M J Schaffer, T'E' Evans,

1
PRELIMINARY STUDY OFITER CORRECTION COILSFOR
ELM SUPPRESSION

• by
• M J Schaffer, T.E. Evans,
• General Atomics
• R A Moyer1, P R Thomas2, M Bécoulet2,
• Y Gribov3, V A Chuyanov3
• 1UCSD
• 2CEA Cadarache
• 3ITER
• Presented at the 45th APS-DPP Annual Meeting
• Jülich, Germany
• 2005 March 1517

2
Why Suppress ELMs?

• ELMs are driven by a combination of large
  pressure gradient and current density at the edge
  of H-mode plasmas.
• ELMs are beneficial
• For a slight confinement penalty, ELMs halt the
  unchecked density increase (hydrogenic and
  impurity) that leads to radiative termination of
  pure H-mode.
• ELMs are damaging
• In a large tokamak like ITER, Type-1 ELMs release
  so much plasma energy in such a short time, that
  they would ablate divertor target material.
  Calculated target lifetime is unacceptably short.
• Suppression of Type-1 ELMs is considered a
  necessary ITER goal.
• Suppression must function over the range of ITER
  plasma parameters without serious degradation of
  confinement.
• ELM suppression has been achieved by weak
  externally-applied magnetic perturbations in some
  DIIID regimes and is being studied.

3
ITER-Shape Plasmas in DIIID are 1/3.6 ITER Size
ITER Correction Coil Set is Scaled by the Same
Ratio for Modeling
ITER Correction Coils (Scaled to DIII-D)
DIII-D with DIII-D Perturbation Coils (I- and
C-Coils)
C-Coil
I-Coil
I-Coil
ITER plasma shape with q surfaces
4
Numerical Tools

• TRIP3D magnetic line tracing code to identify
  stochasticity (by T.E. Evans)
• Fourier harmonic (m,n) analysis code SURFMN (by
  M.J. Schaffer)
• Both codes...
• Obtain axisymmetric equilibrium B from EFIT
• Plasma-generated toroidal and poloidal B treated
  independently of all external fields and of each
  other
• Model externally-generated vacuum field
  contributions realistically
• PF- and TF-coils with measured errors
• DIIID C-coil (set of 6 ex-vessel coils)
• DIIID I-coil (set of 12 in-vessel coils)
• ITER correction coils (scaled down 3.6 times to
  DIII-D size)
• Point dipoles, miscellaneous loops, TF ripple,

5
Fourier Analysis on an Axisymmetric Toroidal
Magnetic Surface

• Procedure
• Set up straight-magnetic-line coordinate system
  on the surface q f/q
• q, f are poloidal, toroidal angle variables
  interval 0,2p
• Use the corresponding Jacobian when integrating
  over the surface
• where
• First parenthesis factor of J is constant on a
  magnetic surface, but R3 and Bq vary. They
  reduce contributions from small-R side and tips,
  respectively.
• Then,
• Tested Fourier analysis of on a surface
  against magnetic island properties
• Fourier Bmn on resonant surface yields same
  island width as Poincaré plot
• Equal and opposite Bmn from two different sources
  yield null m,n island in Poincaré plot

6
DIIID Experiments Are Studying ELM
Suppressionby Weak External Magnetic
Perturbations

• C-coil field was not very effective in ELM
  suppression attempts
• I-coil fields are more effective
• 2003 At high triangularity, high ne
• Weak resonant perturbation with odd I-coil
  parity was most effective.
• Comparable with DIIID intrinsic error and seemed
  to interact with it.
• Damped plasma rotation.
• 2005 At lower triangularity, low ne
• Stronger resonant perturbation with even I-coil
  parity worked well but began to show confinement
  degradation.
• Lots of new data in last few days.
• Rotation, braking, confinement still being
  analyzed.
• What is important? Stochasticity? Braking? Mix
  with multiple n (errors or planned)?
• What to specify for ITER ELM-control coils?
• DIIID goal Establish a physics basis for
  design of ELM control coils on larger tokamaks
  such as JET and ITER.

7
C-Coil Makes a Simple m,n3 Spectrum
Normalized Poloidal Flux
-20 m0 20

• Does not generate n3 field efficiently at pitch
  resonance.Large components at small m.

8
ODD-Parity I-Coil m,n3 Spectrum Has a Null
ValleyClose to the Pitch Resonant Surfaces a
Weak Perturbation
Valley
Asterisks indicatepitch resonanceq n/m
Ridge

• This was the best ELM-suppressing spectrum in
  the first experiments.Has large components at
  intermediate m.

9
EVEN-Parity I-Coil m,n3 Spectrum Has a
RidgeClose to the Pitch Resonant Surfaces a
Stronger Perturbation
Ridge

• This spectrum suppressed ELMs well in the low
  density experiments.It generates pitch-resonant
  components more efficiently.
• Has suppressed ELMs well in 2005 experiments.

10
Ridge and Valley Parallel to Pitch Resonanceis
a Result of the Tokamak Geometry at the Usual
Aspect Ratio
ODD
EVEN

• Outer magnetic lines on low-field side advance
  poloidally almost all at the same rate (blue
  dots).
• They are perturbed similarly.
• Magnetic shear and q are
• determined at tips and small R.

• DIIID outer magnetic lines traverse between
  bottom and top I-coil centers in about 120
  toroidal degrees (figures drawn close to scale).
• DIIID C-coil centers are almost in line, so C-
  and I-coil contributions can be added or
  subtracted.
• Choice of handedness in case of odd-parity I-coil

11
Example of a Left-Hand-Dominant m,3
SpectrumOdd-Parity I-Coil with C-Coil
-20 m0 20

• Right-handed components attenuated But does not
  make pitch-resonant field efficiently

12
Adding C-Coil and I-Coil Fields in Phase Makes
the Strongest Resonant B in DIIID

• Presumably this combination makes the greatest
  stochasticitybut it offers no control of
  handedness

13
ITER Midplane Error Correction CoilsMake an m,3
Spectrum Much Like the DIIID C-Coil
m,3 Spectrum at 95 flux, q95 3
-16 m0 16
-20 m0 20

• Does not generate n3 field efficiently at
  pitch resonance.Large components at small m.
• Adding top bottom coils makes only small
  differences.

14
Port Plug Dipoles (in all 18 ports) Make an m,3
SpectrumPeaked Near Pitch-Resonance
m,3 Spectrum at 95 flux, q95 3
-16 m0 16
-20 m0 20

• This spectrum looks more useful.
• (Model was a point-dipole array, not current
  loops. Might not be accurate.)

15
12 Internal Coils Above and Below Midplane (Like
DIIID)Can Make a m,3 Spectral Peak Matched to
Pitch Resonance
m,3 Spectrum at 95 flux, q95 3
-16 m0 16
-20 m0 20

• Possibly a good m,3 spectrum, matched to pitch
  resonance.
• Coil proportions to get this spectrum are almost
  same as DIII-D I-coil,
• but these coils are farther from plasma
  separatrix than the DIII-D I-coils.

16
Some Discussion and Conclusions

• It is not known yet (2005 mar 11) what
  perturbation spectral features are essential for
  Type-1 ELM suppression, and what features must be
  avoided.
• DIIID is investigating this problem, within the
  possibilities of the DIIID coil set.
• DIIID C-coil has not suppressed the ELMs
  effectively.
• Physics is still unknown.
• ITER error correction coil set spectra are not
  much different from C-coils.
• ITER ELM suppression by magnetic perturbation
  would probably need dedicated coils.
• DIIID I-coil does suppress ELMs effectively.
• Internal coils are difficult in ITER.
• We do not understand the physics of rotation
  damping.
• Gaining ELM suppression while avoiding rotation
  damping and confinement degradation might require
  still more complicated coil arrays, e.g.,
• Multiple toroidal harmonics
• Arrays both far from and close to the midplane,
  to cancel undesired features
• What will the plasma really do, and why?. . . .
  . Stay flexible.