Chapman, S. C.

Dendy, R. O.

JET EFDA Contributors,

Morris, J.

Todd, T. N.

Watkins, N. W.

Webster, A. J.

English

JET EFDA Contributors

Open Research Online

Open Research OnlineThe Open University’s repository of research publicationsand other research outputsAn Apparent Relation between ELM Occurrence Timesand the Prior Evolution of Divertor Flux LoopMeasurements in JETConference or Workshop ItemHow to cite:Chapman, S. C.; Dendy, R. O.; Webster, A. J.; Watkins, N. W.; Todd, T. N.; Morris, J. and JET EFDAContributors (2014). An Apparent Relation between ELM Occurrence Times and the Prior Evolution of DivertorFlux Loop Measurements in JET. In: Proceedings of the 41st EPS Conference on Plasma Physics, article no. P1.010.For guidance on citations see FAQs.c© [not recorded]Version: Version of RecordCopyright and Moral Rights for the articles on this site are retained by the individual authors and/or other copyrightowners. For more information on Open Research Online’s data policy on reuse of materials please consult the policiespage.oro.open.ac.ukAn apparent relation between ELM occurrence times and the prior phaseevolution of divertor flux loop measurements in JETS C Chapman1,2,4, R O Dendy3,1,4, A J Webster2,3,4, N W Watkins1,2, T N Todd3,4,J Morris3,4 and JET EFDA Contributors41Centre for Fusion, Space and Astrophysics, Department of Physics,Warwick University, Coventry CV4 7AL, UK2Max Planck Institute for the Physics of Complex Systems, Dresden, Germany3CCFE, Culham Science Centre, Abingdon, Oxfordshire OX14 3DB, UK4JET-EFDA, Culham Science Centre, Abingdon, Oxfordshire, OX14 3DB UK1. IntroductionStatistical and time domain analysis of ELMs in Joint European Torus (JET) plasmas isproviding fresh insights into the ELMing process. These plasmas are often well adapted tosuch studies because of their long duration, such that large numbers of ELMs occur underquasi-stationary conditions. Understanding the ELMing process is a key challenge inmagnetic confinement fusion plasma physics given the correlation between ELMing andenhanced confinement regimes, and the constraints on ELM magnitudes in future ITERplasmas. The ELMing process is a multiscale nonlinear plasma phenomenon and informationon the underlying process can be acquired by analysing the distribution of events, here, ELMoccurrences. This was noted initially in Refs.[1,2]. Subsequent advances in the scale andquality of the ELM data from JET, in particular, have led to rapid recent progress. Studieshave involved: transitions in Type I ELMing in a sequence of similar JET plasmas in responseto different gas puffing rates[3]; differentiating between Type I and Type III ELMs from firstprinciples, in terms of extreme value distributions of inter-ELM time intervals[4]; and theidentification of strong (and wholly unexpected) structure in the distribution of inter-ELMtime intervals from a week-long sequence of quasi-identical JET plasmas[5]. Here we turn toa newly identified[6] correlation between ELM occurrence times in JET and the timeevolution of a global measure of the plasma state. The latter is provided by the full flux loopVLD2 and VLD3 measurements, which are proportional to the changing poloidal magneticflux through loops that encircle JET toroidally near the divertor coil system.2. ResultsWe determine the ELM occurrence times Nt by identifying the peak of the Be II signal withineach ELM as detailed in [6] and, from these, the intervals between successive ELMs Nt .Figure 1 plots the successive time intervals between one ELM and the next on a delay plot,that is, 1Nt  versus Nt . There are gaps in the delay plot at time intervals where ELMs occurless often and the plot also shows that there is no ordering between the length of one41st EPS Conference on Plasma Physics P1.010Fig.1: Statistics of inter-ELM time intervals Nt in JET plasma 83769. Top: probability density plotted asnormalized histogram (red) with superimposed continuous pdf (black) inferred using kernel density estimationwith a normal kernel with bandwidth of 0.002. Bottom: delay plot [3] of 1Nt  versus Nt . Vertical greenlines indicate 0.015,0.025,0.035t  .inter-ELM interval and the next, that is, a short Nt can be followed by either a long or short1Nt  . From this plot we see that almost no ELMs occur within ~ 0.01 s of the precedingELM and the most likely inter ELM time intervals are clusteredwithin 0.015;0.015 0.025;0.025 0.035t t t        , for longer t clear gaps cannot beseen in this size of statistical sample. Figure 2 shows the VLD3 signal traces for all ELMsJET plasma 83769, corresponding to the first 3 groups of Fig.1. To afford comparison, theVLD3 traces have all been shifted in time such that t=0 is at the first minimum in the VLD3signal following the first ELM, and in amplitude such that the trace is at zero at t=0. We havemarked on these traces the occurrence times of the first (red) and second (green) ELMs.Ordering the data in this manner immediately suggests a clustering of ELM occurrence timeswith the phase of the VLD3 signal. The left hand panel shows that there is a population ofprompt ELMs which can all be seen to arrive after about one-and-a-half to one-and-three-quarters oscillations of the VLD3 response to the previous ELM.An instantaneous phase can be determined from the complex analytic signal as in [6]. InFigure 3 (left panel) we plot the instantaneous phase of the full flux loop signal versus timefor all the ELMs in JET plasma 83769. We again need to choose a zero time from which tomeasure changes in the full flux loop phase following an ELM and we set this to be the timeof the first ELM as determined from the Be II signal. We can see a clear phase bunchingwhich we verified is found for all non-prompt ELMs in the flat-top period of H-mode in allthese plasmas. The inter-ELM time intervals are not random: ELMs are more likely to occurwhen the full flux loop signals are at a specific phase w.r.t. that of the preceding ELM. Thismay explain the structure that can be seen in the inter-ELM time interval histograms, andwhich has been established in a larger statistical sample [5]. We now establish that this is nota trivial correlation. We generated a shuffled surrogate set of ELM arrival times from the dataas follows. The surrogate occurrence time of an ELM is set as 1N N jt t t   where the inter-41st EPS Conference on Plasma Physics P1.010Fig 2: ELM occurrence times superimposed on VLD3 signal. Multiple time traces for different pairs ofsuccessive ELMs are displayed in three panels, corresponding to the first three groups of inter-ELM timesindicated by red vertical lines in Fig.1. The three panels plot VLD3 signals (black dotted lines) for all ELMs forwhich the inter-ELM time interval is in the range: (left) 0.015t  (centre) 0.015 0.025t   (right)0.025 0.035t   . These traces have all been shifted in time such that t=0 is at the first minimum in theVLD3 signal following the first ELM. Amplitude is set to zero at t=0. The VLD3 signal is normalized as in [6].In the upper panels, the ELM times are marked on each VLD3 trace with yellow filled red circles (first ELM)and green circles (second ELM). The lower panels are a stack of the individual VLD3 signals, with ELM timesdenoted by red (first ELM) and green (second ELM) circles.Fig 3: Left set of panels: ELM occurrence times and VLD3 phase difference between all pairs of ELMs in theflat-top of JET plasma 83769. Right set of panels: same format as left panel, but with randomly shuffled timeorder of the inter-ELM time intervals. Each set of panels is as follows. Main panel: VLD3 instantaneous phase,modulo 2 , plotted as a function of time, up to the occurrence time of the next ELM. The coordinates are time,and phase difference from the occurrence time of the first ELM. ELM occurrence times are marked on eachVLD3 trace with yellow filled red circles (first ELM) and green circles (second ELM). Right hand panel:histogram of VLD3 phase difference at the time of the second ELMs, for inter-ELM time intervals 0.015t (magenta) and for all ELMs (cyan). Top Panel: histogram of inter-ELM time intervals.ELM time interval jt is now selected at random from the set of observed inter-ELM timeintervals in the flat top of a given plasma. This preserves the set of inter-ELM times. Underthis operation, the histogram of ELM arrival times shown in the preceding figures isunchanged. This is shown in Figure 3 (right panels), which is identical to the left panel41st EPS Conference on Plasma Physics P1.010except that the sequence of ELM arrival times has been replaced with our surrogate. On thisplot, we see that the statistical distribution of ELM arrival times is unchanged, but the phasebunching is completely lost.3. ConclusionsIn a series of steady-state H-mode plasmas in the Joint European Torus (JET), a phaserelationship has been identified [6] between sequential ELM occurrence times and the phaseof the signal of the changing poloidal magnetic flux in toroidal loops in the divertor region.We focused on ELMs observed in the Be II emission at the divertor, and compared inter-ELMtime intervals with fluctuations of the signal in the full flux loops VLD2 and VLD3. EachELM produces a clear response in the full flux loop signals, whose subsequent time evolutionto the next ELM we study for several hundred pairs of ELMs. This time evolution isirregularly oscillatory, and a time dependent phase can be obtained by Hilbert transform. Thearrival time of the second ELM in each pair is found [6] to fall into one of two categories: (1)prompt second ELMs, which are directly paced by the initial large-amplitude first cycle of theflux loop response to the first ELM; (2) later second ELMs, whose occurrence times arestrongly bunched with respect to the phase difference of the flux loop signal from the time ofthe previous ELM. The full flux loop signals capture aspects of the global dynamics of theplasma, including large scale plasma motion and divertor dynamics. The quasistationaryplasma state is maintained by perturbations from the control system reactingto plasma motion. Integrated over the large scale, the reaction of the plasma to theseperturbations can be seen in the full flux loop signals. These signals reflect the control systemand plasma behaving as a single nonlinearly coupled system, rather than as driver andresponse. Our result, that the instantaneous phase of the full flux loop signals is a predictor ofELM occurrence, may assist design of ELM mitigation strategies and help quantify theireffectiveness. The prompt second ELMs have lower Be II peak amplitude. Insofar as peak BeII amplitude may correlate with ELM energy release, this suggests a possible ELM mitigationstrategy of encouraging prompt ELM occurrence. We found one JET plasma where theprompt ELMs do not occur, suggesting that there may be plasma conditions that favour theoccurrence of prompt ELMs that are intrinsic to JET operation.This project has received funding from the European Union's Horizon 2020 research andinnovation programme under grant agreement number 210130335 and from the RCUKEnergy Programme [grant number EP/I501045]. The views and opinions expressed herein donot necessarily reflect those of the European Commission.[1] A W Degeling, Y R Martin, P E Bak, J B Lister and X Llobet, Plasma Phys. Control. Fusion 43 1671 (2001)[2] J Greenhough, S C Chapman, R O Dendy and D J Ward, Plasma Phys. Control. Fusion 45 747 (2003)[3] F A Calderon, R O Dendy, S C Chapman, A J Webster, B Alper et al., Phys. Plasmas 20 042306 (2013)[4] A J Webster and R O Dendy, Phys. Rev. Lett. 110 155004 (2013)[5] A J Webster, R O Dendy, F A Calderon, S C Chapman, E Delabie, R Felton et al., Plasma Phys. Control.Fusion, 56 075017 (2014)[6] S C Chapman, R O Dendy, T N Todd, N W Watkins, A J Webster, F A Calderon et al., Phys. Plasmas 21062302 (2014)41st EPS Conference on Plasma Physics P1.010

An Apparent Relation between ELM Occurrence Times and the Prior Evolution of Divertor Flux Loop Measurements in JET

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An Apparent Relation between ELM Occurrence Times and the Prior Evolution of Divertor Flux Loop Measurements in JET

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