Gennrich, F.

Hoffmann, Mathias

Juul Rasmussen, Jens

Maszl, Ch.

Naulin, Volker

Schrittwieser, R.

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Downloaded from orbit.dtu.dk on: Dec 19, 2017Empirical Mode Decomposition and its application to Palm Tree Mode analysisMaszl, Ch.; Hoffmann, Mathias; Naulin, Volker; Rasmussen, Jens Juul; Gennrich, F.; Schrittwieser, R.Published in:ProceedingsPublication date:2011Document VersionPublisher's PDF, also known as Version of recordLink back to DTU OrbitCitation (APA):Maszl, C., Hoffmann, M., Naulin, V., Juul Rasmussen, J., Gennrich, F., & Schrittwieser, R. (2011). EmpiricalMode Decomposition and its application to Palm Tree Mode analysis. In Proceedings (pp. P4.064)Empirical Mode Decomposition and its application toPalm Tree Mode analysisCh. Maszl1, M. Hoffmann2, V. Naulin2, J. J. Rasmussen2, F. Gennrich1,R. Schrittwieser1 and JET EFDA Contributors∗JET-EFDA, Culham Science Centre, OX14 3DB, Abingdon, UK1Association EURATOM/ÖAW, Institute for Ion Physics and Applied Physics,University of Innsbruck, Austria2Association EURATOM/RISØ DTU, Technical University of Denmark, Roskilde, DenmarkIntroductionFigure 1: Illustration of an ELM in theexhaust phase at the outboard side of atokamak. If an ELM filament (white) isstopped and captured at e.g. the q= 4 sur-face (green) an outer mode or current rib-bon could be created [1]. Similarly a hole(black) captured on a q= 3 surface couldcreate a palm tree mode (PTM) [2]. PTMsand outer modes are possibly "twins".Recent works report the existence of coherentlong-lived structures or current filaments in theedge of tokamak plasmas. These are found as con-fined current ribbons (outer modes) [1] or palmtree modes (PTM) [2] in the edge of JET for ex-ample. An intuitive model was proposed in [3]which describes the genesis of these structures bya blob/hole creation mechanism during the ELM.ELM filaments with excess current [4], temperatureand density are treated as blobs whereas it is be-lieved that they leave corresponding holes behinddue to current conservation considerations on shorttime scales [5]. It therefore complements the MHDdescription by a blob/hole or "quasi-particle" pic-ture.From pellet injection experiments in DIII-D andTore Supra it is known that maxima of the mass de-position profiles are close to the magnetic q= 2 andq = 3 surfaces. Low order rational surfaces appearto slow down or even stop the polarization drift to-wards the low field side of the plasma [6]. Similarly∗see the Appendix of F. Romanelli et al., Proceedings of the 23rd IAEA Fusion Energy Conference 2010,Daejeon, Korea38th EPS Conference on Plasma Physics (2011) P4.064it is to be expected that the lifetime of blobs and holes is increased in the vicinity of ratio-nal surfaces. The ∇B polarisation of holes is opposite to blobs. Under the assumption that theinterchange drive of a polarised ELM-induced hole moves it into the proximity of a rational sur-face with low q, it should be slowed down or even stopped. Furthermore, large holes and blobscould close on themselves in the vicinity of a rational magnetic field line. For a closed filament,charge interchange imbalance would be short-circuited by parallel currents which would stopthe filament completely. The result would be a closed, well localized filament with a signicantlyincreased lifetime which can only be filled by slow perpendicular transport. Fig. 1 illustrates theproposed events before the holes and blobs reach the resonant surfaces. In this way of think-ing outer modes are ELM filaments which were not able to propagate to the scrape-off layerwhereas palm tree modes are signatures of ELM-induced holes. Nevertheless, the probabilityto create PTMs is smaller because holes travel up the temperature gradient into regions with in-creasing parallel transport. If this is true one can ask why the spectra of outer modes and PTMsshow rich harmonics in the Fourier spectra? Fourier spectral analysis uses linear superpositionsof unlocalised trigonometric functions. Therefore FFT can only be applied to linear and station-ary time series. If nonlinear effects deform the wave profiles towards localisation, FFT needsadditional harmonic components to describe these profiles. Non-stationarity and nonlinearitycan induce spurious harmonic components that cause energy spreading. An example for sucha behaviour would be a Fourier decomposition of a flash light, represented by a delta functionin the time domain. Localised in time functions produce less localised FFTs. Spatial localisedstructures are therefore not independently traveling waves, but highly coherent wave packages.The non-stationary time series may be represented as follows [7].X(t) =n∑j=1a j(t)exp(i∫ω j(t)dt) (1)In order to extract signals from nonlinear or non-stationary time series X(t), the adaptive time-frequency data analysis method "Empirical Mode Decomposition" (EMD) [7] is suitable. EMDacts as a dyadic filter bank to decompose the series into a finite set of so-called Intrinsic ModeFunctions (IMF). Each IMF reflects the data on a different time-scale and admits well-behavedHilbert transforms. EMD ables examinations of noisy linear and nonlinear processes. In con-trast to Fourier spectral analysis the amplitudes a j(t) and frequencies ω j(t) obtained by EMDare functions of time (Eq. 1). Amplitude and frequency modulations described by the IMFs arenow clearly separated.38th EPS Conference on Plasma Physics (2011) P4.064Results and DiscussionPhenomena like PTMs exhibit a current, density and a temperature perturbation. ThereforeEMD was applied to MHD and ECE data of JET. Electron temperature fluctuations of the PTMmeasured by ECE show different behaviour in different channels of the diagnostic (Fig. 2 a).The investigated channels B2:001, B1:012 and B1:011 cover parts of the pedestal region of JETfor pulse #52011, t = 19.164−19.166 s. Channel B1:011 (green) shows large positive temper-ature spikes as the PTM filament enters the detection volume. In contrast, channel B2:001 (or-ange) shows negative spikes compared to the background temperature. Channel B1:012 (blue)suggests a symmetric modulation of the electron temperature without temperature spikes as inchannel B1:011 or B2:001. This observation was quantified in PDFs.a) b)Figure 2: a) Electron temperature fluctuations measured by three different ECE channels atdifferent radial positions. The vertical red line gives insight into the phase relation between thethree signals (JET Pulse: #52011, t = 19.164−19.166 s). b) EMD of channel B1:011. The redsignal shows spiky temperature peaks slightly advanced with respect to the maxima of the blackline. The black line gives the fraction of the current perturbation. A superposition of these twosignals yields the detrended green measured signal from a).Fig. 2 shows the result of EMD. The red signal is the superposition of the first five IMFs,where the black line shows the detrended raw data (green, Fig. 2) minus the red signals. Al-though ECE data sets are pretty noisy, signs of temperatures spikes can be observed in the redsignal. It is assumed that these spikes represent the temperature inside the filament. The blackline is interpreted as distortion of the local equilibrium due to the current perturbation of the38th EPS Conference on Plasma Physics (2011) P4.064PTM and is in phase with the positive temperature spikes. With the Hilbert transform it is pos-sible to compute Hilbert Amplitude spectra (HAS) from the IMFs [7]. This is demonstrated inFig. 3. EMD was applied on magnetics data when a PTM was present (coil T002, JET pulse:#52011).−0.050.000.050.10B (T)051015202530f (kHz)Hilbert amplitude spectrumJET pulse: #52011, Probe: T00219.165 19.166 19.167t (s)log[a(t)+1]0.00000 0.00018 0.00037 0.00055 0.00074 0.00092 0.0011119.165 19.168Figure 3: Hilbert amplitude spectrum ofcoil T002 (JET pulse #52011)The obtained spectrum shows only one dominantmode and some signs of intra-wave modulations.A similar behaviour is observed in HAS of ECEdata although the noisy data sets aggravate the in-terpretation. Usually, in Fourier spectra of PTMsup to seven harmonics are observed. These are alsovisible in wavelet analysis if the popular Morletwavelet is used since it is Fourier based. A draw-back of HAS is that the frequency of the PTM can-not be as easily determined as in FFTs or waveletscalograms. It is therefore useful to combine sev-eral methods to make use of all advantages.ConclusionEMD and HAS from single signals thereby consistently supports the assumption that thePTM is indeed a current filament. The magnitude of the current-induced temperature fluctua-tions can also be deduced and allows an estimate of the influence on the equilibrium.AcknowledgementThis work was supported by EURATOM and carried out within the framework of the Euro-pean Fusion Development Agreement. The views and opinions expressed herein do not neces-sarily reflect those of the European Commission. This work was also supported by grant P19901of the Austrian Science Funds (FWF).References[1] E. R. Solano, Phys. Rev. Lett. 104, 185003 (2010)[2] H. Koslowski et al., Nuclear Fusion 45, 201 (2005)[3] Ch. Maszl et al., Journal of Nuclear Materials (2011), doi: 10.1016/j.jnucmat.2010.12.245.[4] P. Migliucci et al., Physics of Plasmas 17, no. 7, 072507, (2010)[5] J. R. Myra et al., Physics of Plasmas 14, no. 10, 102314, (2007)[6] N. Commaux et al., Nucl. Fus. 50, no. 2, 025011, (2010)[7] N. E. Huang et al., Proc. R. Soc. Lond. A 454 (1998), 903-99538th EPS Conference on Plasma Physics (2011) P4.064

Empirical Mode Decomposition and its application to Palm Tree Mode analysis

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Empirical Mode Decomposition and its application to Palm Tree Mode analysis

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