Kein Folientitel

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MHD Limits to Tokamak Operation and their Control
Hartmut Zohm ASDEX Upgrade credits G.
Gantenbein (Stuttgart U), A. Keller, M.
Maraschek, A. Mück DIII-D credits E.J. Strait,
R.J. La Haye JET credits S. Pinches JT-60U
credits A. Isayama (JAERI), K. Nagasaki (Kyoto U)

• Introduction
• The density limit
• b-limit in conventional scenarios NTMs
• b-limit in advanced scenarios RWMs
• Conclusions

Invited talk at 30th EPS Conference on Controlled
Fusion and Plasma Physics, St. Petersburg,
Russia, 08 July, 2003
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Tokamaks and their operational space

• To obtain the goal of nuclear fusion, tokamaks
  have to maximise
• the energy confinement time tE (? Ip or 1/q for
  fixed B-field)
• the fuel density n (Pfus ? n2 ?sv? or (nT)2 at
  optimum T of 10-20 keV)
• the normalised pressure b pkin/pmag (Pfus ?
  pkin2 or b2 at fixed B-field)

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Tokamaks and their operational space
ITER operational space simulation

• To obtain the goal of nuclear fusion, tokamaks
  have to maximise
• the energy confinement time tE (? Ip or 1/q for
  fixed B-field)
• the fuel density n (Pfus ? n2 ?sv? or (nT)2 at
  optimum T of 10-20 keV)
• the normalised pressure b pkin/pmag (Pfus ?
  pkin2 or b2 at fixed B-field)

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Tokamaks and their operational space
q, n and b are limited by the occurrence of large
scale MHD instabilities (free energy of poloidal
field and plasma pressure)
MHD instabilities can be ideal (tA ms) or
resistive (tR ms) Examples Disruptions at
low q and high density (current driven islands)
Neoclassical Tearing Modes
(pressure driven islands)
Resistive wall modes (current and pressure driven
ideal kink) Two strategies Avoid natural
tendency, but limits operational space
Control needs active tools, but
increases op. space
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The density limit is often accompanied by a
disruption
ASDEX Upgrade, W. Suttrop et al., NF 97

• Actual limitation is a power balance problem at
  the edge
• radiative instability (MARFE) excessively cools
  edge
• edge current is drastically reduced gradient
  drives tearing modes
• neighbouring chains of islands lead to loss of
  confinement
• temperature collapse increases resistance
  current cannot be sustained
• Density limit scales as nmax Ip /(pa2) nG
  (Greenwald limit)

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Practical density limit onset of confinement
degradation
ASDEX Upgrade, V. Mertens et al., EPS 99
ASDEX Upgrade, J Stober et al., EPS 99

• Well before disruptive termination, confinement
  starts to degrade
• H-mode confinement drops when n comes close to
  Greenwald limit
• H-L back transition due to reduced edge
  temperature
• Practical density limit is a confinement issue,
  not an MHD issue!
• Note 'accidents' will still lead to disruptions
  mitigation techniques needed

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b-limit in conventional scenarii Neoclassical
Tearing Modes
ASDEX Upgrade, H. Zohm et al., PPCF 96
Once seeded, island is sustained by lack of
bootstrap current (flat p(r)) ...predicts
rp-scaling of onset bN (bad news for ITER)
Equilibrium current profile Bootstrap drive
Finite ??/??? Polarisation current
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M. Maraschek et al., this conference
Dimensionless NTM onset scaling for JET and ASDEX
Upgrade
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Active control or avoidance of NTMs

• Active control or avoidance is possible by
• reducing the local bp may not be a free
  parameter in a reactor
• preventing seed island formation (e.g. suppress
  sawteeth)
• tailoring the equilibrium current profile (e.g.
  LHCD, ECCD)
• generating a localised helical current in the
  island (e.g. ECCD)

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Active control or avoidance of NTMs

• Active control or avoidance is possible by
• reducing the local bp may not be a free
  parameter in a reactor
• preventing seed island formation (e.g. suppress
  sawteeth)
• tailoring the equilibrium current profile (e.g.
  LHCD, ECCD)
• generating a localised helical current in the
  island (e.g. ECCD)

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bN can be increased above onset level (ASDEX
Upgrade)
H. Zohm et al., Phys. Plasmas 01

• Complete stabilisation of (3,2) NTM with PECCD /
  Ptot 10
• Mode comes back due to deposition mismatch
  (Shafranov shift)
• deposition must be exact within island half
  width (1-2 of major radius)

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DIII-D has successfully implemented radial
feedback
R.J. La Haye et al., Phys. Plasmas 02
'Search and suppress' adjusts Bt or R until (3,2)
mode vanishes
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JT-60U feedback control of launching mirror
A. Isayama et al., IAEA FEC 02
Rational surface inferred from local minimum in
ECE perturbation
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(2,1) stabilisation needs more power (DIII-D)
R.J. La Haye et al., this conference
(3,2)
(2,1)

• Required power substantially higher than for
  (3,2) ok for ITER?
• mode stabilised with 2.8 MW of ECRH power at bN
  2.1
• 'search and suppress' also works for this mode

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(2,1) stabilisation needs more power (ASDEX
Upgrade)
G. Gantenbein et al., this conference

• In ASDEX Upgrade, (2,1) NTM usually occurs at
  high bN and locks to wall
• target plasma has power step-down to obtain
  rotating (2,1) at lower bN

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(2,1) stabilisation needs more power (ASDEX
Upgrade)
At bN 1.9, ECCD power of 2.0 MW just sufficient
for stabilisation
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Injection of ECCD before NTM onset in JT-60U
K. Nagasaki et al., to appear in NF

• Application of ECCD before mode onset is
  advantageous
• for same ECCD power, saturated amplitude during
  ECCD is smaller
• explanation must be based on nonlinearity in
  stability curve

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Modelling of NTM stabilisation
Q. Yu et al., Phys. Plasmas 01

• ECCD current (e.g. Fokker-Planck) inserted in
  temporal evolution equation
• use Rutherford equation or 2d nonlinear
  resistive MHD code
• agreement with experiment gives some confidence
  for extrapolation
• Largest uncertainty in prediction to ITER lies in
  NTM stability, not ECCD

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O. Sauter, PRL 2002

• first demonstrated on JET with ICRH current drive

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Sawtooth tailoring by ECCD in ASDEX Upgrade
A. Mück et al., this conference

• Experiments with slow Bt-ramp, 0.8 MW co-ECCD and
  5.1 MW NBI
• increase of sawtooth period for deposition
  outside inversion radius
• decrease of sawtooth period for deposition
  inside inversion radius
• Ctr-ECCD shows inverse behaviour

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Removal of sawteeth avoids NTM during ECCD pulse
Bt ramp feedback controlled b-ramp maintain
correct ECCD deposition
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b-limit in advanced scenarii Resistive Wall Modes
A. Bondeson et al., PRL 94
Ideal branch
Ideal regime Ideal kink stable if wall is close
enough
RWM branch
RWM regime RWM is stable when slipping
between mode and wall is large enough

• When ideal kink is wall stabilised, RWM can grow
  on wall time scale
• rotation w.r.t. wall can stabilise the RWM if
  wrot gtgt 1/tW
• balance between wall drag and (rotating) plasma
  drag on mode

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Without nearby conducting wall, external kink is
observed
S. Günter et al., NF 00
ASDEX Upgrade very low b-limit (bN 1.8) with
strongly reversed shear Stability analysis and
experimental data suggest coupling to infernal
mode
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With conducting wall, ideal b-limit can be
exceeded
E.J. Strait et al., NF 03
DIII-D with fast plasma rotation, bNno-wall is
substantially exceeded Below threshold value,
mode penetrates wall and becomes a RWM Threshold
value of few of Alfvén speed consistent with
theory
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Above no-wall limit, plasma amplifies error fields

• If b exceeds no-wall limit, external perturbation
  is strongly amplified
• amplification of intrinsic error fields slows
  down rotation if b gt bno-wall
• can be interpreted as resonant amplification by
  marginally stable RWM
• Similar findings on JET confirm this picture
• ? Rotational stabilisation may not work in steady
  state!

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Direct RWM stabilisation by active coils

• Saddle coils for direct stabilisation
• different feedback schemes exist
• first results look promising
• new experiments with in-vessel
• coils under way on DIII-D

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Summary and conclusions

• Tokamak operational space restricted by large
  scale MHD instabilities
• Present strategy aims at avoiding current and
  density limit
• ITER aims at operation within intrinsically
  stable space
• b-limit in conventional (NTM) and advanced
  scenarii (RWM) too low
• Strategies for active control are under
  development
• based on good physics understanding
• involves local j(r) control by ECCD for NTMs
• may ultimately need active saddle coil feedback
  for RWM

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Error field correction results in sustained
rotation
Continuous high beta by error field compensation