low frequency sawtooth precursor in asdex...

/14G. PAPP IAEA Meeting on Plasma Instabilities 2011-09-06

Budapest University of Technology

1

Low frequency sawtooth precursor in ASDEX upgrade

1) Budapest University of Technology and Economics, Budapest, Hungary2) Chalmers University of Technology, Göteborg, Sweden3) Max-Planck-Institut für Plasmaphysik, Garching, Germany

G. Papp1,2, G. I. Pokol1, G. Por1, N. Lazányi1,L. Horváth1, A. Magyarkuti1, V. Igochine3,

M. Maraschek3 and ASDEX Upgrade Team3

ASDEX Upgrade



Introduction• For a safe tokamak operation the sawteeth have to be

controlled. We lack a complete understanding of the crash.• We have to take into account the transient precursor

oscillations.• A Low Frequency Sawtooth Precursor (LFSP) - lower than

the (1,1) mode - was observed on several tokamaks1-3

2

➡ The LFSP on ASDEX Upgrade was analysed in detail➡ It may play an important role in the sawtooth crash

[1] G. Papp et al, PPCF 53 065007, 2011.[2] Y. Sun et al, PPCF 51 065001, 2009.[3] R. Buttery et al, NF 43 69, 2003.



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• Frequent experimental observation: sawtooth-like jumps of the soft x-ray emission in the core plasma.

• Quasi-periodic flattening of the radial parameter profiles - CRASH

• Precursor oscillations before the crash - kink mode with(m,n)=(1,1) spatial structure

Hot core plasma

Toroidal rotationPol

oida

l mov

emen

t J53Core line of sight (J53)

CRASH

Time (s)

Inte

nsity

(W/m

2 s)

core

outside q=1



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The stochastic model• Local ergodic zones4 arise and lead to the transient transport• This theory is consistent with the measurements (q-prof.

evolution, postcursor mode, etc.) - but exact cause is unknown• Experimental result: a Low Frequency Sawtooth Precursor

(LFSP) is observable in the precursor phase with lower frequency than the kink - Properties? Role in the crash?

mode frequencies. The resulting values were found to be lessthan unity,17,18 which agrees with other measurements3–5 andwith the stochastic model assumption.

It should be noted that special cases of sawteeth are sel-dom observed in ASDEX Upgrade !for example, compoundsawteeth, inverse sawteeth, etc.".19 These crashes were notinvestigated in this paper. We have focused on most commonvariants of the sawteeth.

APPENDIX: RECONSTRUCTION OF THE MAGNETICFIELD LINES STRUCTURE

The sawtooth phenomenon was analyzed by means ofHamiltonian mapping in Ref. 7. The applied method usesexperimental mode perturbations and different safety factorprofiles to trace the field lines of the magnetic field. In the

FIG. 9. !Color online" Poincare plots for the same perturbations but different safety factor profiles. Note that stochastization strongly depends on the existenceof the low-order rational surfaces which are marked on safety factor curves: !a" central q-value is 0.7, !b" central q-value is 0.85, and !c" central q-value is0.9.

FIG. 8. !Color online" ECE images of the sawtooth crash are shown for the same crash as in Fig. 1. These measurements support the clockwise rotation ofthe mode which is seen by SXR tomography. One can see start of the heat outflow through X-point.

122506-6 Igochine et al. Phys. Plasmas 17, 122506 !2010"

Downloaded 25 Jan 2011 to 129.16.109.110. Redistribution subject to AIP license or copyright; see http://pop.aip.org/about/rights_and_permissions

[4] V. Igochine et al, PoP 17 122506, 2010.

ECEI



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Time-frequency evolution• Analysis of O(100) crashes from several years of data• The LFSP appears in most of the crashes investigated

Crash occurs a few (~5) ms after the energy gain of the LFSP• Average growth rate ~400 1/s => possibly a core MHD mode

Spectrogram

LFSP

ram

p-up

pha

se

Sawtooth crash

LFSP correlated with (1,1)

!"#$%&#'&$()*+'$%*#,-./0'123'456'427'-%89:;*<=#6

>?9(@#@*;%:'A;*,'

-4.4 ms

100%

10%

1%

0.1%

0.01%

0.001%

Crash-shifted time [s]

Nor

mal

ized

pow

er

100

10-1

10-2

10-3

10-4

10-5

-0.04 -0.03 -0.02 -0.01 0.00

Time [s]

Freq

uenc

y (k

Hz)

10

20

30

40

0

50

2.5 2.51 2.52 2.53 2.54

Ener

gy d

ensi

ty [a

. u.]

(1,1)

(2,2)

(3,3)

5

4

3

2

1

0LFSP

#23068, I_053Spectrogram



Time-frequency evolution

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• Ridge following algorithm based on graph theory to analyse low energy modes - global shortest path search

• 0.5 < LFSP/(1,1) < 0.7 - not a small order rational• (So far) no correlation was observed with plasma parameters

#24006, J_053

Time [s]

Frequency [kHz]

Frequency ratio

Energy density [a.u.] 10

8

6

4

2

0

LFSP/(1,1)

(1,1)/(2,2)

1.61 1.63 1.64 1.65Time [s]

40

30

20

10

01.60 1.61 1.62 1.63 1.64 1.65

0.7

0.6

0.5

0.4

0.8

0.3LFSP

(1,1)

(2,2)



Connection between the modes

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• Integrate the spectrogram in frequency for a given frequency range ➡ time fluctuation of the bandpower

• > 50% Cross-correlation between the bandpowers ➡ Energy fluctuations of the two modes are connected ➡ Spatial localisation: inside, and slightly outside of q=1

!"#$%&'(

Freq

uenc

y (k

Hz)

10

20

30

0

Ener

gy d

ensi

ty [a

. u.]

40

2.12 2.14 2.16 2.18 2.2

5

4

3

2

1

0

CCF5-9 kHz & 10-17 kHz

!"#$%&$'()%*#+,

95%

0.6

0.4

0.2

0.0

-0.20 5 10 15-15 -10 -5

Peak: 50±5%

Spectrogram Bandpower-correlation

(1,1)

LFSP



• Significant bicoherence (phase coupling) between the (1,1) and the LFSP, already 15 ms before crash

• Clear signs of interaction before the crash ➡ LFSP excited by the (1,1) kink?

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Auto-spectrum Bicoherence

Frequency1 [kHz] Frequency 1 [kHz]

Freq

uenc

y2 [k

Hz]

Bicoherence

[a. u

.]

LFSP8-9 kHz

(1,1)12.5 kHz

LFSP+(1,1)21-22 kHz

(2,2)25 kHz

(1,1) - (2,2)

LFSP - (1,1)

1.0

0.8

0.6

0.4

0.2

0.0

105

104

103

102

Connection between the modes



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Toroidal modenumber• Two Identical SXR cameras at different toroidal positions

-3-3

-2

-1

0

1

2

3

-2 -1 0 1 2 3

Q

/

1617

1819

Inversionradius

ASDEX-U Top view

F

G



Toroidal modenumber

10

• Modenumbers are based on phase difference, calculated in the time-frequency plane (cont. wavelet analysis)

• Filtering to globally coherent modes and goodness-of-fit.• Toroidal modenumber is n=1, same as (1,1)

Full Filtered



Poloidal modenumber

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• Tangential channels in the same toroidal cross-section

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&"#$'

("#$%

)"#$')"#$$

!"#$%&'("%)*'+&

Q

“Detector position”(Straight field line coord.)



Poloidal modenumber

12

• Poloidal modenumber m=1, same as (1,1)• Spatial structure is the same as for the (1,1) kink!• Interaction of the two is very likely (magnetic coupling?)

Full Filtered



The possible role of the LFSP• Interaction may lead to the generation of a broader

ergodic zone around the (1,1) island• Steep gradient can onset fast MHD instabilities that

speed up the collapse5

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(1,1) (1,1) + LFSP

[5] I. T. Chapman et al, PRL 105 255002, 2010.



Conclusions• The stochastic model is a promising theoretical

description for the sawtooth crash• Precursor oscillations are of key importance

➡Time-frequency evolution, spatial localisation and structure of the LFSP was determined6

➡Clear signs of interaction between the two modes➡The LFSP is most probably an MHD mode that might play

an important role in the collapse mechanism• MHD simulations could aid our understanding

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[6] G. Papp et al, PPCF 53 065007, 2011.

low frequency sawtooth precursor in asdex...

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