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.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 2nd
stability 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.
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Magnetic Diagnostics are Sensitive to CurrentMagnetic Diagnostics are Sensitive to Current
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Model: hollow Zeff
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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.
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