Conway, G.

Hallatschek, K.

Scott, B.

Tröster, C.

English

MPG.PuRe

Observations on Geodesic Acoustic Mode scaling and corelocalization in ASDEX Upgrade using Doppler reflectometryG.D.Conway, C.Tröster, B.Scott, K.Hallatschek and ASDEX Upgrade TeamMPI Plasmaphysik, Euratom-Association IPP, Garching, D-85748, Germany1. IntroductionZonal flows and associated geodesic acoustic modes (GAM) are radially localized oscil-lating Er × B flows in magnetic confinement devices with an m = n = 0 mode structurebut finite radial extent kr 6= 0. Theory indicates they are generated by non-linear plasmaLOMixerTxRxAcosφ Asinφ    IQdetectorfof LOf     = f  − fref o LOf   + ∆fof  − f     + ∆fo LOv*ivi∇ BO.⊗Bt IpX-modeantennasEr~O-modeantennasu~⊥Microwave sourcem = 0m < 0Figure 1: Schematic of Doppler reflectometerturbulence interactions and in-turnmoderate the turbulence via shearde-correlation - hence they are of ma-jor importance to confinement [1].Coherent fluctuations in the radialelectric field Er have been directlymeasured with high spatial and tem-poral resolution using Doppler re-flectometry on the ASDEX Upgradetokamak (Ro/a ≈ 1.68/0.5 m) [2].2. Measurement TechniquePoloidally tilting a microwave reflectometer, shown schematically in fig. 1, selects, viaBragg scattering, a turbulence k⊥ ≈ 2ko sin θ which generates a Doppler frequency shiftin the backscattered signal, fD = u⊥k⊥/2π, due to the perpendicular movement of theturbulence in the plasma, u⊥ = vE×B + vph [3]. fD is therefore directly sensitive toẼr. MHD fluctuations can also appear in fD, but as they also modulate the backscat-tered signal amplitude A (a measure of ñe at the selected k⊥) they can be discriminated.10 100Frequency (kHz)-4-3-2-1Power (log)κ = 1.59#20737κ = 1.4212kHz18kHzfDARefl.LoS1-4-3-2-1Power (log)Er∼vE×B    (m = 0)∼ne (m = 1)∼10 1001AfDFigure 2: Edge GAM spectra forohmic divertor and limiter geometryUsing a sliding FFT a time sequence of fD and Afluctuations are generated from the weighted meanand the integral of the complex amplitude spectraS(f) of the I and Q fluctuation signals.3. GAM featuresStrong coherent oscillations are observed in thefD spectra between 5 − 25 kHz, even in the ab-sence of MHD activity, with an intensity of 1 to 2orders of magnitude above the background. Theoscillations are generally seen in the edge densitygradient region - where the turbulence vorticityand Er shear are largest [2]. No coherent activityis seen in the open-field SOL region (f−1 spec-tra), nor deep inside the pedestal, i.e. mid-radius34th EPS Conference on Plasma Phys. Warsaw, 2 - 6 July 2007 ECA Vol.31F, O-4.009  (2007)core region (flat spectra). The mode has the features expected of a GAM, its frequencyscales linearly with the sound speed cs =√(Te + Ti)/M (n.b. collisional edge) over awide range of ohmic and L-mode conditions. So far GAMs have not been observed inH-modes. There is no dependence on B or ne. There is no measurable magnetic pertur-bation, and only a weak density perturbation. Since the X-mode Doppler reflectometerantennas are positioned mid-way below the magnetic axis (shown in fig. 2 by red arrows)0 5 10 15 20 25 300510152025GAM frequency (kHz)κ = 1.12κ = 1.27κ = 1.62κ = 1.73κ = 1.40ω = cs/R√Te + Ti35Ohmic ◆L-modeNBI ■L-modeECH ▲Figure 3: GAM frequency vs (Te + Ti)1/2 for var-ious plasma elongation κ at fixed q95 = 3.85the diagnostic is usually insensitive tothe GAM’s m = ±1 pressure side-band mode structure for standard highelongation (κ > 1.5) diverted plas-mas. However, for low elongation non-diverted configurations, when the re-flectometer line-of-sight is closer to them = 1 mode maxima, a correspondingamplitude A peak is often seen (fig. 2).The precise mode structure, however,is still to be confirmed with poloidalmeasurements.4. GAM frequency dependenceAs shown in fig. 3, the mode frequency scales as ωGAM ∝ cs/Ro (sound speed over majorradius) for ohmic and L-mode (NBI and ECRH) Deuterium discharges. The appropriateion mass variation is also seen for Hydrogen and Helium plasmas. The frequency scalingfactor is of the order of unity, but there is a strong inverse dependence on the plasmaelongation κ and a weak direct dependence on the safety factor q. The variation in thescaling is shown in fig. 3 for a series of κ shape scans between 1.116 and 1.737 at a fixedq95 ≈ 3.8 for ohmic plasmas. For single-null divertor configurations the GAM is only0 5 10 15 20 25 300510152025GAM frequency (kHz)Scale f (kHz)L-NBIκ = 1.61, q = 3.88L-ECHκ = 1.737, q = 3.73κ = 1.63, q = 4.45κ = 1.63, q = 3.8κ = 1.62, q = 3.85κ = 1.11, q = 3.66κ = 1.16, q = 3.59κ = 1.27, q = 3.64κ = 1.40, q = 3.79Edge GAMsρ     > 0.95polFigure 4: Edge fGAM vs scale frequencyf = (cs/2πRo)(4π/κb)((1 + κb)−1 − q−195)observed in the edge density gradient re-gion. In fig. 4 the full database of GAMsfor ρpol > 0.95 are plotted against themodel frequency scaling:ωGAM =csRo4πκb(11 + κb− 1q95)where κb is the elongation at the plasmaboundary. The (1 + κ)−1 term arisesfrom the poloidal circumference C =πa(1+κ), the negative q−1 dependence -although not obvious in simple fluid the-ory [4] - may come from the shear, whilethe second κ−1 factor may contain anytriangularity dependence - since δ tendsto increase with elongation.34th EPS 2007; G.D.Conway et al. : Observations on Geodesic Acoustic Mode scaling and core localization in ... 2 of 4#20787 Ohmic κ = 1.12 q95 = 3.5ρ = 0.78ρ = 0.991kHz       100-4-3-2 ρ = 0.950.00.51.01.52.02.5Radius  ρ polDensity (×10   m   )19    -30.7 0.8 0.9 1.0 1.10eV1002003004005001432qne (Refl)Te (ECE)fGAMpeak ×100510152025Frequency (kHz)GAM intensity (arb)00.10.20.3fD rmsω = √2cs/Ro ω = 4πcs/Roκ {(1+κ)  -q  }-1    -1plateaupeaksplitingpedestalFigure 5: ne, Te, q plus fGAM & amp. profiles5. GAM mode-lockingExperimentally the GAM frequency isnot a smooth monotonic function of ra-dius (unlike temperature) but shows aseries of distinct steps and plateaus afew cm wide. The plateaus become pro-gressively wider with decreasing radius.An example is shown in fig. 5 of fGAMagainst normalized radius ρpol for thecircular (κ = 1.12) inner limiter ohmicdischarge #20787. The plateaus coin-cide with maxima in the GAM intensity(fig. 5 lower box) which suggests nestedzonal flow layers where the mode phaselocks across each zone. At the edge ofeach plateau the GAM intensity dropsand the GAM frequency jumps, usu-ally with splitting in the spectral peak.When the GAM intensity is weak be-tween zones the mode unlocks and itsfrequency increases with cs.6. Core GAM behaviourFor inner limiter configurations the edge density pedestal can be weakened (ne ∼ 1×1019compared to > 2.5 × 1019 m−3 for divertor configuration) allowing the GAM to reachfurther into the core, as far as ρpol ∼ 0.75 for low κ and high q95. The mean frequency ofthese core GAMs, however, diverges from the edge GAM scaling in fig. 4 and now tendsto follow more closely the classical circular plasma scaling ωGAM =√2cs/Ro as seen inκ = 1.11, q = 3.66 (e)κ = 1.16, q = 3.59 (e)κ = 1.10, q = 3.00κ = 1.09, q = 3.04κ = 1.09, q = 3.81-3.57κ = 1.11, q = 5.75-5.510 5 10 15 20 25 300510152025GAM frequency (kHz) f (kHz) = √2cs / 2πRoEdge ρ    > 0.95Core ρ    < 0.95polpolFigure 6: Core fGAM vs f =√2cs/2πRofig. 5. The fit to the circular scaling isshown in fig. 6 for the GAM databasewith κb < 1.16 and a range of q95.For GAM peaks outside ρpol ≈ 0.95the points are marked in lighter greycolour. These points do not fit the cir-cular scaling but still follow the previ-ous edge frequency scaling, indicatingthat (even at κ = 1.1) the physics isdifferent in the density gradient region,where effects such as higher turbulencedrive, higher collisionality, larger q andmagnetic shear, larger vorticity and thestronger Er shear are present.34th EPS 2007; G.D.Conway et al. : Observations on Geodesic Acoustic Mode scaling and core localization in ... 3 of 40.00.10.60.50.40.30.20.75 0.80 0.85 0.90 0.95 1.00 1.05Radius ρpolL-modeNBIOhmichigh q95GAM Intensity (arb.)κ = 1.63, q = 4.20κ = 1.61, q = 3.84κ = 1.61, q = 3.84κ = 1.74, q = 3.69κ = 1.61, q = 3.88κ = 1.11, q = 5.75κ = 1.09, q = 3.81κ = 1.09, q = 3.04κ = 1.10, q = 3.00κ = 1.11, q = 3.66κ = 1.16, q = 3.59κ = 1.27, q = 3.64κ = 1.40, q = 3.79Figure 7: GAM spectral intensity vs radius ρpol7. GAM localization & dampingFig. 7 shows the GAM spectral peak in-tensity vs radius ρpol for a range of dis-charges. The GAM is generally mostintense in the edge density gradient re-gion (excepting the ohmic low κ high q95case). There is no clear preferred radialpeak position and there is no alignmentwith rational q surfaces. The peaks be-come broader towards the core. The ef-fect of increased turbulence drive withadditional heating is also evident in thestronger L-mode peaks.10−610−410−21001021040.00.1Damping rate γ = ω        exp(−q  )2GAM0.60.50.40.30.2GAM Intensity (arb.)GAM dampedin low q coreGAM weak inhigh q edgeγ −0.2Figure 8: GAM intensity vs damping rate γFig. 7 also shows the GAM intensityand radial extent increase with q95.Plotting the GAM intensity vs the fluiddamping rate [5] γ = ωGAM exp(−q2)in fig. 8 shows the suppression of theGAMs in the core as q local falls, aswell as at very high q in the edge. Theradial maxima points are marked witherror bars. The GAMs also disappearat high collisionality.8. ConclusionsTwo distinct groups of GAMs separated by the density pedestal are observed. In thegradient region the GAM frequency universally scales inversely with κb and q95. The shapedependence is expected from the m = 0 to m = ±2 mode coupling due to elongation.Reducing the pedestal influence via the limiter reveals a second GAM branch extendinginto the core. For circular plasmas these GAMs scale as ω ≈√2cs/Ro (note q > 1 soits role is weak). Radial steps in fGAM indicate mode-locking across zonal layers withfrequency splitting at zone boundaries. The mode damping, intensity ∝ exp(−q2), is notinconsistent with either fluid or parallel (sound wave) losses etc. Studies are in-progressto check for shear and profile scale length (R/LT etc.) sensitivity, as well as comparisonswith various fluid and gyrokinetic predictions.9. References[1] P.H.Diamond et al. Plasma Phys. Control. Fusion 47, R35 (2005)[2] G.D.Conway et al. Plasma Phys. Control. Fusion 47, 1165 (2005)[3] G.D.Conway et al. Plasma Phys. Control. Fusion 46, 951 (2004)[4] N.Winsor et al. Phys. Fluids 11, 2448 (1968)[5] P.Angelino et al. 33rd EPS Conf. Plasma Phys. (Rome), ECA 30I, P1.195 (2006)34th EPS 2007; G.D.Conway et al. : Observations on Geodesic Acoustic Mode scaling and core localization in ... 4 of 4

Observations on Geodesic Acoustic Mode scaling and core localization in ASDEX Upgrade using Doppler reflectometry

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Observations on Geodesic Acoustic Mode scaling and core localization in ASDEX Upgrade using Doppler reflectometry

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