ASDEX Upgrade Team

Dunne, Michael G.

EUROfusion MST1 Team

Fischer, R.

Fuchs, J. C.

Giannone, L.

McCarthy, Patrick J.

Schuhbeck, K.-H.

Irish Universities

Time-dependent elm-resolved equilibrium reconstruction on ASDEX upgrade

Cork Open Research Archive

Title Time-dependent elm-resolved equilibrium reconstruction on ASDEXupgradeAuthor(s) McCarthy, Patrick J.; Giannone, L.; Dunne, M.G.; Fischer, R.; Fuchs,J.C.; Schuhbeck, K.-H.; ASDEX Upgrade Team; EUROfusion MST1TeamPublication date 2017Original citation McCarthy, Patrick J., L. Giannone, M.G. Dunne, R. Fischer, J.C. Fuchs,K.-H. Schuhbeck, ASDEX Upgrade Team and EUROfusion MST1Team (2017) ‘Time-dependent ELM-resolved equilibriumreconstruction on ASDEX Upgrade’, 44th EPS Conference on PlasmaPhysics, Belfast, Northern Ireland, 26-30 June.Type of publication Conference itemLink to publisher'sversionhttp://ocs.ciemat.es/EPS2017PAP/pdf/P2.131.pdfAccess to the full text of the published version may require asubscription.Item downloadedfromhttp://hdl.handle.net/10468/4872Downloaded on 2018-08-23T19:15:53ZTime-dependent ELM-resolved equilibrium reconstruction on ASDEX Upgrade.P.J. Mc Carthy,1 L. Giannone,2 M.G. Dunne,2 R. Fischer,2 J.C. Fuchs,2K.-H. Schuhbeck,2 ASDEX Upgrade Team,2 and EUROfusion MST1 Team31 Department of Physics, University College Cork, Cork, Ireland.2 Max Planck Institut fu¨r Plasmaphysik, Boltzmannstrasse 2, D-85748 Garching, Germany3see H. Meyer et al., Nuclear Fusion FEC 2016 Special Issue (2017)Introduction and MotivationType I edge-localized modes (ELMs) on ASDEX Upgrade are accompanied by negative voltagespikes of magnitude ≃ 10V measured near the lower divertor, current spikes ≃ 10 kA in measuredpoloidal SOL currents corresponding to several tens of kA of SOL current flowing toroidally, and a≃ 10 kA transient increase in the typically 1MA plasma current (including the SOL toroidal cur-rent) [1]. Inboard and outboard poloidal SOL currents, which are measured at a number of toroidallocations, are reasonably axisymmetric (see fig. 1) and hence ELM-resolved equilibrium reconstruc-tion using an axisymmetric equilibrium code incorporating the SOL poloidal current measurementsbecomes feasible, despite the known 3D character of ELMs [2]. The task of generating loop voltageprofiles from numerical differentiation of a sequence of static equilibrium reconstructions is a chal-lenging one, since there is a trade-off between noisiness and time resolution of such reconstructedloop voltages. Nevertheless, the validity of results such as those presented in [1], in particular themodelling of strong, transient SOL currents during and immediately following a Type I ELM crash,can be questioned as long as the voltage spikes, examples of which are included in fig. 2 cannotbe reconstructed. Accordingly, the present work is motivated by the advantages that would resultfrom a method of solving the time-dependent Grad-Shafranov equation (GSE) in the form−∂∂t∆∗ψ(R,Z, t) = µ0R2 ∂∂tp′(ψ) +∂∂tff ′(ψ) (1)that avoids (a) the above-stated problem of noise or poor time resolution for loop voltage profilescalculated from a sequence of independent static equilibria or (b) having to resort to predictivecurrent diffusion calculations [3].! !!!"#$% "#$& "#$' "#$( "#$" "#$) "#$*+,-.!/012%332"33"3%33%"3 !4567(8''"$9:;5<4:=;>/31:(4567!4567%38''"$9:;5<4:=;>/31:%34567!45;7%(8''"$9:;5<4:=;?/31:%(45;7!45;7%&8''"$9:;5<4:=;>/31:%&45;7!45;7%38''"$9:;5<4:=;>/31:%345;7Fig 1. Measurements of  inboard (green, blue traces) and outboard (magenta, black)  divertor tile currents at 4 separate toroidal locations spanning  six  Type I ELMs for ASDEX Upgrade discharge #33589.  Fig 2. !"#$%#&'())*+,!""-.*)&-(,/-#)0&012*),-)&3"*&'())*+,"#$%""--4"2-",#5*$"at displayed locations for a 30 msec time window containing 3 Type I ELMs for ASDEX Upgrade standard H-mode discharge #33589.  A 7     5.770 5.775 5.780 5.785 5.790 5.795 5.800-15-10-50510  Ip-1MA(kA):33589 Ulid12f:33589 ULi22p:33589 Ipolsola/(kA):33589Ulid12f (V) Inboard voltage loop Loop voltage in divertor region Uli22p (V) Outer divertor Tile poloidal current Ipolsola (kA) Ip offset by 1 MA (kA) Fast signals:  100 µs  moving average pp_PLOT: ipp_PLOTJphi (blue), conf.bands (black),  <Jphi> (red) [MA/m^2]           Pressure (red) [kPa], conf.bands, Input Data (blue)             Knots 372 744 791 837 884 912 921 931 940 968 996                                                          c0p,FF   0.287   2.646 Ipres   50.4% Fax-Fbd   1.62 Vs                   dSOL,pri  251   5 mVs Isol,pri   27.9   0.17 Ipol  0.66 kA                  Jax,Jxp 2.057  0.006 MA  li(3) 1.048    C1fac 0.5615                    bp 0.677 Li 1.233  Qo  1.19 Q95  4.686  Wmhd    0.425 MJ                         Xp( 1.440, -0.955) dF    0 muVs  Xp2( 0.000,  0.000) dF    0 muVs         i 23 re   1 dF 1.7mT  2.4% dB  1.1mT  0.5% dFB 1.30mT                     Loop 12 Loop 22 T ile !"#$ !%&' )*++#,-./&0%.1/23$4.)%&'(!%&'("$*++#,-./&0%.1/23$4."$%&'(!%&/(")*++#,-./&0%.1/53$4.")%&/(!%&/("6*++#,-./&0%.1/23$4."6%&/(!!"!"#$%&'(%!"#$%&'(%Equilibrium reconstruction with multiple timepointsA “multipoint mode” has recently been developed within the CLISTE equilibrium code [4] based ona single solution of the GSE to a narrow window of timepoints. The method, which simultaneouslydetermines ψ(R,Z) and ∂ψ/∂t(R,Z), parameterizes the source terms in the Grad Shafranov equationby free parameters that fit both static amplitudes and time derivatives to a set of spline basisfunctions, and takes account of the dynamics of active coil currents and eddy currents. So far, thetime-dependent terms are constrained by multi-timepoint magnetic data (10 kHz acquisition rate)and SOL tile current data (200 kHz acquisition rate) in an interval < 1 msec centred on the selected44th EPS Conference on Plasma Physics P2.131static equilibrium timepoint. The method is implemented in CLISTE, which extends force balanceinto the open fieldline region and can achieve high fidelity reconstructions of edge pressure data inboth pedestal and SOL regions [5]. Though CLISTE contains an explicit model for vacuum vesselcurrents, the routine method for taking account of passive currents in equilibrium reconstructions,particularly those driven by rapid changes in the fast control coils which lie inside the toroidal fieldcoils on ASDEX Upgrade, is to allow deviations from the measured values of poloidal field (PF) coilcurrents, with the exception of the central solenoid OH current. This method, whose justificationrelies on the vacuum vessel acting to delay the penetration through the vessel wall of changes inPF currents on timescales shorter than the resistive time τR≈ 5msec, succeeds in fitting magneticdata in the presence of significant eddy currents with a quality similar to that of more quiescentphases of the discharge. The favourable results that will be presented here support this approach.In what follows, sample results for an ASDEX Upgrade discharge with Type I ELMs (#33589)are presented, and the new method will be seen to agree quantitatively with experiment once anecessary pre-reconstruction data processing step is taken. It should be noted that the measuredloop voltage at the location of ‘loop 22’ (see fig. 2) played no part in the reconstructions.sxaug35  pjm26154134.pplot  page:   1  Wed Oct 26 15:41:38 2016??Ü????? pp_PLOT: ipp_PLOTpjm 0586280.8127s / 001                                     Version:                                                                   2.04   0.5      1.0      1.5       1.10     1.30     1.50     1.70     1.90     2.10   R  (m)      69.6    15.0     30.0     45.0     60.0     1.10     1.30     1.50     1.70     1.90     2.10   R  (m)    1        2        3        4        5       -0.50    -0.25     0.25     0.50      1.10     1.30     1.50     1.70     1.90     2.10   Jphi (blue), conf.bands (black),  <Jphi> (red) [MA/m^2]           Pressure (red) [kPa], conf.bands, Input Data (blue)             q(R) (red), conf.bands (black)=1/(1/q +/- sigma_iota)                                                                                        Local shear (blue), 2nd axis                                                                                            Spatial errors x 5:    1 cm:    psi error: 100%=1m     midplane sigma[R] profileCLISTE AUG # 33589 t  5.8628 Ip  1.002 MA Bo -2.4972 T nt  1 dt   0.0ms  V1o      V1u      V2o      V2u     V3o     V3u     Coio    Coiu                                              0.33     1.46    -0.22    -0.97    -0.25    -0.25     0.00    -0.00 MAt                                   3.50    15.70    -2.55   -11.32   -8.84    -8.95     0.65    -0.23  kA                                 OHo      OHu      PSLu     PSLo    Quh     Qul     OH2o    OH2u                                            -12.70   -12.70     0.00     0.00     0.00     0.00     1.67     2.24 MAt                                 -37.24   -37.24     1.93     1.35    0.00     0.00    20.67    27.71  kA                                                                                                     sum|Ij|     32.80 MAt               R,Zmag ( 1.682,  0.071) cur ( 1.667,  0.054) geo ( 1.607,  0.019)         a 0.495 b 0.820 k 1.656 ko 1.315 D  0.128 A  1.250 V   12.62              Rin 1.125 Rout 2.135  Ztop 0.818 Zbot -0.948  Fstab/Fun  1.44             Knots 372 744 791 837 884 912 921 931 940 968 996                                                          c0p,FF   0.270   2.592 Ipres   50.3% Fax-Fbd   1.59 Vs                   dSOL,pri  246   5 mVs Isol,pri   72.4   0.89 Ipol  5.85 kA                  Jax,Jxp 1.996  0.147 MA  li(3) 1.102    C1fac 0.5428                    bp 0.651 Li 1.289  Qo  1.23 Q95  4.628  Wmhd    0.417 MJ                         Xp( 1.443, -0.948) dF    0 muVs  Xp2( 0.000,  0.000) dF    0 muVs         i 23 re   1 dF 1.7mT  2.4% dB  1.1mT  0.5% dFB 1.28mT                     MSE 0.00 dP    0Pa dJ.B   0 kAT/m^2 dFR 0.00 dg dq 0.000SOL Fig 3 CLISTE  equilibrium reconstruction during an ELM crash. PF currents (except for OH current) are allowed  to deviate from measured values to mimic vessel currents. RMS fit error for 59 magnetic signals: 1.28 mT ! 1.4% of RMS magnitude. Toroidal SOL current: 72 kA = 7.2% of Ip. A wide SOL width (shown) is necessary to successfully model large SOL currents during ELM crashes when remote divertor tiles (see red dots in graphic to the right of main plot) carry currents which, while smaller than those flowing in the tiles highlighted in the inset in fig. 1, are nevertheless significant. Spati l errors x 5 δ(ψ) error: 1m ! 100% Midplane δ(R) profile 1  Examples of CLISTE equilibrium reconstructions during ELM crashesBefore proceeding to the application of the new method, we present some examples of CLISTEreconstructions during an ELM crash and compare pre-ELM and within-ELM cases. Fig. 3 showsa typical equilibrium reconstruction during an ELM crash, approximately 1 msec after ELM onset.A noteworthy feature is the wide current-carrying SOL magnetic depth (depicted in fig. 3) whichextends to ρpol=1.075 and is required because in addition to the tiles shown in the inset to fig. 1which carry the largest SOL currents, more remote tiles such as those highlighted by red dots inthe graphic to the right of fig. 3 also carry significant current during an ELM crash. The root meansquared fit error to the 59 magnetic signals (17 flux differences and 42 magnetic pick-up coils) was1.42 mT (where each flux difference was converted to an average 〈Bθ,⊥〉 = ∆ψ/A, with A beingthe area between the two participating loops) corresponding to 1.4% of the rms signal magnitude.This is similar to the magnetic signals fit error for inter-ELM timepoints. The measured poloidal44th EPS Conference on Plasma Physics P2.131SOL current of 5.85 kA, which is accurately matched by the reconstructed value, corresponds forthis case to a toroidal SOL current of 72 kA, or 7.2% of the 1MA plasma current.An example comparing magnetic midplane profiles of toroidal current density jφ and equilibriumpressure 0.3msec before and 0.5msec after an ELM onset is shown in Fig. 4. In this case, thejφ peak in the pedestal region which, prior to the ELM, lies ≈ 8mm inside the separatrix (seevertical green markers on the horizontal axes) has moved out to the separatrix at tELM +0.5msec.The pressure pedestal has weakened considerably. These reconstructions were constrained bothby magnetics+tile currents and edge kinetic data interpolated between available Integrated DataAnalysis timepoints [6].Fig 4. Magnetic midplane profiles of current density and pressure from CLISTE reconstructions at tELM – 0.3 msec and tELM +0.5 msec constrained by magnetics and edge kinetics, the latter interpolated from available IDA timepoints [6] (see pressure profile edge region). The dark red vertical markers on the horizontal axes indicate the 11 knot locations for the p (ψ) and ff  (ψ) spline basis functions.sxaug35  pjm23213942.pplot  page:   1     2.04   0.5      1.0      1.5       1.10     1.30     1.50     1.70     1.90     2.10   R  (m)      65.9    15.0     30.0     45.0     60.0     1.10     1.30     1.50     1.70     1.90     2.10   R  (m)   sxaug35  pjm23214007.pplot  page:   1     1.92   0.5      1.0      1.5       1.10     1.30     1.50     1.70     1.90     2.10   R  (m)      67.6    15.0     30.0     45.0     60.0     1.10     1.30     1.50     1.70     1.90     2.10   R  (m)   t = tELM +0.5 msec    ISOL= 92 kA  Wmhd = 427 kJ  t = tELM −0.3 msec,   ISOL= 33 kA,  Wmhd = 456 kJ  MA kPa MA kPa Jϕ (R) with 1σ error bars P(R)   with 1σ error bars Jϕ (R) with 1σ error bars P(R)   with 1σ error bars (R) !Jϕ"  (R) !Jϕ" !            !Application of multipoint mode to an ASDEX Upgrade standard H-mode dischargeTo illustrate the operation of the new multipoint method, it has been applied to equilibrium andloop voltage reconstruction during a sequence of Type I ELMs for ASDEX Upgrade standardH-mode discharge #33589, relevant signals of which have been plotted in figs. 1 and 2. Wepresent results generated by running CLISTE in multipoint mode to obtain ∂ψ/∂t (R,Z) (as wellas ψ(R,Z)) constrained by magnetics and tile current data at 100µs intervals across a 65msectime window containing four Type I ELMs. At each timepoint, data from three neighbouringtimepoints on either side of the central point are used to identify the temporal gradients of thespline basis function amplitudes that parameterize the right-hand side of eq. (1). Thus the temporalresolution of the reconstructed loop voltage function is ±300µs. First results are shown in fig.5, which displays time traces of −(∂ψ/∂t)equilibrium (blue trace), the plasma flux contribution−(∂ψ/∂t)plasma (green trace), and the experimental loop voltage (red trace) at the location of‘Loop 22’, at the location of the red dot in fig. 2. The experimental signal is a moving average ofthe data with a 300µs window. The qualitative agreement is good, insofar as the reconstructedvoltage spikes are almost perfectly coincident with experiment. However, the magnitudes of thespikes are systematically stronger, and the inter-ELM reconstructed signal is noisier.Detailed analysis of the results identified the OH (transformer) current as the cause of the problems.As remarked earlier, this current, unlike other PF currents is not allowed to deviate from itsmeasured value in mimicing the effects of otherwise neglected vessel currents. Since the OH current,by design, generates a very weak in-vessel magnetic field, it would be counterproductive to allowdeviations from experimental values, since these would be very poorly defined by poloidal fieldmeasurements. However, on timescales shorter than the vessel resistive time of ≈ 5msec, changesin the OH current, and hence the in-vessel loop voltage will be shielded. This can be taken intoaccount in a deterministic manner by pre-filtering the OH current signal as follows:I∗OH(t) =∫ t−∞IOH(x)e−(t−x)/τR dx (2)The filtered signal I∗OH(t) is then used in the equilibrium reconstructions where it will have littleor no effect on the ψ(R,Z) solution, but can dramatically affect ∂ψ/∂t (R,Z). Reconstructionsidentical to those shown in fig. 5, except for the substitution of I∗OH(t) for the measured OH current,44th EPS Conference on Plasma Physics P2.131are reported in fig. 6. Here, in contrast to fig. 5, the peak amplitudes of −(∂ψ/∂t)equilibrium agreevery well in all cases with the experimental data (as before, averaged over 300µs) and the inter-ELM behavior is smoother, in closer agreement with experiment, although for two of the four ELMcycles, the experimental loop voltage decays more slowly than the reconstructed signal.!"#! !"#$ !"## !"#% !"#& !"%'!(!!('!!!('Loop 22 data:    300 µs moving avg.  −∂ ψEquil. ∂ t −∂ ψplasma contrib. ∂ t Fig. 5:  Experimental  loop voltage data and CLISTE equilibrium loop voltage, with the .plasma contribution.shown separately, from  a multipoint analysis evaluated at the location of flux loop 22 for a 65 msec window containing 4 ELMs in ASDEX Upgrade disch. #33589. The loop voltage data is smoothed with a  300  µs window!"""V !"#! !"#$ !"## !"#% !"#& !"%'!(!!('!!!('Fig. 6:  Same analysis as in Fig. 5, but this time with OH currents filtered using a 5 msec delay. This mimics the ≈ 5msec resistive time of the AUG vacuum vessel and results in much better agreement between peak values in the CLISTE and experimental loop voltage signals at each ELM crash as well as less noisy inter-ELM behaviour. −∂ ψEquil. ∂ t Loop 22 data:    300 µs moving avg.  −∂ ψplasma contrib. ∂ t V SummaryBy extending the SOL range to include remote tile currents, CLISTE can model an ELM crashwith inter-ELM goodness of fit. A new multipoint mode with time derivative parameters allowsmulti-timepoint magnetic and current data to be fitted with a single GSE solution. Loop voltagesderived from the multipoint fit, while in good qualitative agreement with experiment, were still notsatisfactory. Pre-filtering the OH current with a time constant of 5msec, a representative resistivetime for the ASDEX Upgrade vacuum vessel, is a necessary prerequisite for the good quantitativeagreement between CLISTE reconstructions and experimental loop voltages shown in fig. 6.[1] P.J. Mc Carthy et al., 30th EPS Conf. Plas. Phys. Control. Fusion, St. Petersburg (2003) P-164.[2] A. Kirk et al., PRL 96 (2006) 185001.[3] R. Fischer et al., P 4.133, this conference.[4] PJ Mc Carthy and ASDEX Upgrade Team, Plasma Phys. Control. Fusion 54 015010 (2012).[5] MG Dunne et al., Nucl. Fusion 52 (2012)123014 .[6] R Fischer, Plasma Phys. Control. Fusion 45 (2003) 1095-1111.This work has been carried out within the framework of the EUROfusion Consortium and has received fundingfrom the Euratom research and training programme 2014-2018 under grant agreement No 633053. The viewsand opinions expressed herein do not necessarily reflect those of the European Commission.44th EPS Conference on Plasma Physics P2.131

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Time-dependent elm-resolved equilibrium reconstruction on ASDEX upgrade

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