Active control of multiple resistive wall modes

1
Active control of multiple resistive wall modes
RFP Workshop 2005, Madison, September 26-28, 2005
presented by J. R. Drake

• 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

2
Outline

• Headline
• RWM active control system on EXTRAP T2R
• Experimental observations of unstable RWMs
• Measurement of the plasma response to external
  fields
• Summary and an idea for new experiment

3
RWM feedback control with the full 4x32 coil array

• EPS Conference June Data
• red Reference shot w/o fb black With feedback
  control
• With 4x32 coils all unstable RWMs are
  individually controlled (no coupled modes)
• Unstable RWMs are suppressed (16 modes)
• Remaining dominant field (n2) is field error
  amplification.
• Feedback results in a two-fold increase of the
  discharge duration

4
RWM feedback control with the full 4x32 coil array

• September Data
• red Reference shot w/o fb black With
  intelligent shell feedback control
• Refined intelligent shell mode of operation.
• All unstable RWMs are suppressed (16 modes)
• The field error amplification (n2) is
  suppressed.
• Feedback results in a three-fold increase of the
  discharge duration
• Stabilization is achieved for 10 wall times

5
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 Telt400 eV
• pulse length ?pulselt 60 ms

• Copper shell
• two layers
• 1 mm thickness

Pulse lengths ?pulsegtgt ?ver allow studies of RWM
stability and methods for active control of RWMs
6
Flux loop sensor arrays
7
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
8
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
9
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

10
Growth for each mode described by
is the mode is the control
field plus the intrinsic error field
is the mode growth rate is
the inverse wall time for the harmonic
Mode amplitude spectrum (left) and Theoretical
growth rate (right)
11
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

12
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.

13
RWM feedback control with the full 4x32 coil array

• September Data
• red Reference shot w/o fb black With
  intelligent shell feedback control
• Refined intelligent shell mode of operation.
• All unstable RWMs are suppressed (16 modes)
• The field error amplification (n2) is
  suppressed.
• Feedback results in a three-fold increase of the
  discharge duration
• Stabilization is achieved for 10 wall times

14
Shot data for the discharges with full feedback
control of modes in the range -16 n 15
Plasma currentIp-kA
The shot length is limited by the power supply
for the vertical field.
radial position DR-mm
W (n-12) krad/s
W (n-13) krad/s
W (n-14) krad/s
0 10 20 30 40 50
60 Time ms
15
Metal lines for the discharges with and without
full feedback control.
Without FB
Mo line arb
With FB
The spectral line intensities for metal
components of the wall are reduced with
feedback. Mo limiters Cr stainless steel
vacuum vessel
Cr line arb
0 10 20 30
40 50 Time ms
16
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
17
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

18
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
19
Summary

• All the nonresonant unstable RWMs can be
  simulataneously stabilised.
• Resonant amplification of field error harmonics
  can be suppressed.
• Plasma response to an external field in excellent
  agreement with linear MHD model
• In T2R the pulse length is extended with no sign
  of mode growth.
• All 16 unstable RWMs are individually controlled
• With fb Suppression of all unstable RWMs
  throughout the discharge duration ( 10 wall
  times)
• Higher plasma toroidal rotation, sustainment of
  tearing mode rotation, three-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

20
Summary and Idea for a new experiment

• What are the important ingredients for active
  control of RWMs in order to get really long
  pulses?
• Sufficient saddle coil array so that dangerous
  modes are not coupled by side bands.
• Real time controller.
• Only a thin shell with an appropriate penetration
  time (no thick shell).
• Radial equilibrium control and density control
• Important fundamental observations.
• Linear theory is OK. No mode coupling seen so
  far.
• Localised field errors produce a spectrum of
  field error harmonics,but the resonant field
  error amplification effect caused by localised
  field errors can be suppressed by feedback on the
  harmonics.
• Does this open up the possibility for big port
  holes?
• The need for bigger access ports is evident.
• Local first order field error correction can
  lower the amplitude of the field error harmonics,
  but not completely reduce them to a benign level.
• Can a combination of local FE correction plus a
  saddle coil array allow big port holes without
  the usual FE problems?