Reimerdes, H.

Sauter, O.

Wenninger, R.

Zohm, H.

English

MPG.PuRe

3D structure of the non-linear ELM phaseRP Wenninger1, H Reimerdes2, O Sauter2, H Zohm31Universitätssternwarte der Ludwig-Maximilians-Universität, 81679 München, Germany2 Ecole Poytechnique Fédérale Lausanne (EPFL), CRPP, Euratom Association, Lausanne,Switzerland3 Max-Planck-Institut für Plasmaphysik, EURATOM Association, Garching, GermanyEdge localised modes (ELMs) allow sufficient purity of tokamak plasmas to be maintained andthus enable stationary H-mode. However in a future device large unmitigated ELMs are be-lieved to cause divertor power flux densities far in excess of tolerable material limits. Hence thesize of energy loss per ELM and the resulting ELM frequency must be controlled. The ELMsize is determined by its non-linear evolution [1, 2]. It is therefore important to understand thenon-linear evolution of the ELM associated perturbation and the resulting pedestal erosion in3D. This paper concentrates on an analysis of the toroidal structure of magnetic perturbationsduring type I ELMs in TCV.The operational space of the TCV tokamak [3] includes H-mode plasmas in X-point config-uration with a wide range of plasma shapes. Discharge 42062 is performed in a diverted lowersingle null configuration [4]. Key parameters are: Plasma current 300kA, magnetic field onmagnetic axis 1.43T, safety factor at 95% poloidal flux 2.3, central (pedestal top) electron den-sity 5   1019m  3  3  8   1019m  3  , central (pedestal top) electron temperature 2.5keV (0.5keV).The discharge is heated with 135kW ohmic power, 900kW ECRH power (X3) launched fromthe top of the vacuum vessel and 520kW ECRH power (X2) launched from the low field sidein the X-point vicinity. In a similar discharge (42547) an increase in X2 input power leads to anincrease in ELM frequency, documenting the type I character of these ELMs [4].TCV is equipped with an extensive set of magnetic probes, which are mounted on the innerwall of the vacuum vessel [5]. All magnetic data presented in this paper are acquired by a setof 16 toroidally equally spaced probes in identical poloidal positions on the magnetic low fieldside (LFS). These probes sample the time derivative of the poloidal magnetic field componenttangential to the wall with 250kHz.The time, at which the Dα -radiation from divertor and main chamber exceeds 5% of its maxi-mum value during the ELM, is used as ELM reference time tDα  ons.The magnetic perturbation δB, which is the focus of this work, is obtained by integration fromtDα  ons  0  15ms and subtraction of the n  0 component. Figure 1(a) shows the magnetic per-turbation δB during an ELM in discharge 42062 as function of time t and toroidal angle φ . Thistype of data presentation allows to identify trajectories of peaks and dips of δB in φ  t  space.A trajectory of a peak of δB obtained by application of a dedicated tracing algorithm is alsoillustrated in figure 1(a). Figure 1(b) displays the evolution of the perturbation on the trajectory(δBtra j) and Dα -radiation. Assuming the perturbation is field aligned during the growth phaseof δBtra j, the propagation direction of single excursions can be mapped into the electron dia-magnetic drift direction as observed earlier on other experiments [6–8].39th EPS Conference & 16th Int. Congress on Plasma Physics O3.1050246φ [rad]δB−0.1 −0.05 0 0.05 0.1 0.1500.511.522.5x 10−3t−tDα,ons [ms]  δ Btraj [a.u.]Dα [a.u.]0 \pi/2 \pi 3\pi/2 2\pi−1−0.500.511.542062 at 0.701sφ [rad]δ BnormFigure 1: Evolution of profiles of δB in the rise phase of an ELM at 0.7011s in discharge 42062: (a) δBas function of t and φ . The identified trajectory is marked by dots (the larger ones in color indicate timesteps shown in (c)). (b) Evolution of δBtra j and Dα -radiation during the same time interval. (c) Shiftedtoroidal profiles of δB normalized by δBtra j(t). For the identification of time instances the same colorcode as for the dots in (a) and (b) is used.Figure 1(c) shows the evolution of toroidal profiles of δB for an ELM during a phase, in whichδBtra j is growing more than a factor of 10 up to its maximum value. The profiles have beenshifted for each time instance in a way, that the main peak is at a fixed toroidal position1 andnormalized by δBtra j. The minimum at φ  1  5 has some evolution in relative depth. Howeverthe fundamental shape of the profile is maintained throughout the entire time interval displayedand may be described as stiff. A similar behavior has been observed for the vast majority ofELMs.This observation documents that the temporal and the spatial dependence of the magnetic per-turbation are approximately separable,allowing the magnetic perturbation to be described as:δB  t 	 φ   g  t  f  φR  with φR  φ  ωt (1)where φR is the toroidal angle in the system rotating with the perturbation, g is a functiondescribing the overall growth and decay of the perturbation and f is the stiff toroidal modestructure.In order to investigate the stiff toroidal mode structure again the frame is chosen, in which theperturbation is at rest. After the toroidal shift the profiles are averaged for each toroidal positionover time. The criteria for the selection of time instances t to include are:1From the average apparent toroidal velocity a toroidal angle φshi f t  t  is calculated, by which the profile ata given time has to be shifted, to stay in the frame where the main peak is at a fixed toroidal position. To copewith the problem of discretisation of toroidal positions Fourier transformation in combination with the equalityFT  B  φ  φshi f t  t  t  eiφshi f t  t  FT  B  φ  t  is applied. From the obtained Fourier coefficients the shifted profilesin real space are reconstructed.39th EPS Conference & 16th Int. Congress on Plasma Physics O3.1050 pi/2 pi 3pi/2 2pi0δ Bav [mT]0 2 4 6 800.51n0 pi/2 pi 3pi/2 2pi00 2 4 6 800.51n0 pi/2 pi 3pi/2 2pi−0.800.80 2 4 6 800.51nδ Bn av [a.u.]0 pi/2 pi 3pi/2 2pi−0.500.5δ Bav [mT]0 2 4 6 800.510 pi/2 pi 3pi/2 2pi−0.400.40 2 4 6 800.510 pi/2 pi 3pi/2 2pi−0.500.50 2 4 6 800.51δ Bn av [a.u.]0 pi/2 pi 3pi/2 2pi−1−0.500.51φ [rad]δ Bav [mT]0 2 4 6 800.20.40.60.811.21.41.60 pi/2 pi 3pi/2 2pi−0.400.4φ [rad]0 2 4 6 800.20.40 2 4 6 8051015nmaxFigure 2: Shifted and averaged toroidal profiles of δB during the growth phase of 8 ELMs in discharge42062: All figures except the bottom right one show for an individual ELM the magnetic perturbationδBav averaged over a number of selected time instances as a function of φ (black). In the same plotsthe compensated amplitudes of the mode components δBnav are illustrated (right and top axis, blue).The blue dashed lines represent the Fourier transform of the inter-ELM fluctuation level. The bottomright plot shows the histogram of the mode number nmax corresponding to the maximum compensatedamplitude of the mode component over a set of 23 ELMs.1. δBtra j  t  0  5  max  δBtra j  ,2. the set of time instances is without gaps and ends at t  t  δBtra j  max  δBtra j  .Normalization to the overall growth described by g in equation 1 is not applied, as the variationin profile peak (dip) size is limited by the first selection criterion. More than 50% of the ELMsare deselected due to failure of the tracing algorithm or less than 4 time instances fullfillingthe criteria. Figure 2 displays the shifted and averaged profiles of δB for 8 ELMs in discharge42062. A considerable range of profile shapes can be observed. In most cases the entire toroidalcircumference is affected by a significant perturbation.The radial decay of magnetic perturbations depends on the local poloidal mode number, whichis determined by the local field line inclination in combination with the toroidal mode number.Close to the separatrix at the LFS the local field line inclination is almost constant. Therefore itis straight forward to compensate this radial decay in the Fourier representation. The extent ofthe radial decay is estimated by a code evaluating synthetic probe signals evoked by a mode inthe plasma edge, which is represented as a superposition of current filaments [9]. An exponentialfit gives a radial decay ofδB  δBmode ∝  r  rP   0  91  n 	 (2)39th EPS Conference & 16th Int. Congress on Plasma Physics O3.105where δBmode is the magnetic perturbation at the mode location (plasma edge), r  rP  1  41 isthe ratio of minor radii of probe and mode location and n is the toroidal mode number.Figure 2 displays in blue amplitudes of the mode components of δBav, where the mode numberdependent radial decay is compensated. Higher absolute values of the amplitude of the modecomponent for low toroidal mode numbers can be observed as a general trend. This is con-firmed by the bottom right plot in figure 2, which displays the histogram of the mode numbernmax corresponding to the maximum compensated amplitude of the mode component for the setof ELMs selected. The n  1 component is the strongest for the majority of these ELMs.The Fourier transform of the inter-ELM fluctuation level has been indicated as a dashed linein figure 2. Only in some cases the absolute value of the coefficients corresponding to highertoroidal mode numbers are below this level. However this casts no doubt on the general trendof components with low toroidal mode number dominating. Furthermore by comparison of thesigns of the toroidal velocities of the main profile peak and the phase of the Fourier coefficientsa dominant aliasing effect has been excluded.In this paper it has been demonstrated that the magnetic perturbations in the ELM growth phaseof a relatively strongly heated TCV discharge has a stiff toroidal mode structure. This stiffnessis a sign of coupling of toroidal mode components. As this is incompatible with a linear pertur-bation it indicates non-linear interaction. Furthermore it has been shown that in this phase n  1is the dominant component of this stiff toroidal mode structure in the majority of cases. Thisis of special significance when compared to results from linear stability analysis [10]. Here atoroidal mode number n of 1 or 2 is even below mode numbers of the most unstable modes fortypical kink/peeling modes (n  3  6) and clearly below the ones for typical peeling-ballooningmodes (n  5  20). In summary there is a strong indication that in contrast to the linear ELMphase in the non-linear ELM phase low toroidal harmonics (n  1  2) become the dominantcomponent of the perturbation.References[1] G. Huysmans and A. Loarte. J.Nucl.Mater., submitted, (2012).[2] P. B. Snyder, H. R. Wilson, and X. Q. Xu. Physics of Plasmas, 12 (2005).[3] S. Coda for the TCV team. Nuclear Fusion, 51 (2011), 094017.[4] J. Rossel, J.-M. Moret, et al. Nuclear Fusion, 52 (2012), 032004.[5] J.-M. Moret, F. Buhlmann, et al. Review of Scientific Instruments, 69 (1998), 2333.[6] M. Valovic et al. 21th EPS Conference on Controlled Fusion and Plasma Physics, (1994).[7] J. Neuhauser, V. Bobkov, et al. Nuclear Fusion, 48 (2008), 045005.[8] R. Wenninger et al. Accepted by Nuclear Fusion - preprint available athttp://arxiv.org/abs/1202.3603, (2012).[9] H. Reimerdes, O. Sauter, et al. Phys. Rev. Lett., 88 (2002), 105005.[10] P. Snyder, N. Aiba, et al. Nuclear Fusion, 49 (2009), 085035.39th EPS Conference & 16th Int. Congress on Plasma Physics O3.105

3D structure of the non-linear ELM phase

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3D structure of the non-linear ELM phase

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