MCZ 041103 1 Equilibrium and Stability of High- Plasmas in Wendelstein 7-AS M.C. Zarnstorff 1, A....
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Transcript of MCZ 041103 1 Equilibrium and Stability of High- Plasmas in Wendelstein 7-AS M.C. Zarnstorff 1, A....
![Page 1: MCZ 041103 1 Equilibrium and Stability of High- Plasmas in Wendelstein 7-AS M.C. Zarnstorff 1, A. Weller 2, J. Geiger 2, E. Fredrickson 1, S. Hudson.](https://reader037.fdocuments.us/reader037/viewer/2022110323/56649d6b5503460f94a4a4a2/html5/thumbnails/1.jpg)
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
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MCZ 041103 2
Outline• limits and sustainment in Wendelstein-7AS• Limiting mechanisms• Equilibrium & Stability properties• Conclusions
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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
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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%
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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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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 (
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
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MCZ 041103 7
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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MCZ 041103 8
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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MCZ 041103 9
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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MCZ 041103 10
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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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 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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MCZ 041103 12
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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MCZ 041103 13
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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MCZ 041103 14
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.
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MCZ 041103 15
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MCZ 041103 16
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