Nuclear Instruments and Methods in Physics Research A 720 (2013) 128–130

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Nuclear Instruments and Methods inPhysics Research A

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Preliminary investigations of equilibrium reconstruction qualityduring ELMy and ELM-free phases on JET

M. Gelfusa a,n, A. Murari b, E. Peluso c, P. Gaudio a, F.P. Orsitto c, S. Gerasimov d, JET-EFDAContributors e,1

a Associazione EURATOM-ENEA—University of Rome ‘‘Tor Vergata’’, Rome, Italyb Associazione EURATOM-ENEA per la Fusione, Consorzio RFX, 4-35127 Padova, Italyc Associazione EURATOM-ENEA sulla Fusione, ENEA C.R. Frascati, C.P. 65, I-00044 Frascati, Rome, Italyd EURATOM/CCFE Fusion Association, Culham Science Centre, Abingdon, Oxon OX14 3DB, UKe JET-EFDA, Culham Science Centre, OX14 3DB, Abingdon, UK

a r t i c l e i n f o

Available online 21 December 2012

Keywords:

Equilibrium

Polarimetry

ELMs

Grad–Shafranov

Pick-up coils

02/$ - see front matter & 2013 EURATOM. Pu

x.doi.org/10.1016/j.nima.2012.12.018

esponding author.

ail address: gelfusa@ing.uniroma2.it (M. Gelfu

e the appendix of F. Romanelli et al. 2010

Conf, Daejeon, Korea, October 2010.

a b s t r a c t

On JET, the magnetic topology is normally derived from the code EFIT, which solves the Grad–Shafranov

equation with constraints imposed by the available measurements, typically the pick-up coils. Both the

code and the measurements are expected to perform worse during ELMs. To assess this hypothesis,

various statistical indicators, based on the values of the residuals and their probability distribution,

have been calculated. They all show that the quality of EFIT reconstructions is clearly better in absence

of ELMs. How the responsibility, for the lower quality of the reconstructions, is shared between the

measurements and EFIT is a subject under investigation. & 2001 Elsevier Science. All rights reserved.

& 2013 EURATOM. Published by Elsevier B.V. All rights reserved.

1. The problems of EFIT and the pick-up coils during ELMs

A proper reconstruction of the magnetic topology is a prerequisiteto almost every investigation of tokamak plasma physics. On JET, themagnetic reconstruction is obtained with the code EFIT [1], whichsolves the Grad–Shafranov equation trying to fit the availablemeasurements. Normally in JET only the measurements of the pick-up coils are used as constraints for EFIT. A previous investigation ofthe quality of JET equilibria [2] analysed systematically the residualsof the pick-up coils, i.e., the difference between the original measure-ments and the ones reconstructed from EFIT output. The statisticalindicators used in that work showed that the reconstructions of thepick-up coil measurements was typically of not excellent quality. Theresiduals could be as large as 10% and many coils present a multi-modal residual distribution, typically with two peaks. A candidate toexplain the not completely satisfactory results of the reconstructionsare the instabilities called ELMs [3]. Since the vast majority of JETplasmas present an H-mode phase, they are typically affected bythese instabilities.

Both EFIT and the measurements of the pick-up coils areexpected to present problems during the ELMs. With regard tothe reconstruction code, two main assumptions underlie EFIT:toroidal symmetry and equilibrium between the kinetic and the

blished by Elsevier B.V. All rights

sa).

, in: Proc. 23rd IAEA Fusion

magnetic pressure. The validity of both assumptions is question-able during ELMs. Indeed ELMs are instabilities, in which energyand material are ejected from the plasmas. Moreover, in JET, as inother machines, videos of visible cameras show that the ELMs arenot axial symmetric helical structures [4]. The pick-up coils, intheir turn, are typically surrounded by metallic casings, whichconstitute a shield introducing a delay in the response of thesensors. This delay is of course more relevant during ELMs, whichare fast transients of sub-millisecond scale. The measurements ofthe pick-up coils are therefore also to be considered of lowerquality during the fast transients induced by the ELMs.

With regard to the organization of the paper, in Section 2, thequality of JET magnetic reconstructions is quantified with statis-tical indicators in the ELMy and ELM-free periods. Section 3 isdevoted to more detailed investigations to start assessing therelative importance of EFIT inadequacies during ELMs withrespect to the problem of the pick-up coils delay.

2. The statistical analysis of the residuals

The typical time evolution of the magnetic signals, during thesteady state phase of an ELMy H mode plasma, is shown in Fig. 1.The rapid variations of the magnetic measurements during theperiod of the instabilities appear very clearly. The main diagnos-tics used for the tomographic reconstructions reported in thispaper are pick-up coils and flux loops measuring the localmagnetic field. A pick-up coil is a small cross-section, multiple-turn

reserved.

Fig. 1. Top: Da signal during an ELMy H mode phase; Bottom:the experimental

measurement of coil CX06 for the 75412 shot. The vertical lines indicate the time

intervals assumed affected by the ELMs.

Table 1The w parameters for 10 shots.

Shot number wWELM�10�4 wNELM�10�5 Z-test

75202 1.5170.16 9.0570.97 3.23

75203 1.6970.17 9.771.0 3.65

75205 1.8170.19 6.4970.68 5.75

75208 1.7070.16 8.6170.89 4.58

75209 1.7770.16 8.6570.88 4.96

75210 1.6570.15 6.5070.67 6.09

75229 1.3570.13 9.3170.91 2.64

75230 1.4570.14 8.9570.86 3.38

75412 1.6870.15 7.9470.80 5.21

75554 0.9570.10 5.7870.62 3.16

Fig. 2. Residual distributions for the coil P805B of the shot 75202: (a)total

distribution; (b) without ELMs; (c) only during ELMs.

M. Gelfusa et al. / Nuclear Instruments and Methods in Physics Research A 720 (2013) 128–130 129

coil of wire, used to measure the component of the local magneticfield along the axis of the coil. The output voltage is proportionalto the time derivative of the average magnetic flux linked withthe windings: Voutpdf/dt where Vout is the output voltage of thecoil, and f is the magnetic flux through the coil. Flux loops aresimply coils of larger surface typically located further away fromthe plasma. There are several pick-up coils and flux loopssubsystems at JET placed in different poloidal and toroidalpositions. The results reported in this paper have been obtainedby EFIT, using all available pick-up coils and flux loops available,located in different positions around the machine [2].

The reconstructions presented poloidal and toroidal positionsin this paper. The results reported in this paper have beenobtained by EFITJ (a well-known version of EFIT, described indetail in Ref. [5]), using all available pick-up coils and flux loopsavailable, located in different positions around the machine [2].EFITJ contains an iron core model validated with a series of tests

also reported in Ref. [5]. The spatial derivatives of the pressureand current profiles, p0 and f0, respectively, are represented by firstorder polynomials, which is considered the most conservativesolution when, as in this paper, only the magnetic measurementsare used as inputs to the code.

In order to assess the quality of the equilibrium in the variousphases of the discharge, statistical indicators are required. First ofall, for a given shot and for a given coil ‘‘i’’, a parameter called wi,defined in the following relation (1), has been used:

wi ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiSNi

1 j½BimeasðjÞ�BirecðjÞ�2

q=Ni ð1Þ

where Bimeas is the magnetic field measured by the pick-up coils i

and Birec is the value of the field at the same coil determined onthe basis of the EFIT equilibrium, while the sum is over thenumber Ni of points used, one for each time slice available for anygiven shot, within the particular time interval being consideredfor analysis. An individual w, which describes the overall situationfor a shot and for a given time interval, is then obtained byaveraging the wi over all the individual coils.

A series of 10 discharges, with different values of the mainplasma quantities, has been analysed. In all of them, the para-meter w is significantly higher during the ELMs than in the ELMfree period. This result is quantified for a series of discharges inTable 1. To finally check that the different values of w for the ELMyand ELM-free phases are indeed significantly different, in thestatistical sense, the zeta test has been performed. This impliescalculating for each shot the quantity:

Z ¼ 9cNELM2cWELM9=O s2NELMþs2

WELM

� �: ð2Þ

In relation (2), wNELM is the w computed excluding the timeintervals with ELMs, while wWELM is computed only during ELMs;finally sNELM and sWELM are the corresponding statistical errors.In the hypothesis that the pdf of the residuals are Gaussians, if Z islarger than 1.96, which corresponds to a 95% confidence interval,then the two values are considered significantly different. Fig. 2,depicting the residual distributions for a particular probe, showsthat the Gaussian approximation is more than reasonable, even ifthere are small asymmetries in the pdfs indicating the presence ofsystematic errors. As also shown in Table 1, for all the shots theZ value is 2.64 or higher. In addition, the quality of the recon-structions during the ELMs is worse than in ELM-free periodssince wWELM is always greater than wNELM.

To gain further insight into the issue, the statistical distribu-tion of the residuals has also been calculated for each probe. Asmentioned, the residual distribution is often multimodal in EFITreconstructions. An example is shown in Fig. 2a. In the vastmajority of cases, the second smaller peak is due to the ELMs; thisis illustrated in Fig. 2c and b, in which the residual distribution ofthe ELMs (Fig. 2c) and ELM free phases (Fig. 2b) of the selecteddischarge are reported for a typical coil. In practice, all or asubstantial part of the second peak can be ascribed to the errors

Table 2Zeta-test results after comparing the mean values for the two residuals distribu-

tions (WELM & NELM) for each probe. For each shot more than 50 probes have

been found to work properly and have been therefore included in the analysis.

Shot number Probe number with Z-test inferior to 1.96

75202 Ø

75203 1

75205 8

75208 Ø

75209 Ø

75210 2

75229 1

75230 2

75412 2

75554 2

M. Gelfusa et al. / Nuclear Instruments and Methods in Physics Research A 720 (2013) 128–130130

during the ELMs. This is coherent with what reported in Ref. [2],in which it was shown, using linear and nonlinear correlations ofthe residuals that it was unlikely that the multimodal character ofthe residual distribution function could be due only to systematicerrors in the measurements. Residuals are indeed too uncorre-lated even during different phases of the same discharges to beattributed only to systematic errors in the measurements andhave to be linked to the behavior of the plasma, such as ELMinstabilities.

3. Investigation of individual coil behavior

The analysis of the residuals, amplitude and distribution,indicates quite clearly that the quality of the magnetic recon-struction is lower during the ELMs with respect to the ELM-freephases in JET. This conclusion is valid for all the dischargesinvestigated and the statistical relevance of this conclusion issupported by the results of the Z-test.

Less clear is the main cause of the increased inadequacy of thereconstructions during ELMs. A possible culprit is the delayinduced on the pick-up coils by the shielding and the surroundingmetallic structures. Another cause could be the assumption ofequilibrium between the kinetic and magnetic pressures at thebasis of the Grad–Shafranov equation and therefore of EFIT.Discriminating between these two hypotheses is not an easy taskbut certainly a closer look at the behavior of the individual coils

could shed some light on the issue. To this end, the wi parameterfor the individual coils has been analysed again using the Z-test.This allows determining for which coils the wi are statisticallydifferent and therefore which individual coils are less accuratelyreconstructed during ELMs. In Table 2 the results of the Z-test, asapplied to the mean values of the residuals distributions with orwithout ELMs for each shot, are reported. Practically all the coilsare better reconstructed in the ELM-free period and therefore thisanalysis does not really allow discriminating between the twohypotheses. As a consequence, even if the analysis of individualcoils is very informative and adds confidence to the conclusionthat the reconstruction of the magnetic topology is of lowerquality during ELMs, additional investigations are required todetermine which is the real cause of the problem. A complemen-tary approach consists of assessing whether the coils with moreshielding, and therefore longer delays, are systematically moreaffected during ELMs. Preliminary tests have been performed,using data of a dry run, in which the currents in the divertor coilshave been designed explicitly to investigate the time responseof the pick-up coils. They indicate that there are coils withstatistically longer time response but the residuals of these coilsduring ELMs have an average value significantly less differentfrom zero. This result suggests than the time constant of the coilsis not the major cause of the lower quality of the reconstructionsduring ELMs.

Acknowledgments

This work, supported by the European Communities under thecontract of Association between EURATOM/ENEA, was carried outwithin the framework of the European Fusion DevelopmentAgreement. The views and opinions expressed herein do notnecessarily reflect those of the European Commission.

References

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