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The influence of non-resonant perturbation
fields Modelling results and Proposals for
TEXTOR experiments
S. Günter, V. Igochine, K. Lackner, Q. Yu IPP
Garching

• Resistive wall modes and error field
  amplification
• Error field amplification and plasma rotation
• Suppression of neoclassical tearing modes by
  external helical fields

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Ultimate limit to maximum ?N is external kink
mode
For optimised current profiles (avoid double low
order rational surfaces of same helicity)
nBwall 0
External kink mode can be stabilised by ideal
walls nBwall 0
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External kink mode in AUG advanced scenarios
Good agreement between theory and experiment
Closeness to rational qa destabilising
eigenfunction
Günter et al., NF 2000
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Stabilising influence of an ideal conducting wall

• Closed wall in distance rw from plasma can be
  strongly stabilising, especially for
• broad current and pressure profiles
• strong shaping of plasma cross section

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3d geometry of ideally conducting walls
CAS3D First code dealing with 3D wall and 3D
plasma
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Destabilising effect of wall resistivity RWMs
Garofalo et al., PRL 1999
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Simple model for RWMs and error field
amplification
Fitzpatricks (PoP 9(2002) 3459) analytical
(inertial layer) model
Instability drive of plasma mode increases
Plasma rotation
? stability parameter ?gt0 ideal kink mode
stabilised by infinitely conducting wall ?lt0 in
absence of rotation plasma is stable
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Effect of rotation for varying wall distance

• can be modified by
• - distance of wall (0 lt ? lt1) at given
  instability drive

ideal (plasma) mode unstable
detailed shape of marginal curve depends on
plasma (dissipation) model
torque balance between mirror current forces and
viscous drag (or inertia) determines mode
rotation frequency
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Effect of rotation for varying instability drive

• can be modified by
• - variation of the MHD instability drive at
  given wall distance

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Numerical treatment of RWMs anderror field
amplification

• In realistic geometry (coupling to internal
  resonances)
• MARS (Bondeson)
• VALEN (Bialek, Boozer)
• CASTOR-A (Holties, Kerner)
• - response to frequency dependent external
  perturbation field
• modified to include differential plasma
  rotation, viscosity
• resistive wall included (so far high resistivity
  only)

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Numerical results Error field amplification

• Here for comparison with simple analytical
  theory
• frequency dependent external (3,1) perturbation
  field (qa lt 3)
• no internal resonances, no viscosity

(torque onto plasma)
Change in plasma stability by varying distance of
ideally conducting wall
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Numerical results Error field amplification

• Here for comparison with simple analytical
  theory
• frequency dependent external (3,1) perturbation
  field (qa lt 3)
• no internal resonances, no viscosity

Maximum of absorbed power

-?W?2pl
Good agreement with analytical model for ideal
plasma (scan in wall distance)
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Numerical results Error field amplification

• Here for comparison with simple analytical
  theory
• frequency dependent external (3,1) perturbation
  field (qa lt 3)
• no internal resonances, no viscosity

Maximum of absorbed power
Good agreement with analytical model for ideal
plasma (scan in ?N)
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Numerical results torque on plasma
Torque on the plasma due to external error fields
Maximum torque
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Influence of error fields on plasma rotation
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Experiments on error field amplification on JET
59223
Saddle currentA
NB due to low field Bt1T and high NBI w/walfven
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3.4li bN()
PNBIMW
Signal which sees no vacuum (or low bN) pick-up
clearly rises as bN approaches ideal limit
br(0o)
br(90o)
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Influence of error fields on plasma rotation
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Proposals for error field amplification
experiments on TEXTOR comparisons with theory

• Frequency dependence in error field
  amplification
• discharges with qalt3 (and qagt3 for comparison),
  low li
• scan in ?N/plasma rotation within one discharge,
  measure (3,1) amplitude increase compared to
  vacuum case
• repeat for different frequency of antenna
  current
• comparison with code calculations possible
• Influence of error fields on plasma rotation
• compare torque onto plasma with theory (with and
  without q3 surface) for different coil current
  frequencies and plasma pressures

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Proposals for resistive wall mode experiments
on TEXTOR

• Develop scenarios with external (3,1) RWM mode
• vacuum vessel rw/a 1.35, ?w 14 ms
• try to stabilize RWM by rotating external (3,1)
  perturbation fields
• (compare required rotation velocity with theory)

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Physics of neoclassical tearing modes (NTMs)
Helical current parallel to plasma current drives
magnetic islands unstable
Magnetic islands driven by the loss of bootstrap
current inside island
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Interaction of NTMs with different helicity
No simultaneous large NTMs of different
helicities
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Stabilising effect of additional helical field
For finite perpendicular heat conductivity
helical field perturbation reduces BS current
perturbation caused by single magnetic island
Contour plots of BS current perturbation
Single magnetic island with external
perturbation field
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Stabilization of NTMs by external error fields
DIII-D suppression of (3,2) NTM onset
successful, but strong reduction in
plasma rotation observed
n3 perturbation field
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Stabilization of NTMs by external error fields

• On TEXTOR rotating perturbation fields possible
• (3,2) NTM stabilization by external (3,1) fields

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Stabilization of NTMs by external error fields

• On TEXTOR rotating perturbation fields possible
• NTM stabilization by external (3,1) fields for
  qa lt 3
• if perturbation field too small use conditions
  with error field amplifications
• Influence plasma rotation by external fields,
  study effect on NTM stability

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Conclusions

• Rotating external perturbation fields of a
  single helicity opens new possibilities for MHD
  experiments on TEXTOR
• error field amplification experiments,
  comparison with theory
• - frequency dependence of error field
  amplification
• - influence on plasma rotation
• Resistive wall mode studies
• Stabilization of NTMs by external perturbation
  fields

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Newcomb criterion
Cylindrical plasma pointing vector into vacuum
region - ??ra For zero growth rate (ok for
RWMs) it describes the energy released from
plasma from infinitely slow perturbation (no
energy converted to kinetic energy)
r(?0) closer to plasma the larger ?ra (the
more unstable the smaller r(?0)
more unstable
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Error field amplification influences plasma
rotation
Error field amplification ? reduced plasma
rotation ? RWM growth
Strait et al., IAEA 2002
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Critical Rotation Scaling
Strait et al., IAEA 2002