ASDEX Upgrade Team

Burckhart, A.

Dunne, M. G.

Fischer, R.

Giannone, L.

Lackner, K.

McCarthy, P. J.

Schneider, P. A.

Wolfrum, E.

English

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H-mode edge current density profiles and scaling at ASDEX Upgrade

Dunne, M.

Schneider, P.

McCarthy, P.

MPG.PuRe

H-mode edge current density profiles and scaling at ASDEXUpgradeM.G. Dunne1, A. Burckhart2, P.A. Schneider2, P.J. McCarthy1, E. Wolfrum2, R.Fischer2, L. Giannone2, K. Lackner2, ASDEX Upgrade Team21Department of Physics, University College Cork, Association Euratom-DCU, Cork, Ireland2Max-Planck-Institut für Plasmaphysik, EURATOM Association, D-85748 Garching, GermanyThe most tested theory to describe Edge Localised Modes (ELMs) is the peeling-ballooning theory. This linear MHD theory predicts a critical edge pressure gradient andcurrent density. Above these critical values unstable mode growth occurs, leading to anELM crash. Observations of the critical pedestal pressure parameters have been madeat several tokamaks [1, 2], all leading to the conclusion that the edge electron pressuregradient saturates before the ELM crash occurs; in some cases the gradient may remainsaturated for several milliseconds. In other cases the ELM occurs just as the gradientreaches this value. The main unknown in all of these situations is the current density inthe pedestal and its behaviour prior to an ELM crash.Current density measurements in a tokamak rely mainly on determining the pitchangle of the magnetic field[3]; the confined plasma region is inaccessible to internal probesdue to the high heat loads they would experience. However, the edge poloidal magneticfield in a medium sized tokamaks, such as ASDEX Upgrade, changes only slightly withthe growth of a large edge current density, and the resulting small variations of pitchangle are challenging to measure.However, there exists an alternative method of determining the edge current density.Through the use of an equilibrium solver the current density is obtained directly from thesolution of the Grad-Shafranov equation. It was shown in [4] that, for an x-point plasma,moments of the current density distribution in the edge region can be recovered usingonly standard magnetic data. The examples shown in [4] are based on the geometry ofASDEX Upgrade, from which the data considered in this paper is also taken.While the integrated edge current can be recovered, moments of the pressure profilecannot; only the total beta can be recovered from the magnetic data alone. However, oncea pressure profile is experimentally determined it can then be used as a constraint for theCLISTE equilibrium solver. This, in combination with the magnetic measurements, nowallows a shape and integrated value of the edge current density to be interpreted. Inaddition, the current in the scrape off layer (SOL) can also be constrained via shunt mea-surements of the poloidal current, providing a valuable extra constraint on the currentdensity distribution. CLISTE fits these measurements by comparing the latest predic-tion for the measurements from a solution of the Grad-Shafranov equation. This is acombination of two source profiles, one being the pressure gradient and the other beingrelated to the poloidal current, described by a curvature regularised cubic spline with, inthe cases here, 11 knots. The final result is a minimisation of all residuals coupled witha pre-determined convergence criterion for the flux grid.An example of this is shown in figure 1 for three timepoints from ASDEX Upgrade dis-charge #23223 in which a Neutral Beam Injection (NBI) power scan was performed. Theelectron pressure profiles were created by applying modified hyperbolic tangent (mtanh)139th EPS Conference & 16th Int. Congress on Plasma Physics O4.110fits to data from ECE and Thomson Scattering diagnostics (electron temperature) andLithium beam, DCN interferometer, and Thomson scattering diagnostics (electron den-sity). The ion temperature was assumed to be equal to the electron temperature, and theion density was diluted from the electron density according to a Zeff of 1.9. The Thomsonscattering data was used to align the temperature and density profiles.0102030Pressure (kPa)Input dataCLISTE fitSepratrix00.511.522.50.85 0.9 0.95 1 1.05Current Density (MAm-2)ρpoloidal#23223 1.875,3.225,5.325 s(a)(b)Figure 1: Current density from discharge#23223 with 5 MW (red), 7.5 MW (blue), and10 MW (black) NBI heating. The boxes in (a)show the input pressure data. The error barsin (b) indicate the one sigma confidence bandsAs the applied power is increased, alongwith a density variation, the pedestal top pres-sure increases (figure 1(a). The pedestal widthalso increases (though the effect is small for thefinal power step), becoming dominated moreby the electron temperature pedestal width.The peak edge gradient also increases, drivinga larger amount of current (via bootstrap andPfirsch-Schlüter mechanisms), as shown in fig-ure 1(b). The ELM frequency in these timeintervals changes from 125 ± 45Hz (red) to100 ± 22Hz (blue) and finally to 105 ± 22Hz(black).In order to asses the validity of the fits, aswell as to determine the ability of magnetic andkinetic data to return a unique current densityprofile, the pressure profile from the high powerphase of discharge #23223 was varied. First,the pressure profile was shifted radially in increments of 2 mm. Second, the parametersof the mtanh fits were varied to give a steeper (narrower) or shallower (wider) pedestalgradient (profile). The sensitivity of external magnetic measurements to changes in thecurrent density distribution could be determined with these two methods. The influenceof these changes to the pressure profiles on the fitting errors of the normal (dΨ) andtangential (Btheta) components of the poloidal magnetic field is shown in figure 2.0.60.811.2-2 -1 0 1 2Pedestal width change (sigma of fit)dΨBtheta0.60.811.2-6 -4 -2 0 2 4 6% deviationPressure profile shift (mm)dΨBtheta#23223 5.325 sFigure 2: % fitting errors from normal (red)and tangential (black) magnetic measurementsin pedestal width (a) and position scans (b)from discharge 23223 (NBI heating = 10 MW).There is a well defined region in which themagnetic errors converge, indicating that thisis the optimal region of parameter space for thepressure profile location and gradient. The xaxis in (a) indicates the change to the pedestalwidth in terms of the confidence bands of theoriginal tanh fit; -1 sigma means the narrowestpossible fit with the allowed fitting parameters.The x axis in (b) denotes the shift of the pres-sure profile; 0 indicates a pressure profile witha separatrix temperature of 100 eV. Minimisingthe errors gives a peak gradient location withan error of ±2mm, outside of which the errorsin the magnetic signals increase. The pedestal width (and hence peak gradient) cannotbe determined with such high accuracy from magnetic data alone (though there seems239th EPS Conference & 16th Int. Congress on Plasma Physics O4.110to be a maximum width, below which the normal field error increases sharply). Thesefindings indicate that the reconstruction of a unique (and accurate) current density profileis indeed possible using the combination of external magnetic and internal pressure data.150250350450550-4 0 4 8 120.60.811.2Pressure gradient (kPam-1)Current density (MAm-2)Time to ELM (ms)Pressure gradient (CLISTE)#24681 2.5 sMeasured pressure gradientPeak edge jFigure 3: Time trace of peak pressure gradientfrom CLISTE (red) and from the input data(black points) and peak edge current density(blue) for ELM sycnhronised discharge #24681.Determination of pre-ELM current densityprofiles is only one facet of analysis allowedby this method. Since several diagnostics withhigh time resolution ([5] and references therein)are combined and synchronised to a single ELMit is possible to obtain a picture of the currentdensity evolution over an ELM cycle with hightime resolution. Shown in figure 3 are the peakpressure gradient and peak edge current den-sity timetraces for ASDEX Upgrade discharge#24681. In the pre-ELM phase the pressuregradient remains at a constant level and fluc-tuates leading up to the ELM crash, indicatingthat it is not a steady growth which eventually causes the ELM. It has been thought that,for such a time evolution, a delayed current density could be responsible for the eventualELM crash.It can clearly be seen in figure 3 that this is not the case and that the current den-sity fluctuates in the same manner as the pressure gradient, as was also reported in [5].Another interesting feature of the current density evolution in this case is the absence ofa resistive delay in the current density evolution relative to the pressure gradient. Thislack of delay can be accounted for by the recovery of the plasma volume after the ELMcrash, also reported in [5].0.40.81.21.6-4 0 4 8 12〈j⋅B〉 (MATm-2)Time to ELM (ms)〈j⋅B〉 (CLISTE)〈jneo⋅B〉〈jboot⋅B〉#24681 2.5 sFigure 4: Time traces of 〈j ·B〉 from CLISTE(red), 〈jneo·B〉 (black), and 〈jboot·B〉 (blue) overa complete ELM cycle.Since the current density is made up of sev-eral separate drives, a complete study wouldinvestigate each of these in turn. The localcurrent density at the plasma edge is drivenby bootstrap current, Ohmic current, and aPfirsch-Schlüter current. The latter parallelcurrent averages out to zero on a flux surface,which allows an easier analysis. Use of thetheoretical formulae for the bootstrap currentand neoclassical resistivity given by Sauter etal.[6, 7] allows a value of 〈jneo · B〉 = 〈jboot ·B〉 + 〈jOhmic · B〉 to be calculated and com-pared to 〈j · B〉 from CLISTE. This is shownin figure 4 for discharge #24681. The large error bars in the CLISTE fit, especially justafter the ELM crash, are reflective of the fact that each timepoint is independent of eachother one, despite the smooth nature of the timetrace.The excellent fit of the theoretical calculation to the CLISTE prediction allows analysisof the current density from the point of view of its individual components. The drop inthe bootstrap current at the ELM crash is much more than the drop in the CLISTE339th EPS Conference & 16th Int. Congress on Plasma Physics O4.110predicted 〈j · B〉; the large drop in non-inductive current is partially compensated by alarge increase in the toroidal electric field in the plasma edge. 〈jboot · B〉 also recoversat a much more gradual pace. This signifies the importance of the Ohmic contribution.The difference that can be seen between 2 and 6 ms in figure 4 is possibly due to differentrecovery rates of Ti and Te profiles.An important addition to this study is an understanding of how the current densityscales. Kinetic profiles, created using an mtanh fitting routine, were taken from a largedatabase of ASDEX Upgrade discharges [8] and the magnetic equilibria reconstructed.The resulting 35 individual current density profiles were then tested for scalings basedon physical assumptions. One of the most significant findings is a nonlinear dependenceof the normalised current density (given by j = jLFS/〈j〉) on the pressure gradient, asshown in figure 5. 0.4 0.8 1.2 4  8  12  16  20  24  28Normalised j (j LFS/<j>)αFigure 5: Peak LFS edge current density plot-ted against normalised pressure gradient for 35ASDEX Upgrade discharges.This figure shows a saturation and declineof the current density as we approach highernormalised pressure gradients (defined as α =−2µ0 ∗ Rq2B0dpdr). The relevance of this regime toITER is that the edge current density is respon-sible for the form of the magnetic shear profileand this can have a stabilising effect on the bal-looning mode. If the edge current density weresuppressed relative to a linear scaling to a highalpha regime predicted for ITER the form ofthe edge safety factor would be affected. Thiswould help to stabilise the current driven low-nmodes but would also reduce the low shear region.AcknowledgementsThis work was partially supported by EURATOM.References[1] A Burckhart et al. Plasma Physics and Controlled Fusion, 52(10):105010, October 2010.[2] D Dickinson et al. Plasma Physics and Controlled Fusion, 53(11):115010, November 2011.[3] M F M De Bock et al. Plasma Physics and Controlled Fusion, 54(2):025001, February 2012.[4] P.J. McCarthy and ASDEX Upgrade Team. Plasma Physics and Controlled Fusion, 54(1):015010,January 2012.[5] M.G. Dunne et al. Submitted to: Nuclear Fusion, 2012.[6] O. Sauter, C. Angioni, and Y. R. Lin-Liu. Physics of Plasmas, 6(7):2834, 1999.[7] O. Sauter, C. Angioni, and Y. R. Lin-Liu. Physics of Plasmas, 9(12):5140, 2002.[8] P.A. Schneider et al. Submitted to: Plasma Physics and Controlled Fusion, 2012.439th EPS Conference & 16th Int. Congress on Plasma Physics O4.110

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H-mode edge current density profiles and scaling at ASDEX Upgrade

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