Burckhart, A.

Dunne, M.

Fischer, R.

McCarthy, D.

Wolfrum, E.

English

MPG.PuRe

Inter-ELM pedestal current density evolution in ASDEXUpgradeMike G. Dunne1, P.J. McCarthy1, E. Wolfrum2, R. Fischer2, A. Burckhart2, ASDEXUpgrade Team21Department of Physics, University College Cork, Association Euratom-DCU, Cork, Ireland2Max-Planck-Institut für Plasmaphysik, EURATOM Association, D-85748 Garching, GermanyEdge Localised Modes (ELMs) are of great interest in both experimental and theo-retical studies. The current favoured operating scenario for ITER is the Type-I ELMyH-mode. This gives the largest and most sustainable power output. However, the largenumber of particles expelled from the plasma during ELMs could cause problems for thelongevity of the divertor[1, 2]. Studies of the predicted ELM energies in ITER show thatsuch large outbursts are intolerable, given current material designs. This has generated alarge interest in understanding ELMs, as well as in their control.The currently most favoured explanation for the triggering of ELMs is magnetohydro-dynamic (MHD) activity in the form of peeling-ballooning modes[3]. It is thought thatthe edge pressure gradient builds up to a peak value, along with the edge current density.When the stability boundary is breached up to 10% of the total plasma is released over avery short timescale.At ASDEX Upgrade, the edge pressure gradient has previously been analysed[4, 5].However, the current density is more challenging. Techniques such as Motional StarkEffect in the edge, used at MAST(MSE)[6], or Zeeman splitting of the edge Lithiumbeam[7] in D-IIID can be used. These are not presently available at ASDEX Upgrade,and are challenging measurements due to very small effects of a large current peak on aflat poloidal field profile. Another option for obtaining the edge current density comesfrom the Grad-Shafranov equation, of which the exact local current density is a directoutput, given by−∆∗ψ = µ0R2dpdψ+ fdfdψ= µ0Rjφ (1)Using the CLISTE code[8] as an equilibrium solver, the edge current density has beenreconstructed for a full representative ELM cycle. One of the specific advantages of theCLISTE code is its ability to model current density in the scrape off layer.In order to prepare an accurate equilibrium, several diagnostic constraints are required.The only necessary input set is the magnetic measurements. This consists of 38 poloidalmagnetic field coils and 18 poloidal flux measurements. To increase the quality of thedata, all signals were synchronised to an ELM. Events occurring faster than 100 Hz wereexcluded to ensure greater homogeneity of the data set. An example of this procedure,applied to discharge #23225 at 3.0-3.8 s can be seen in figure 1(a). The peak divertorcurrent, shown in figure 2, was taken as the onset of the ELM.It has been shown by McCarthy[9] that the magnetic measurements alone are sufficientto determine the edge current density. Following from this, it is expected that the magnetic138th EPS Conference on Plasma Physics (2011) P1.070 270 275 280 190 195 200 205 365 370 375 380Magnetic field (mT)-125-120-115-110-4  0  4  8Time to ELM (ms)#23225(iv)(iii)(ii)(i)1.00 1.25 1.50 1.75 2.00 2.25 2.50-1.0-0.50.00.51.0#23225 2.999 s:(iv)(iii)(ii)(i)Figure 1: (i)-(iv) show the recorded magnetic signals at various points around the torus, as indicatedin (b), which shows the equilibrium at -3 ms to an ELM.signals in the vicinity of the x point would show the greatest reaction to an ELM crash.Comparing the measurements at different coil locations around the torus, as shown infigure 1(b), this is indeed the case. The coils close to the upper and lower divertorsshow the greatest relative reaction, as expected. This is due to the larger concentrationof current at the outer flux surfaces towards the x-point and the upper portion of theelongated plasma.-20-10 0 10-4  0  4  8Divertor Current (kA)Time to ELM (ms)OuterInner#23225Figure 2: ELM averaged divertor cur-rents. The currents are measured as flow-ing into a divertor tile.However, since the magnetic measurements areinsufficient to recover moments of the pressure pro-file, pressure data, in the form of fitted profiles,is required for an accurate reconstruction. For-tunately, ASDEX Upgrade is well diagnosed withedge electron temperature and density diagnostics.Electron temperature used in this work is mea-sured using Electron Cyclotron Emission (ECE)and density with a combination of Lithium beamand Deuterium-Cyanide-Nitrogen (DCN) interfer-ometry. Pressure due to fast particles has been as-sumed to be negligible in the edge and as such was not included.Integrated Data Analysis (IDA)[10] is a Bayesian approach to data analysis. It com-bines complementary diagnostics, such as the Lithium beam and DCN interferometer inthe case of density, to obtain more accurate profiles. These fits are then ELM synchro-nised in the same fashion as the magnetic measurements. The final diagnostic input is thedivertor currents, shown in figure 2, determined from a tile shunt resistance. This actsas a constraint on the poloidal scrape off layer (SOL) current, and hence the ff’ sourceprofile of the Grad-Shafranov equation.Due to the relatively slow time resolution of the charge exchange diagnostics at the238th EPS Conference on Plasma Physics (2011) P1.070time of the discharges analysed in this study, ion temperatures have not been includedin the analysis. They have been assumed to be equal to the electron temperature. Thishas been shown to be a reasonable approximation in the pedestal at high collisionalityby Wolfrum et al.[5]. The ion density is less well known and relies on an effective chargerelation to the electron density.Sample ELM synchronised pressure and current density profiles output from CLISTEare shown for discharge #23225 at -1.5 ms to an ELM in figure 3 with input constraints,where appropriate. Data was taken between 3 and 3.8 s during the discharge. This has a-2.5 T toroidal magnetic field, 1 MA plasma current, 7.5 MW of neutral beam injectionheating, 0.7 MW of electron cyclotron resonance heating and a 9 × 1021s−1 deuteriumgas fuelling. The kinetic constraints act in this case to strongly localise the edge currentdensity peak. While the integral current densities agree quite well between the red andblue curves up to the point of maximum pressure gradient, the pressure is required formore precise information. This information, combined with an accurate pressure gradientprofile, is important for stability analysis. It is important to note at this point that,although the current density can be constrained by calculating the bootstrap current,〈jneo · B〉, with the formula given by Sauter et al.[11, 12] and a neoclassical resistivityprofile for the Ohmic current, this was not done in this case.. 4 8 12 16Pressure (kPa)Input dataCLISTE fitMagnetics only fitSeparatrix 0 0.4 0.8 1.2 0.8  0.85  0.9  0.95  1  1.05Current density (MAm-1)ρpoloidal#23225(a)(b)Figure 3: (a) Pressure profile. (b) current den-sity profile. The blue line denotes a fit made onlywith magnetics constraints, while the red line is thefit using a prescribed pressure profile. Black boxesrepresent input data points. Error bars are 1 sigmaconfidence bands.Since there are only three dominantcontributions to the edge current den-sity, Ohmic current, bootstrap current andPfirsch-Schlüter currents, a comparison ofthe CLISTE output can be made with the-oretical predictions. Current drive due tofast ions was assumed to be negligible inthe pedestal region. By default, the out-put from the Sauter et al. formula is of theform of a flux surface averaged j · B. Thisis also a standard output of the CLISTEcode. Since the Pfirsch-Schlüter currentscancel out on a flux surface, we require onlythe calculated 〈jneo ·B〉 and the Ohmic cur-rent for this comparison.In order to calculate the Ohmic currentcontribution, the plasma toroidal electricfield was calculated using the method de-scribed in Burckhart et al.[4]. This was combined with a calculated neoclassical resistivityprofile to give 〈jOhmic · B〉 at the same position as the maximum 〈jneo · B〉. Figure 4(a)shows the calculated electric field. The initial value corresponds well with the steady stateloop voltage measured outside the plasma. This diverges during the recovery phase of the338th EPS Conference on Plasma Physics (2011) P1.070ELM cycle, with a negative electric field being modelled.Figure 4(b) shows the edge peaks of the CLISTE output (red) and the calculatedprofile (black). The error bars on the CLISTE fit correspond to a 1 sigma value of theconfidence band. There is excellent agreement between the two curves, especially in thepre-ELM phase. Further improvements to the Ohmic model can be made by using theactual plasma geometry rather than a cylindrical approximation, by combining it withASTRA calculations to determine the current drive due to external sources, and by makinga neoclassical correction to the resistivity.-0.05 0 0.05Electric field (Vm-1) 0 0.4 0.8 1.2 1.6-4  0  4  8<j.B> (MATm-2)Time to ELM (ms)CLISTE outputNeoclassical+OhmicNeoclassical#23225(a)(b)Figure 4: (a) shows the electric field cal-culated at the peak bootstrap position usinga resistive current propagation model. (b)shows the flux surface averaged current den-sity from CLISTE (red), 〈jneo · B〉 (blue) and〈jneo · B〉 + 〈jOhmic · B〉 (black).The neoclassical formula for bootstrap cur-rent from Sauter et al. has been validated bycomparing to CLISTE output, which was con-strained with magnetic signals and input ki-netic profiles. This allows the separate tem-perature and density gradient contributions tothe current density to the analysed, which isquite valuable in the search for an ELM trig-ger. Further work will focus more specificallyon the growth of the ion temperature gradi-ent contribution to both the pressure gradientand bootstrap current. The movement of thestrikepoints, which has been observed to varyby 10-20 mm over an ELM cycle with CLISTE,will also be analysed in more detail. Individ-ual ELMs, rather than ELM-synchronised data,will also be analysed in order to evaluate differences between slow and fast ELM cycles.The authors would like to thank Sibylle Günter and Karl Lackner for valuable discus-sions. This work was supported by EURATOM.References[1] G Federici et al. Plasma Physics and Controlled Fusion, 45(9):1523–1547, September 2003.[2] A Loarte et al. Plasma Physics and Controlled Fusion, 45:1549–1569, 2003.[3] H R Wilson et al. Plasma Physics and Controlled Fusion, 48(5A):A71–A84, May 2006.[4] A Burckhart et al. Plasma Physics and Controlled Fusion, 52(10):105010, October 2010.[5] E Wolfrum et al. Plasma Physics and Controlled Fusion, 51(12):124057, December 2009.[6] M F M De Bock et al. 37th EPS Conference on Plasma Physics, pages 35–38, 2010.[7] D. M. Thomas et al. Physics of Plasmas, 12(5):056123, 2005.[8] P. J. Mc Carthy. Physics of Plasmas, 6(9):3554, 1999.[9] P.J. McCarthy et al. In EPS, Dublin, 2010.[10] R Fischer et al. Fusion Science and Technology, 58(2):675–684, 2010.[11] O. Sauter, C. Angioni, and Y. R. Lin-Liu. Physics of Plasmas, 6(7):2834, 1999.[12] O. Sauter, C. Angioni, and Y. R. Lin-Liu. Physics of Plasmas, 9(12):5140, 2002.438th EPS Conference on Plasma Physics (2011) P1.070

Inter-ELM pedestal current density evolution in ASDEX Upgrade

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Inter-ELM pedestal current density evolution in ASDEX Upgrade

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