Small to midsized stellarator experiments:

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Small to mid-sized stellarator experiments topolo
gy, confinement, and turbulence
Jeffrey H. Harris Research School of Physical
Sciences Engineering Australian National
University University of Sydney 6 October
2004
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Outline of talk

• Fusion energy toroidal plasma confinement
• Stellarators
• Rational magnetic surfaces
• Stability
• Confinement scaling
• Turbulence

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• Fusion reactions
• Many reactions
• Energy production
• Synthesis of heavier nuclei
• Primordial physics
• Use on earth for low-emissions electricity

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Generic magnetic fusion reactor

• Challenges
• Heat to ignition with rf (MHz) and microwaves
  (GHz)
• Confinement physics (magnetics,stability,
  turbulence)
• Steady-state heat flux on wall   5 MW/m2
  (?materials!)
• Diagnosis, feedback control

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Basic plasma physics

• Ionized gas that is charge neutral over Debye
  scale length
• ?e (kTe/ne 2) 10-2 mm
• Behaves as fluid and as particles.
• Larmor gyration in magnetic field
• rL VT/ ?c
• ?c eB/m

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Toroidal magnetic confinement

• Toroidal magnetic field
• BT µ0I/2pR
• Vertical drifts lead to charge separation
• Vd (m /e RB T)(v 2v ?2 /2)
• and destroy confinement
• Poloidal field component adds twist (rotational
  transform) compensates drift.
• tokamak (toroidal current)

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Worldwide effort to make fusion reactors
economically viable

• Confinement of plasma energy ? reactor size
• Factors 2-5 critical
• "Improved confinement" modes
• Underlying physics of turbulence
• Advances in physics gt reduce size
• ITER
• Eliminate plasma current
• ?stellarator
• External helical fields 3-D
• LHD (Japan)-4 m
• Wendelstein-VII-6 moperates 2008
• Huge endeavors, staff in hundreds
• ? Need (and room) for agile fundamental research
  ? role for Australia

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Progress toward fusion In the last 20 years,
experiments have advanced orders of magnitude in
fusion confinement parameters and are now in the
reactor regime. D-T experiments in the Joint
European Torus produced 16 MW of neutrons for 1
s. Reactor p 1 atm ? p/(B2/2?0) 5
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H-1NF Heliac from concept to experiment

• Magnet coils structure designed by PRL,
  fabricated by RSPhysSE mechanical workshop
• Req'd precision of coils 2 mm

Computed
Measured w/ electron beams
Major radius 1 m Plasma minor radius 0.2 m
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Magnetic field lines in sheared toroidal
confinement geometry (tokamak) show complex
topology
q 2 m/n ?? 0.5 rational surface
Schussman et al, UC-Davis/General Atomics
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Geometrically resonant fields break rational
surfacesHamiltonian dynamics and chaos
healed equilibrium with good surfaces
NCSX expt (under constr)
2cm
coil adjustment to remove resonant fields (not
to scale)
original equilibrium with islands and chaos
Stuart Hudson (ANU PhD) Princeton Univ.
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What is a small-medium stellarator?

• Plasma minor radius lt 20 cm, B 2 T
• Aspect ratios gt 5 in present generation
• 2? larger in overall size than sm-med tokamak
• historical inflation of definition!
• Heating power kw to few MW
• ECH, ICH, NBI
• Ohmic heating current used mainly to trim
  transform
• Quiet, stable operation ideal for high precision
  expts
• small stellarators in particular toroidal Q
  machines
• Density constrained by power, not disruptions,
  runaways
• Flexibility in collisionality (but beware
  neutrals)
• Astonishing variety of non-axisymmetric coils
• This talk how these expts combine to contribute
  to physics base

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Magnetic configurations vary in detail
-
Torsatron/heliotron (well shear- 0.2-0.3 ?
lt 1-1.5) CHS (1 m), TJ-K (0.6 m), U-2M, L-2M ?
LHD (4 m) big!
Highly optimized W7X (helias) big ! NCSX (low
R/a) QPS (low R/a)

• Common features
• helically rippled fields (which one must never
  forget)
• transform from average of helical fields and/or
  torsion

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What do they look like?
H-1 Australian National Univ. R 1 m
HSX Univ. of Wisconsin (USA) R 1.2 m
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Magnetic topology features ? resonances
-

• Confinement in low-shear stellarators has long
  shown resonant dependence on ? n/m
• Optimum confinement in gaps adjacent to
  low-order resonances

-

• Not simply due to magnetic islands
• Obtains even at very low ?

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Empirical heat diffusivity model reproduces
effects
Brakel et al, NF 42, 903 (2002)
RTP model

• Physical mechanism at resonances
• local MHD activity, turbulence?

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Transform scan in H-1 heliac at low ICRF power
(60 kW)

B
navg
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Coherent density fluctuations in QHS (U.
Wisconsin)

• Quasi-helical symmetry

D. Brower et al
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QHS fluctuation fast-electron driven GAE mode?
Global Alfven Eigen mode unstable if 1.
Ve,nonthermal VAlfvén 2. fdia gt f
GAE Dispersion Parallel wave number Alfvén
speed Density, mass dependence check in
expt Calculations by D. Spong (ORNL)
suggestive
small near resonance !
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NBI (MW) driven Alfven instabilities in W7-AS ?
active in ramp-up when density lower
J. Geiger et al, Fusion Technology, Sept. 2004
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Alfven activity in H-1 heliac w/ 60 kW ICRF?

• Alfven bursts sensitive indicator of p(r)
  behaviour at resonances ?

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Resonances in reversed shear DIII-D tokamak
plasmas

• JET Alfven cascade signals improved
  confinement at resonant qmin
• In low-? or advanced stellarators, only p(r)
  evolves
• Sheared flow/E modifies xport near resonances?

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TJ-II (Madrid) islands ? shear in parallel flow
Er

• Island is local confinement zone
• Generates E, flow, turbulence, etc
• K. Shaing, Phys. Plasmas 9, 3470 (2002)
• non-axisym. ? ambipolar Er
• K. Ida et al, LHD, NF 44, 290 (2004)
• E. D. Volkov et al, Uragan-3
• TJ-II posters PS 168-183, Thurs. 1500

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Heliotron-J (Kyoto U.) edge config. determines
conf. transitions

• Small chgs in topology move configuration in/out
  of optimum window.
• Wall connection-interaction crucial see also
  W7AS HDH mode
• Radial electric field?
• Related LHD expts S. Morita

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Magnetic island studies in WEGA (IPP-Greifswald)
6 kW ECH, in various schemes B 875 G (for
minutes) New effort looking at island plasma
behaviour flows, turbulence etc.

• M. Otte K. Horvath

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Stochastic island layer controls ELMs in DIII-D
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MHD equlibrium at high plasma pressure
W7-AS A. Weller

• Shafranov shift of axis with increasing pressure
  ? magnetic well
• Shift reduced by factor 2 by optmisation of
  orbits, P-S currents

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MHD interchange instabilities are not disruptive
. . . . . . and become less unstable
with increasing ?
See also results CHS, LHD, ATF (moderate
shear)
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Purely pressure driven instabilities are not
violently disruptive
a truly small experiment
W7AS Interchange
Rayleigh-Taylor
Tolerance for confinement experiments in somewhat
unstable conditions!
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Diverse configurations ? common confinement
scaling . . .but with configuration
renormalization
IEA Stellarator Committee Scaling Study