High operation in W7AS
A. Weller, J. Geiger (2001)
Maximum quasistationary (~ 3.0 %) in stellarators so far
the predicted stability limit < > = 2% is exceeded
almost quiescent high phase
magnetic well formation and inward shift of = 1/2 improves stability at high
no hard stability limit observed
I / 21
Resumee on plasma equilibrium and high operation
measured equilibria accord with theory
reduction of PScurrents by field optimization is confirmed
no deleterious MHD activity at high
no hard limit observed
the predicted limit has been exceeded in W7AS and LHD
I / 22
Neoclassical transport in stellarators
e.g.: Kadomtsev, Pogutse, Nucl. Fusion 11 67 (1971)
particle transport: div = div ( D dn/dr) = S
D = d2 diffusion coefficient (random walk)= collision frequency
d = displacement from fluxsurface between collisions (determined by particle drift incl. electric fields)
Stellarators:
at low collisionality (lmfpregime) d becomes very large for particles locally trapped in the helical ripple ( Bdrift)
the vertical Bdrift can be averaged out by a poloidal E x B drift
B x B |
B |
Er x B
Er
B
B |
passing |
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toroid. trapped |
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helically trapped
coordinate along B
I / 23
Neoclassical diffusivity
W7AS @ r = 10.1 cm |
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1/ |
Er/v [10 4 Vscm 2] |
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= 0, 1, 3, 10 |
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helically trapped
particles
PS
plateau
1/ |
banana (tokamak) |
2 |
[cm1]
icot ucrak lm raa k
H. Maaßberg
1/ regime (Er = 0):
D, ~ T2/ ~ T7/2
inhibits access to high T
stellarators require
inherent reduction of neoclassical transport
or a radial electric field
collisionality: * (v /R) with R/ = 600 cm |
I / 24 |
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First plasma results from the
Helically Symmetric eXperiment (HSX)
D. T. Anderson, Stell. Workshop, Madison (1999) |
D. T. Anderson, Stell. News, 76,1 (2001) |
QHS: quasihelical symmetry
Mirror: toroidal mirror by auxiliary coils
MonteCarlo Simulation |
Experiment |
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B = 0.5 T, PECRH = 50 kW @ 28 GHz |
Te ~ 1.5 keV
The radial electric field
H. Maaßberg, Phys. Fluids B, 5, 3627 (1993)
Er adjusts itself selfconsistently by the ambipolarity of (neoclassical) particle fluxes
e = i
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n |
q |
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E |
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T |
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= n |
D11 |
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r |
+ D12 |
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n |
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T |
T |
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(+ , external)
Te |
ne |
Ti |
r |
D = D(Er) multiple solutions
example: ECRH plasma
ne ~ 0Ti ~ 0 D12 >> D11
e = n D12e (E r) |
Te |
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Te |
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= n Di |
(E |
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i |
11 |
r |
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Ti |
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I / 26
Electric field pulsations in CHS
A. Fujisawa, 17th IAEA Fus. Conf., CN69/EX5/1 (1998)
Electric potential measured by „Heavy Ion Beam Probe“
the plasma bifurcates between two states of high and low potential
I / 27
Electric field bifurcations and
internal electron transport barrier in CHS
A. Fujisawa, Phys. Rev. Lett. 82 2669 (1999)
central potential (schemat.) |
potential distribution |
electron temperature |
transport
barrier transport barrier
bifurcated states of different electric potential exist at low collisionality
an internal electron transport barrier with reduced anomalous transport develops due to the ExB flow shear for the „dome“shape profile
I / 28
High electron temperatures in W7AS
M. Kick, Plasma Phys. Contr. Fus., 41A 549 (1999)
density scan at PECRH = 1.2 MW
improved central confinement
high central Te goes along with strong positive radial electric field
(electron root)
In this type of discharge:
Maximum Te (~ 7 keV) achieved in stellarators so far
1/n
dT/dr P / (n ) f (n)
I / 29
The electron root in W7AS
R. Brakel, Plasma Phys. Contr. Fus., 39B 273 (1997)
PECRH = 770 kW
improved central electron confinement
(Te(0) = 4 keV)
strong positive Er in the center
Er and e consistent with neoclassical prediction up to r/a 0.7
e strongly anomalous at the edge
I / 30