Low frequency sawtooth precursor in ASDEX...
Transcript of Low frequency sawtooth precursor in ASDEX...
/14G. PAPP IAEA Meeting on Plasma Instabilities 2011-09-06
Budapest University of Technology
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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
/14G. PAPP IAEA Meeting on Plasma Instabilities 2011-09-06
Budapest University of Technology
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
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➡ 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.
/14G. PAPP IAEA Meeting on Plasma Instabilities 2011-09-06
Budapest University of Technology
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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
/14G. PAPP IAEA Meeting on Plasma Instabilities 2011-09-06
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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
/14G. PAPP IAEA Meeting on Plasma Instabilities 2011-09-06
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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)
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>?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
/14G. PAPP IAEA Meeting on Plasma Instabilities 2011-09-06
Budapest University of Technology
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)
/14G. PAPP IAEA Meeting on Plasma Instabilities 2011-09-06
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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
!"#$%&'(
Freq
uenc
y (k
Hz)
10
20
30
0
Ener
gy d
ensi
ty [a
. u.]
40
2.12 2.14 2.16 2.18 2.2
5
4
3
2
1
0
CCF5-9 kHz & 10-17 kHz
!"#$%&$'()%*#+,
95%
0.6
0.4
0.2
0.0
-0.20 5 10 15-15 -10 -5
Peak: 50±5%
Spectrogram Bandpower-correlation
(1,1)
LFSP
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• Significant bicoherence (phase coupling) between the (1,1) and the LFSP, already 15 ms before crash
• Clear signs of interaction before the crash ➡ LFSP excited by the (1,1) kink?
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Auto-spectrum Bicoherence
Frequency1 [kHz] Frequency 1 [kHz]
Freq
uenc
y2 [k
Hz]
Bicoherence
[a. u
.]
LFSP8-9 kHz
(1,1)12.5 kHz
LFSP+(1,1)21-22 kHz
(2,2)25 kHz
(1,1) - (2,2)
LFSP - (1,1)
1.0
0.8
0.6
0.4
0.2
0.0
105
104
103
102
Connection between the modes
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Toroidal modenumber• Two Identical SXR cameras at different toroidal positions
-3-3
-2
-1
0
1
2
3
-2 -1 0 1 2 3
Q
/
1617
1819
Inversionradius
ASDEX-U Top view
F
G
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Toroidal modenumber
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• Modenumbers are based on phase difference, calculated in the time-frequency plane (cont. wavelet analysis)
• Filtering to globally coherent modes and goodness-of-fit.• Toroidal modenumber is n=1, same as (1,1)
Full Filtered
/14G. PAPP IAEA Meeting on Plasma Instabilities 2011-09-06
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Poloidal modenumber
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• Tangential channels in the same toroidal cross-section
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("#$%
)"#$')"#$$
!"#$%&'("%)*'+&
Q
“Detector position”(Straight field line coord.)
/14G. PAPP IAEA Meeting on Plasma Instabilities 2011-09-06
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Poloidal modenumber
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• 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
/14G. PAPP IAEA Meeting on Plasma Instabilities 2011-09-06
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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.
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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.