RFX-mod: RWM and equilibrium control
Towards a fully integrated RWM control in real 3D environment
Presented by:
T. Bolzonella
In collaboration with:
M. Baruzzo, S.C. Guo, G. Marchiori, A. Soppelsa, Z. R.Wang, S. Ide, Y.Q.
Liu, Y. In, G. Manduchi, M. Okabayashi, M. Takechi, F. Villone, E. Gaio, L.
Grando, A. Luchetta, L. Marrelli, L. Novello, D. Terranova, P. Zanca
T. Bolzonella, RWM in RFX-mod, 14th ws on Active MHD control, Princeton 2009
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RWM control is essential for RFP configuration
Plasma current and MHD instability
amplitude (radial field component)
RWMs are at present the only instability causing
fast discharge termination in the RFP.
T. Bolzonella, RWM in RFX-mod, 14th ws on Active MHD control, Princeton 2009
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RWM common issues
Multi-mode control
Little help from plasma rotation
Importance of 3D effects
Mode rigidity studies
Optimum (minimum) set of active coils
T. Bolzonella, RWM in RFX-mod, 14th ws on Active MHD control, Princeton 2009
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Outline
1. Introduction: RWMs in Reversed Field Pinches and RFX-mod
2. New experiments: RWMs in a 3D environment
3. Improved control plant modeling
4. Virtual active control reconfiguration
5. Conclusions
T. Bolzonella, RWM in RFX-mod, 14th ws on Active MHD control, Princeton 2009
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Outline
1. Introduction: RWMs in Reversed Field Pinches and RFX-mod
2. New experiments: RWMs in a 3D environment
3. Improved control plant modeling
4. Virtual active control reconfiguration
5. Conclusions
T. Bolzonella, RWM in RFX-mod, 14th ws on Active MHD control, Princeton 2009
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RWM instabilities in RFP Plasmas
βp=0, Θo=1.5 b/a=1.12 a/R=0.2295
4.0
3.0
γτb
■ Current driven external kink mode
F=-0.05
F=-0.1
F=-0.2
F=-0.5
F=-1.0
3.5
2.5
■ Mode rational surfaces are outside
plasma--- non resonant modes
■ Very strong rotation speed is required to
2.0
1.5
stabilize the mode (Vo ∼ (0.2-1.0) VA)
1.0
■ Many n mode unstable (m=1)
0.5
■ Weak ballooning structure
0.0
-7 -6 -5 -4 -3 -2 -1
0
1
n
2
3
4
5
■ Toroidal effects are less important ?
F can be easily related to q(a)
Equilibrium model:
r
r
r
µ B × ∇p
∇ × B o = j|| + j⊥ = µ Bo + o o 2
Bo
µ=
2
Θ o [1 − rˆα ]
a
[Guo et al., oral presentation, EPS 2009]
T. Bolzonella, RWM in RFX-mod, 14th ws on Active MHD control, Princeton 2009
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Equilibrium during current driven RWM growth
Current driven RWMs grow during the whole
discharge and the growth rate is kept constant
by controlling the equilibrium profiles (or q(a)
from the operational point of view).
The current profile that is driving the instabilities
is the equilibrium one.
Different from the tokamak current driven RWM
case.
This allows physics studies under well controlled
and reproducible esperimental conditions.
Important difference: by controlling Br(a) RWM
are stabilized, TM are controlled (at the edge).
While loocking at RWM passive growth, TM Br(a)
is always kept controlled.
T. Bolzonella, RWM in RFX-mod, 14th ws on Active MHD control, Princeton 2009
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RFX-mod
The largest RFP in the world, located in Padova, Italy
A fusion facility for MHD mode control
a=0.459 m, R=2 m, plasma current up to 1.8 MA (I=2 MA design target)
T. Bolzonella, RWM in RFX-mod, 14th ws on Active MHD control, Princeton 2009
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192 active coils, covering the whole plasma surface
Each saddle coil is independently driven (60 turns)
Produces br from 50 mT (DC) to 3.5 mT (100 Hz)
Power supply: 650 V x 400 A
T. Bolzonella, RWM in RFX-mod, 14th ws on Active MHD control, Princeton 2009
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RFX-mod active control system
saddle coils
magnetic diagnostics
b
ext
plasma
power
amplifiers
192 I coil
192 I ref
Digital Controller
Sideband Correction
Br extrapolation
2x48 MODES can be independently controlled
192 bϕ
192 br
More than 576 signals enter the MHD real time controller!
T. Bolzonella, RWM in RFX-mod, 14th ws on Active MHD control, Princeton 2009
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The MHD feedback control action
RFX-mod real time measurements enter as input the feedback control system that performs a 2D
cylindrical real time FFT.
The controller then generates suitable references for the active coil power supplies, depending
on the selected control scheme.
Note that in this way the feedback react to a single harmonic (input) by producing an external
mode. The harmonic content of the external action is of course as important as the exact
knowledge of the harmonic composition of the unstable mode.
Generation of (m=1 n =−7) mode.
The figure displays the magnetic field
spectra obtained without (transparent) and
with decoupling (solid), respectively.
[T. Bolzonella, et al. FED (2007)]
T. Bolzonella, RWM in RFX-mod, 14th ws on Active MHD control, Princeton 2009
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Outline
1. Introduction: RWMs in Reversed Field Pinches and RFX-mod
2. New experiments: RWMs in a 3D environment
3. Improved control plant modeling
4. Virtual active control reconfiguration
5. Conclusions
T. Bolzonella, RWM in RFX-mod, 14th ws on Active MHD control, Princeton 2009
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MHD instabilities in a real boundary
Plasma instabilities develop in a toroidal environment.
Experimental analysis reconstruct magnetic perturbations in terms of 2D Fourier
harmonics using cylindrical coordinates: toroidal effects on plasma instabilities are
described with a “richer” Fourier spectrum. In alternative one could reformulate the
diagnostic analysis on a different coordinate system (possible, but not done at present).
The plasma mode in toroidal geometry is no more a monocromatic single (cylindrical)
Fourier harmonic.
In presence of a non-uniform passive boundary, additional harmonic distortions can
add.
Further distortions due to non-circular cross section or high beta effects are negligible in
the RFX-mod case.
In summary: an MHD instability can be identified by a growth rate (eigenvalue of a
stability problem). The representation of the plasma mode (eigenfunction of a stability
problem) is given in terms of several cylindrical Fourier harmonics. This have obviously
important implications when the mode control is under consideration.
T. Bolzonella, RWM in RFX-mod, 14th ws on Active MHD control, Princeton 2009
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Poloidal harmonic distortions
a)
c)
b)
d)
The presence of strong poloidal harmonic distortions (panels c and d) to the main unstable one
(panels a and b) has been carefully measured and suggest toroidal and 3D effect relevance
with clear implications on control schemes. Comparison with numerical models is ongoing.
[T. Bolzonella, et al., EPS 2009]
T. Bolzonella, RWM in RFX-mod, 14th ws on Active MHD control, Princeton 2009
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RWM mode identification
a)
c)
b)
d)
RWM structure identification by subcritical gains: time traces of (0,6), (1,+6) and (2,6)
amplitudes follow the time behaviour of the main unstable mode, suggesting a close
relation between the (1,-6) growth and the growth of its poloidal harmonics.
[T. Bolzonella, et al., EPS 2009]
T. Bolzonella, RWM in RFX-mod, 14th ws on Active MHD control, Princeton 2009
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RWM coupling effects are negligible
a)
c)
b)
d)
Experiments on toroidal harmonics generation suggest instead that the coupling due to
poloidal gaps is less important in the RFX-mod case:
In the figure black lines belong to the same case of point 3, while the green ones describe the
case of free growth of other unstable RWMs (different n).
The growth rate of the main unstable mode is not modified by the different control on the
[T. Bolzonella, et al., EPS 2009]
closest unstable toroidal harmonics.
T. Bolzonella, RWM in RFX-mod, 14th ws on Active MHD control, Princeton 2009
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Outline
1. Introduction: RWMs in Reversed Field Pinches and RFX-mod
2. New experiments: RWMs in a 3D environment
3. Improved control plant modeling
4. Virtual active control reconfiguration
5. Conclusions
T. Bolzonella, RWM in RFX-mod, 14th ws on Active MHD control, Princeton 2009
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Model-based Full Simulator of RWM Control System
• Dynamic models of the control system cast in the more convenient state variable
representation have been developed.
• CarMa code has been adapted to RFX-mod in order to have a model coupling the
relevant MHD physics to a 3D description of passive and active boundary (plant
description).
• As first, non-trivial application of the new integrated tool, closed-loop RWM stability
analyses have been benchmarked against experimental data provided ad hoc.
T. Bolzonella, RWM in RFX-mod, 14th ws on Active MHD control, Princeton 2009
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Control system “flight simulator”
Scheme of the control system with blocks representing the Plant (P), the Controller (R), the Mode
Cleaner (C). Blocks performing DFT and inverse DFT are also shown. Experimental PID gains can
be used to compare model results to plasma experiments.
[G. Marchiori, et al., EPS 2009]
T. Bolzonella, RWM in RFX-mod, 14th ws on Active MHD control, Princeton 2009
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Model benchmark
The model has been benchmarked against experiment to reproduce RWM growth rates under
subcritical control. In figure experimental data (red asterisks, see inlet for the full time
behavior) are compared to simulations (in blue).
[G. Marchiori, et al., EPS 2009]
T. Bolzonella, RWM in RFX-mod, 14th ws on Active MHD control, Princeton 2009
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Outline
1. Introduction: RWMs in Reversed Field Pinches and RFX-mod
2. New experiments: RWMs in a 3D environment
3. Improved control plant modeling
4. Virtual active control reconfiguration
5. Conclusions
T. Bolzonella, RWM in RFX-mod, 14th ws on Active MHD control, Princeton 2009
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Effects of different actuators geometry and number
The MHD feedback control system can be on purpose “downgraded” both in power and
number of coils for selected harmonics, to study tokamak-relevant problems.
• The effect of reduced available power
• Effects of mode non-rigidity with a reduced set of coils
• Minimum/optimum surface coverage for RWM control
• Effect of different passive boundaries on control effectiveness
T. Bolzonella, RWM in RFX-mod, 14th ws on Active MHD control, Princeton 2009
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Effects of different actuators geometry and number
The MHD feedback control system can be on purpose “downgraded” both in power and
number of coils for selected harmonics,
• Effects of mode non-rigidity with a reduced set of coils
• Effect of different passive boundaries on control effectiveness
?
?
T. Bolzonella, RWM in RFX-mod, 14th ws on Active MHD control, Princeton 2009
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The concept of MC reconfiguration for RWM studies
We want to change the number or the shape (or both) of active coils only for the selected
mode: optimized plasma and test of different control hardware together!
The references sent to the amplifiers go again through a FFT block: then the selected RWM
harmonic alone is decomposed via FFT-1 in 192 references relative to the RWM control
only.
T. Bolzonella, RWM in RFX-mod, 14th ws on Active MHD control, Princeton 2009
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The concept of MC reconfiguration for RWM studies
The reconfiguration game now can start: one could decide to use only one toroidal array for
RWM control purposes. All the other references are then set equals to zero for the selected
harmonic only.
T. Bolzonella, RWM in RFX-mod, 14th ws on Active MHD control, Princeton 2009
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The concept of MC reconfiguration for RWM studies
Or one could investigate the role of active coil geometry while keeping a complete surface
coverage by taking averages of neighbor coil references.
In any case, after this step the references relative to all the harmonics are summed together
again and the result is a still optimized target plasma where only the RWM control strategy
has been modified.
T. Bolzonella, RWM in RFX-mod, 14th ws on Active MHD control, Princeton 2009
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RWM control with one toroidal array only
Full gain scan on control of (1,-6)
using only the inner toroidal array
26780 Gp=600
26782, Gp=800
26781, Gp=1000
26783, Gp=1400
26784, Gp=2000
Importance of integral gain
action in order to control
since the beginning of the
discharge the (1,-6) RWM
with a reduced set of active
coils. The plot is done for the
top array case.
T. Bolzonella, RWM in RFX-mod, 14th ws on Active MHD control, Princeton 2009
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Partial coverage modeling
35
EQ4b, FB
n=−6, θc=0
30
critical gain
25
int. pol.
20
rad.
15
10
5
0
0
0.5
1
1.5
2
∆θ/π
[Y. Liu, et al., NF (2004)]
Feedback assumptions:
– Feedback coils located at outboard mid-plane
– Sensor signal = magnetic field (bs)
– Control signal = active current
– Proportional real gain = -brv/bs, where brv is
free space radial field at sensor position,
produced by active current
[MARS-F for RFP equilibria, courtesy of Y. Liu]
T. Bolzonella, RWM in RFX-mod, 14th ws on Active MHD control, Princeton 2009
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Outline
1. Introduction: RWMs in Reversed Field Pinches and RFX-mod
2. New experiments: RWMs in a 3D environment
3. Improved control plant modeling
4. Virtual active control reconfiguration
5. Conclusions
T. Bolzonella, RWM in RFX-mod, 14th ws on Active MHD control, Princeton 2009
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Conclusions
RFP research can complement tokamak experience in evaluating and dealing with 3D
effects on mode identificationa and mode control
New experiments carefully identified poloidal distortions of unstable RWMs.
RWM couplings to other instabilities proved to be negligible in RFPs.
Decoupling strategies are being tested to further reduce harmonic distortions of external
(control) fields.
Simulation tools allow to “plug into” a full control flight simulator different models of plant
and controllers for easy tests and benchmark against experimental data.
RWM control software reconfiguration offers an unprecedent flexibility to study the effect
of different control systems on the same unstable mode(s).
T. Bolzonella, RWM in RFX-mod, 14th ws on Active MHD control, Princeton 2009
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