performance limiting mhd phenomena in fusion devices: physics and active control m. baruzzo

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


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

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Outline







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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


Outline







5


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


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


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


9

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


Outline







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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)


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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)


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


RWM behaviour in RFX-mod

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RWM behaviour, discharge 17304

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Flat plasma current profile


RWM behaviour, discharge 17327

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Peaked plasma current profile


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)


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


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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Statistical study for an internal mode, n=-5

Negative trend with IFI in agreement with

theory


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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


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


Outline







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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)


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


Radial localization of NTM in JET tokamak

With the help of B. Alper


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)


Radial localization of NTM in JET: Analysis procedure

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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


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


Outline







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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


Absolute amplitude and frequency

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Radial localization of tearing modes (tracked)

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Checked consistency with EFIT

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Outline







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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


Thanks for your attention!

The end

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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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Average RWM growth rates

IFI < 0.10.1< IFI < 0.20.2< IFI < 0.3

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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


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


Mode analysis for JET pulse 72669

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Radial localization of tearing modes

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Checked consistency with EFIT

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performance limiting mhd phenomena in fusion devices: physics and active control m. baruzzo

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