October 2008, MPI fϋr Plasmaphysik, Garching
1
Performance limiting MHD phenomena
in fusion devices:
physics and active control
M. Baruzzo
Consorzio RFX, Associazione Euratom-ENEA sulla fusione, Padova
Università di Padova
October 2008, MPI fϋr Plasmaphysik, Garching
Outline
Introduction to MHD limiting phenomena
Short description of RFX-mod experiment and of its MHD active control system
RWM in RFX-mod, phenomenology and statistical analysis
NTMs, physics and a method for radial localization
Examples of NTMs localization at JET
Conclusion and future developments
2
October 2008, MPI fϋr Plasmaphysik, Garching
Outline
Introduction to MHD limiting phenomena
Short description of RFX-mod experiment and of its MHD active control system
RWM in RFX-mod, phenomenology and statistical analysis
NTMs, physics and a method for radial localization
Examples of NTMs localization at JET
Conclusion and future developments
3
October 2008, MPI fϋr Plasmaphysik, Garching
4
Introduction to MHD limiting phenomena
Reactorial high beta (tokamak) steady state operation
(tokamak, RFP)
Determination of q profile's evolutionDetermination of
q profile's evolutionPrevention of beta collapses
and disruptionsPrevention of beta collapses
and disruptions
October 2008, MPI fϋr Plasmaphysik, Garching
Outline
Introduction to MHD limiting phenomena
Short description of RFX-mod experiment and of its MHD active control system
RWM in RFX-mod, phenomenology and statistical analysis
NTMs, physics and a method for radial localization
Examples of NTMs localization at JET
Conclusion and future developments
5
October 2008, MPI fϋr Plasmaphysik, Garching
RFP equilibrium
6
The goodness of confinement is identified by poloidal beta
RFP equilibrium is characterized by the two field components of the same order of magnitude, and
the reversal of B at the edge
The equilibrium parameters are
B
aBF
)(
B
aB )(
02 2/)(
aB
p
October 2008, MPI fϋr Plasmaphysik, Garching
Large RFP, major radius 2m, minor radius 0.459m.
Vacuum toroidal field up to 0.7T, maximum plasma current of 2MA.
Conductive shell with vertical field penetration time of 50ms, discharge length 500ms
Control of MHD instabilities by mean of an extensive set of active saddle coils (2005)
The shell's external surface is covered by 48(toroidal)x4(poloidal) active coils, each independently fed, each able to produce a radial magnetic field up to 50mT
Each active coil corresponds to a radial magnetic sensor that covers the same solid angle, placed on the internal surface of the shell
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Experiment overview: RFX-mod
October 2008, MPI fϋr Plasmaphysik, Garching
MHD active control in RFX-mod
Possibility to let predefined modes free of control
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ALGORITHMS FOR MHD ACTIVE CONTROL
Control applied to each active coil with different control parameters (PID), freezing to zero the radial magnetic flux in each sensor, real space control
Mode Control
Control applied to each MHD mode with different control parameters (PID), Fourier space control
Virtual Shell
Acquisition of192x3 signalsfrom sensors
FFTAction of control
algorithm
inverseFFT
Creation of 192references to feed
active coils
500μs
Digital controller (PID)
More information in L. Piron’s talk
October 2008, MPI fϋr Plasmaphysik, Garching
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0
0.3
0.6
0.9
1.2
Pla
sma
Cu
rre
nt
(MA
)
0
2.5
5
7.5
(1,-
6)
Am
p (m
T)
0
0.3
0.6
0.9
(1,-
5)
Am
p (m
T)
0
0.3
0.6
0.9
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
(1,-
4)
Am
p (m
T)
Time (s)
MHD active control in RFX-mod
October 2008, MPI fϋr Plasmaphysik, Garching
Outline
Introduction to MHD limiting phenomena
Short description of RFX-mod experiment and of its MHD active control system
RWM in RFX-mod, phenomenology and statistical analysis
NTMs, physics and a method for radial localization
Examples of NTMs localization at JET
Conclusion and future developments
10
October 2008, MPI fϋr Plasmaphysik, Garching
Resistive Wall Modes
In absence of conductive structures near the plasma they grow as ideal kink modes (helical deformation of field lines, radial displacement)
These modes are stabilized by a perfectly conductive wall very close to the plasma edge
If the wall is a resistive shell their growth rate is related to the timescale of the magnetic field penetration time in the wall (First discovery in a RFP experiment, B. Alper, PPCF 31 no. 2, 205-212, 1989) their control is compulsory for long time operation
Control strategies
Fluid rotation of bulk plasma
(partially effective in tokamaks)
Active feedback control (effective in RFPs
and tokamaks)
October 2008, MPI fϋr Plasmaphysik, Garching
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Resistive Wall Modes
All important for tokamaks as well!!
Drake J., Bolzonella T. IAEA 2008,
Bolzonella T. et. al. Phys.Rew.Lett, accepted to publication
Villone F. et. al. Phys.Rew.Lett 100 255055 (2008)
October 2008, MPI fϋr Plasmaphysik, Garching
MHD instability description
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The displacement of magnetic field lines from their equilibrium position is:
m,n is called mode's growth rate, if it is positive the mode is unstable, if it is negative or null the mode is stable
m and n are the mode wave numbers, they point out the periodicity of the mode in toroidal geometry
Example of kink perturbation m=1, n=8 (x10)
0
)(,
,)(),(m Zn
nmitnm eert nm ξrξ
October 2008, MPI fϋr Plasmaphysik, Garching
RWM behaviour in RFX-mod
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October 2008, MPI fϋr Plasmaphysik, Garching
RWM behaviour, discharge 17304
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Flat plasma current profile
October 2008, MPI fϋr Plasmaphysik, Garching
RWM behaviour, discharge 17327
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Peaked plasma current profile
October 2008, MPI fϋr Plasmaphysik, Garching
RWM growth rates predictions
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Linear MHD calculation of RWM growth rates normalized to the shell's time costant for two equilibria: Θ=1.55 (solid) e Θ=1.78 (dashed) in T2R RFP
P.R. Brunsell et all. Phys. Rev. LettPhys. Rev. Lett.. 93 (2004)
October 2008, MPI fϋr Plasmaphysik, Garching
Statistical analysis of RWM growth rates
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• Statistical study of growth rates as a function of plasma parameters (I, F, n, βθ) • Selected parameters are considered independent among theirselves, dependencies in
F and βθ are known from the theory; I, n are considered to complete the variables set
• In the picture are shown the variation ranges of the considered plasma parameters
• An overall number of 234 pulses were analyzed
October 2008, MPI fϋr Plasmaphysik, Garching
Growth rates calculation
For each free mode the logarithm of the signal was linearly interpoled in the range in which a single exponential growth was found
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October 2008, MPI fϋr Plasmaphysik, Garching
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Statistical study for an internal mode, n=-5
Negative trend with IFI in agreement with
theory
October 2008, MPI fϋr Plasmaphysik, Garching
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Statistical study for an internal mode, n=-6
Negative trend with IFI in agreement with theory
Negative trend with IFI in agreement with
theory
October 2008, MPI fϋr Plasmaphysik, Garching
Code Benchmarking on RWM statistical data
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Equilibrium A Equilibrium B ETAW MARSF CarMa Exp. ETAW MARSF CarMa Exp. n=4 5.27 5.07 7.30
7.48 6 4.09 4.04 5.63
5.78 4.5
n=5 8.63 8.55 12.8 13.1
12 6.81 6.89 9.91 10.2
8
n=6 14.5 14.4 22.6 23.4
22 11.8 11.7 17.6 18.2
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Villone F. et. al. 35° EPS Conference, Crete, July 2008
Equilibr. A: F=-0.073
Equilibr. B: F=-0.136
October 2008, MPI fϋr Plasmaphysik, Garching
Outline
Introduction to MHD limiting phenomena
Short description of RFX-mod experiment and of its MHD active control system
RWM in RFX-mod, phenomenology and statistical analysis
NTMs, physics and a method for radial localization
Examples of NTMs localization at JET
Conclusion and future developments
23
October 2008, MPI fϋr Plasmaphysik, Garching
Neoclassical Tearing Modes
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TM are modes that cause tearing and reconnection of magnetic field lines, creating magnetic islands at the singular layer q=m/n (resonant modes) because of finite plasma resistivity.
TM linear stability is determined by the plasma current profile (minimum magnetic energy principle)
Bootstrap current is a toroidal effect induced by momentum unbalance between passing and trapped particles, this unbalance is determined by the radial gradient of plasma pressure, therefore bootstrap current depends on the beta parameter
NTMs are TM destabilized by an helical perturbation of bootstrap current, caused by the flattening of the pressure profile inside the island, which can change the local bootstrap profile and affect the non linear stability of the TM
NTMs appearance leads to a strong degradation of confinement and beta, and also may lead to disruptions
NTM radial location can flag the position of a resonant surface, giving the possibility to reconstruct the radial magnetic q profile, for this reason NTMs are also called MHD markers
H. Zohm et. Al, Nucl. Fus. 41, No. 2 (2001)
R.J. La Haye, PoP 13, 055501 (2006)
October 2008, MPI fϋr Plasmaphysik, Garching
Radial localization of modes using coherence
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m~
d~
)~(mFM Magnetic fluctuation
Diagnostic fluctuation
Study of the average cross-coherence in Fourier space
)~
(dFD
22DM
MDCmd
mdC mdC1tan
• Chance to inspect the radial structure of the magnetic perturbation by studying profiles of
• Chance to radially locate magnetic islands localized at phase inversion radius (flattening of internal temperature of the island, P. De Vries PPCF 39 (1997) 439-451
mdC
October 2008, MPI fϋr Plasmaphysik, Garching
Radial localization of NTM in JET tokamak
With the help of B. Alper
October 2008, MPI fϋr Plasmaphysik, Garching
Radial localization of NTM in JET: used diagnostics
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• High resolution magnetic coils (H302..) (up to 500kHz)
• Off axis high resolution ECE radiometer KK3
KK3F signals (250kHz-1MHz)
October 2008, MPI fϋr Plasmaphysik, Garching
Radial localization of NTM in JET: Analysis procedure
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October 2008, MPI fϋr Plasmaphysik, Garching
Coherence and phase radial profiles
The phase jump radii are recognized automatically.
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n=2 n=2
n=2 n=2
n=3 n=3
October 2008, MPI fϋr Plasmaphysik, Garching
Coherence and phase radial profiles
The phase jump radii are recognized automatically.
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n=2 n=2
n=2 n=2
n=3 n=3
October 2008, MPI fϋr Plasmaphysik, Garching
Outline
Introduction to MHD limiting phenomena
Short description of RFX-mod experiment and of its MHD active control system
RWM in RFX-mod, phenomenology and statistical analysis
NTMs, physics and a method for radial localization
Examples of NTMs localization at JET
Conclusion and future developments
31
October 2008, MPI fϋr Plasmaphysik, Garching
Detailed analysis for JET pulse 73519
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TFS1 High current, high triangularity, 2.5MA, 2.7TMove inner strike point of 14 cm from 18.8 to 19.8s
October 2008, MPI fϋr Plasmaphysik, Garching
Absolute amplitude and frequency
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October 2008, MPI fϋr Plasmaphysik, Garching
Radial localization of tearing modes (tracked)
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October 2008, MPI fϋr Plasmaphysik, Garching
Checked consistency with EFIT
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October 2008, MPI fϋr Plasmaphysik, Garching
Outline
Introduction to MHD limiting phenomena
Short description of RFX-mod experiment and of its MHD active control system
RWM in RFX-mod, phenomenology and statistical analysis
NTMs, physics and a method for radial localization
Examples of NTMs localization at JET
Conclusion and future developments
36
October 2008, MPI fϋr Plasmaphysik, Garching
Conclusions and (near) future developments
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RWM statistical studyFor internal RWM a negative trend of growth rates in respect to IFI was found. Other dependencies are negligible
For external RWM the trend in IFI is not totally clear in the present database, more experimental time is needed to better understand n=6 behaviour
All of the modes have negligible rotation speed, and grow locked to the wall
The statistical analysis may be extended to plasma rotation speed (important in tokamaks)
Future work will aim at enlarging the statistical database, comparing experimental results with modelling, and investigating Resonant Field Amplification phenomena, with emphasis on issues common to tokamaks and RFPs
NTM radial localizationSame analysis method of Central Acquisition Trigger System, but totally automatic and independentSame diagnostic as CATS with a window of 12 seconds (six times larger)Rather large number of points and high temporal resolutionUnder development an algorithm to track mode’s position temporal evolution, the ultimate goal is unattended batch implementation and PPF writing
October 2008, MPI fϋr Plasmaphysik, Garching
Thanks for your attention!
The end
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October 2008, MPI fϋr Plasmaphysik, Garching
Multi-parameter fit
Growth rates fitted using the trial function:
• Negative trend of growth rates in IFI for external modes, positive trend
for external modes (according to theory)
•Strange behaviour of n=6 mode (error fields?)
•βθ and n trend negligible
• High uncertainty and poor statistic for external modes (new
experiments planned)
dcba nFAI
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October 2008, MPI fϋr Plasmaphysik, Garching
Average RWM growth rates
IFI < 0.10.1< IFI < 0.20.2< IFI < 0.3
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October 2008, MPI fϋr Plasmaphysik, Garching
Radial localization of NTM in JET: Analysis procedure
Calculation of |M|2, |D|2, MD* for each sub-blockAverage of this quantities on (16) sublocksCalculation of amplitude and phaseAll the calculation is performed in a narrow frequency band
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22DM
MDCmd
mdC mdC1tan
October 2008, MPI fϋr Plasmaphysik, Garching
ECE density cut off
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eC m
eB
e
eP m
en
0
2
Two plasma mode: O-mode, linear polarization with E//BX-mode, elliptically polarized with E┴B
O-mode cutoff at
X-mode cutoff at
p
P
And at 2
4 22pcc
October 2008, MPI fϋr Plasmaphysik, Garching
Mode analysis for JET pulse 72669
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October 2008, MPI fϋr Plasmaphysik, Garching
Radial localization of tearing modes
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October 2008, MPI fϋr Plasmaphysik, Garching
Checked consistency with EFIT
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