Active control of multiple resistive wall modes

1
Active control of multiple resistive wall modes
32nd EPS Plasma Physics Conference, Tarragona, 27
June - 1 July, 2005
presented by P. R. Brunsell

• P. R. Brunsell1, D. Yadikin1, D. Gregoratto2, R.
  Paccagnella2, Y. Q. Liu3, T. Bolzonella2, M.
  Cecconello1, J. R. Drake1, M. Kuldkepp4, G.
  Manduchi2, G. Marchiori2, L. Marrelli2, P.
  Martin2, S. Menmuir4, S. Ortolani2, E. Rachlew4,
  G. Spizzo2, P. Zanca2
• 1) Alfvén Laboratory, Association EURATOM-VR,
  Royal Institute of Technology, Stockholm, Sweden
• 2) Consorzio RFX, Associazione EURATOM-ENEA sulla
  fusione, Padova, Italy
• 3) Dept. of Applied Mechanics, Association
  EURATOM-VR, Chalmers University of Technology,
  Gothenburg, Sweden
• 4) Dept. of Physics, Association EURATOM-VR,
  Royal Institute of Technology, Stockholm, Sweden

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Outline

• EXTRAP T2R reversed field pinch
• Cylindrical linear MHD model for resistive wall
  modes (RWMs)
• RWM active control system on EXTRAP T2R
• Experimental observations of unstable RWMs
• Measurement of the plasma response to external
  fields
• RWM feedback control experiments

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Background and motivation

• Stabilization of ideal MHD modes with a
  conducting wall is used in
• Advanced Tokamak, Reversed-field Pinch (RFP),
  Spheromak
• For a wall with finite conductivity, the ideal
  MHD mode is converted to an unstable resistive
  wall mode (RWM) growing on the time scale of the
  magnetic flux diffusion through the wall
• In the absence of plasma rotation, active
  feedback control of RWMs is required
• The RFP configuration is well suited for studies
  of RWM control
• Toroidal arrays of coils control individual
  unstable modes
• The RWMs are described by the cylindrical linear
  MHD model

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EXTRAP T2R reversed field pinch
EXTRAP T2R vessel and shell during assembly at
Alfvén laboratory, KTH, Stockholm

• Machine parameters
• major radius 1.24 m
• plasma minor radius a18 cm
• shell norm minor radius r/a 1.08
• shell time constant ?ver6 ms
• plasma current Ip80 kA
• electron temperature Te250 eV
• pulse length ?pulselt 45 ms

• Copper shell
• two layers
• 1 mm thickness

Pulse lengths ?pulsegtgt ?ver allow studies of RWM
stability and methods for active control of RWMs
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Cylindrical linear MHD model - RFP equilibrium

• RFP equilibrium
• B?? B??are of the same order
• B? reverses near the edge

• Perturbed field
• expanded in Fourier harmonics
• poloidal mode number m
• toroidal mode number n

ngt0
nlt0
qr B? /B?R
Sign convention m1 and n lt 0 for helical modes
resonant inside reversal radius
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Cylindrical linear MHD model - Resistive wall
modes

• RWM is described by the marginal linearized
  ideal MHD equation
• thin wall boundary condition
• wall long time constant ?w ???rw?w
• linear MHD model gives resistive wall mode
  growth rates ?m,n

• For the RFP
• RWMs due to non-resonant, current driven, ideal
  MHD m1 kink modes
• mode stability is unaffected by sub-Alfvenic
  plasma rotation
• mgt1 are stable
• finite range of unstable m1 with different
  toroidal mode number n
• range increases with aspect ratio
• EXTRAP T2R 16 unstable modes

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Cyl. linear MHD model - Plasma response to an
externally applied field
Mode wall time ?m,n - diffusion of a field
Fourier harmonic through the wall
Without plasma, the radial field harmonic at the
wall bwbrm,n(rw) is obtained from an ordinary
diff. equation
With plasma, the corresponding equation
describing the plasma response to the external
field includes the RWM growth rate ?m,n

• The plasma response
• amplifies the field for ?m,n?m,ngt-1
• attenuates the field for ?m,n?m,nlt-1

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Flux loop sensor arrays
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Active saddle coil arrays

• 2-D array 4x32 coils (100 cover)
• 128 coils, 4 poloidal, 32 toroidal pos

• 2-D array 4x16 coils (50 cover)
• 64 coils, 4 poloidal, 16 toroidal pos

• Outside shell rc/a1.3
• Each saddle coil extends
• 90o poloidally, 11.25o toroidally
• m1 series connected

out - in
top - bottom
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Active control system
Plasma - wall system Cyl. linear MHD model

• Saddle coils
• L/R time 1 ms
• field lt 3 mT

• Audio amplifiers
• 1 Hz - 25 KHz
• current lt 20 A

• Digital controller (RFX)
• 64 inputs/outputs, 100 ?s cycle
• 400 MHz CPU, signal processing implemented in
  software
• real time FFT, calc b1,n
• intelligent shell feedback
• mode control feedback
• open loop operation

Sensor flux loops
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Range of m1 RWMs observed in EXTRAP T2R

• black Measured m1 ampl.
• blue MHD exponential growth
• red Estimated field error
• Exp. and MHD RWM growth are in agreement for
  n-10, 5
• Disagreement for n2 can be explained by field
  errors
• Assuming MHD growth rates, the field errors are
  estimated from the MHD model

• Experimental RWM growth is in agreement with the
  MHD model assuming field errors in the range 0.02
  - 0.2 mT

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Measurement of the plasma response to an
externally applied field
black Measured m1 harmonics red Calculated
plasma response blue Vacuum field n-8 ??0.5
(unstable) n-4 ??0.09 (marg. unstable) n12
??-5.0 (stable) Plasma response calculated using
the cylindrical linear MHD model

• Cylindrical MHD model plasma response is in
  excellent agreement with measurement

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Control of a RWM with a pre-programmed external
field

• Pre-programmed coil current step-pulse is applied
  at t8 ms.
• n6 mode has a shot-to-shot reproducible phase,
  due to machine field errors
• amplitude and phase of the n6 coil current is
  selected to cancel the RWM
• The RWM is suppressed
• The suppressed field is sum of inherent RWM and
  the plasma response to a constant external field.

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m1 mode spectrum with different coil arrays,
for n6 coil current harmonic
Array with 4x16 coils
Array with 4x32 coils

• Side band harmonics ?n 32
• Mode amplitudes two times higher
• No coupled unstable RWMs

• Side band harmonics ?n 16
• With feedback control, linear coupling of side
  band modes
• pairs of coupled unstable RWMs

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RWM feedback control with the full 4x32 coil array

• red Reference shot w/o fb
• black Shot with intelligent shell feedback
  control
• With 4x32 coils all unstable RWMs are
  individually controlled (no coupled modes)
• All unstable RWMs are suppressed (n-11...-2,
  n1...6) (16 modes)
• The remaining field is due to low proportional
  feedback gains used.
• Feedback results in a two-fold increase of the
  discharge duration
• Stabilization is achieved for 7 wall times

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Effect of RWM feedback on plasma rotation and
resonant modes

• Intelligent shell fb with
• 4x32 coil array
• m1 rms amplitude suppressed with feedback
• n-12 tearing mode wall locks around t15 ms w/o
  feedback
• With feedback, tearing mode rotation is
  sustained
• Plasma toroidal rotation is estimated from OV
  impurity Doppler shift.
• With feedback, plasma rotation velocity is higher

For more info, see posters P4.067, M. Cecconello,
and P4.079, S. Menmuir
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Comparison of intelligent shell and mode control
feedback for coupled modes n5, -11 with 4x16
coil array

• red Reference shot
• blue Intelligent shell fb
• black Mode control fb with different complex
  gains for the coupled modes
• Intelligent shell fb ineffective for coupled
  modes
• Mode control fb suppresses rotating coupled modes
  
• Mode control fb induces mode rotation.

For more info, see poster P4.066, D. Yadikin
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Mode control feedback of selected target
modeswith 4x16 coil array

• red Reference shot
• black Mode control feedback (real gain).
• n-11, -10, -9, -8 are selected as target
  modes
• Feedback is disabled on all other modes.
• (including the coupled modes n5, 6, 7, 8)
• The target modes are stabilized (n-11,-8)
• Other modes are unaffected (n2)
• Coupled modes are affected. (n5)

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Summary

• Observation of inherent unstable RWMs in EXTRAP
  T2R
• Growth in agreement with linear MHD, assuming
  small field errors
• Comparison of cylindrical linear MHD model with
  experiment
• Plasma response to an external field in excellent
  agreement with linear MHD model
• Feedback control with full 4x32 coil array
• All 16 unstable RWMs are individually controlled
• With fb Suppression of all unstable RWMs
  throughout the discharge duration ( 7 wall times)
• Higher plasma toroidal rotation, sustainment of
  tearing mode rotation, two-fold increase of the
  pulse length
• Feedback control with partial 4x16 coil array,
  coupled unstable RWMs
• Intelligent shell fb ineffective for
  stabilization of coupled modes
• Mode control fb can suppress slowly rotating
  coupled modes