Dux, R.

Flaws, A.

Maggi, C.

Maraschek, M.

Peeters, A.

Sassenberg, K.

Scarabosio, A.

Schirmer, J.

Urso, L.

Zohm, H.

English

MPG.PuRe

Rotation Frequencies of MHD Modes in ASDEX UpgradeJ.Schirmer, C.F.Maggi, H.Zohm, G.D.Conway, R.Dux, A.Flaws, M.Maraschek, A.Peeters,K.Sassenberg, A.Scarabosio, L.Urso & ASDEX Upgrade TeamMax-Planck-Institut f̈ur Plasmaphysik, EURATOM AssociationD-85748 Garching b. M̈unchen, GermanyIntroduction Plasma rotation plays an important role for understanding and controllingMHD activity in fusion devices. It is believed that plasma rotation influences the stabilityof MHD modes and may also prevent disruptions. It is still debata le which physics mecha-nisms determine the rotation frequencyfo of different MHD modes in the plasma rest frame.Various assumptions include:fo = flab−n ftor (1)fo = flab−n ftor −m fpol (2)fo = flab−n ftor +m fdia (3)fo = flab−n ftor −m fpol +m fdia (4)fo = flab−m fE×B (5)wheren andm are the toroidal and poloidal mode numbers andflab is the frequency of themode in the lab frame of reference measured by the Mirnov pick-up coils. ftor [= vtor/(2πR)],fpol [= vpol/(2πr)], fdia [= v∗e/(2πr)] and fE×B [= vE×B/(2πr)] are the frequencies derivedfrom the toroidal velocityvtor, poloidal velocityvpol, electron diamagnetic velocityv∗e andthe E×B velocity vE×B respectively at the major radiusR (and minor radiusr) where themode is localized.The frequencyfo is often associated with the plasma toroidal rotation at themodes’ rationalq surface (i.e. assumption (1)) since this rotation dominates in the plasma core. However,recent measurements at JET imply that the poloidal rotationmay also contribute and thereforeassumption (2) is relevant. Previous analysis in ASDEX Upgrade considered assumption (3)[1]. In addition, it is predicted that certain modes, such asideal and resistive MHD modes,rotate with the ExB velocity, giving assumptions (4) and (5)[2]. These two assumptions areidentical and differ only in the methods in which they are measured. The rotation and modefrequency of various MHD modes, such as neoclassical tearing modes (NTM) and toroidicityinduced Alfven eigenmodes (TAE), are investigated here in co-NBI injected discharges andused to test these various assumptions.Technique In the calculation offo, the toroidal rotation is measured by Charge ExchangeRecombination Spectroscopy (CXRS), where the carbon impurity velocity is assumed to bethe main ion velocity. The poloidal rotation is determined by the neoclassical code NEOART[3], the diamagnetic velocity is computed from the electronde sity and electron temperature(both provided by the Thomson scattering diagnostic) and theE×B velocity is measured byDoppler reflectometry, assuming that the phase velocity of the turbulence is small [4]. Theerrors in fo are calculated using the partial derivatives of the variousr tation terms.Two methods are presented for assessing thefo assumptions. For NTMs, the frequencies ofthe modes are compared with the frequencies of their harmonics, wherefo is the mode fre-quency, 2fo, the frequency of the second harmonic, 3fo, the frequency of the third harmonic34th EPS Conference on Plasma Phys. Warsaw, 2 - 6 July 2007 ECA Vol.31F, P-1.133  (2007)and so forth. In addition, the magnitude and sign of the frequencies are investigated. Here, +(-) fo corresponds to the mode rotating in the ion (electron) diamagnetic direction. For TAEs,the frequenciesfo may be compared with theoretical predictions, in which the TAE moveswith a frequencyfo = vA/(4πqR), wherevA = B/(µoρm)0.5 andq = (2m+1)/2n [5].Case Study 1 - NTMs In ASDEX Upgrade, NTMs are triggered by rapidly steppingNBI heating power up to high power levels at the start of the discharge as seen in figure (1).Once the NTM is established, ECRH heating is applied during aramp in the magnetic fieldto hit the resonance surface and stabilize the mode. In discharge #20774, a (2,1) NTM and itsharmonics are detected on a frequency spectrogram of the magnetic pick-up coils. The modeis localized at normalized radiusρpol ≈ 0.70, determined by electron cyclotron emission(ECE) and soft-Xray diagnostics. At this radial position, the rotation and mode frequencies       0.00.51.01.52.02.53.0        02468101214           0123   02468    NBIICRHECRHH98βNStored EnergyIpBtedge necore nekm/s        10   m     MJ, arb. units     MW           MA ,T19    -31 2 3 4 5Time (s)1501000-5050 vtor   Shot 20774: MHA:B31-141 2 3 4 5Time (s)05101520Frequency (kHz)4,26,32,1Figure 1: Time traces of plasma parameters in discharge #20774. On therig t hand side is thespectrogram from the mirnov pick-up coils, showing the onset of a (2,1) NTM and its harmonics at 2s.fo (kHz)fo (kHz)Time (s)Time (s)Time (s)fo (kHz)Time (s)fo (kHz)fo=flab-nftor-mfpol1 1.5 2 2.5 3 3.5 4-10-50510fo=flab-mfExBfo=flab-nftor-mfpol+mfdia1 1.5 2 2.5 3 3.5 4-10-50510fo=flab-nftor1 1.5 2 2.5 3 3.5 4-10-50510=f +mf-nffo lab tor dia1 1.5 2 2.5 3 3.5 4-10-50510Figure 2: Frequencies of a (2,1) NTM mode (black©), its 4,2 harmonic (red) and 6,3 harmonic(blue△) in discharge # 20774.34th EPS 2007; J.Schirmer et al. : Rotation Frequencies of MHD Modes in ASDEX Upgrade 2 of 4are calculated using assumptions (1) to (5) and are shown in figure (2) for the mode and itsharmonics.In all cases, thefo calculated for the mode and its harmonics agree as expected.Usingassumptions (1) and (2),fo is small and the mode is moving in the ion diamagnetic direc-tion. This has been reported previously on other fusion devices [6, 7]. However, when thediamagnetic velocity is also included, the mode appears to be at rest at 0kHz. The singlemeasurement from Doppler reflectometry at 3.4s confirms this. As umptions (3) and (4) givesimilar frequencies since the poloidal velocity is small and negligible here. Note the error barsare larger when includingv∗e due to the uncertainty in the electron density and temperatureprofiles.A similar trend in fo can be seen in discharge # 20097 in which a (3,2) NTM is localizedat ρpol ≈ 0.73. The calculations show that when considering purely poloida and toroidalplasma rotation at this q surface,fo is about +8kHz, as seen in figure (3). In this particularcase, the poloidal rotation is very small. The diamagnetic velocity contribution reduces thefo to about 0kHz, in agreement with four values offo calculated from theE×B velocity. If   Shot 20097: MHA:B31-141 2 3 4 5 6Time (Seconds)01020304050Frequency (kHz)3,26,41,1fo=flab-nftor-mfpol+mfdiafo =flab-nftorfo=flab-nftor+mfdiafo=flab-nftor-mfpolfo=flab-mfExB1 2 3 4 5 6-20-15-10-5051015nfo (kHz)Figure 3:Frequencies of (3,2) NTM mode in discharge #20097.NTMs rotate with the plasmaE×B velocity (assumptions (4) and (5)) as predicted [2], thenthe modes have a rest frequency of 0kHz. This means that NTMs have no intrinsic rotation.Case Study 2 - TAE TAE modes are destabilized on ASDEX Upgrade by ICRF heat-ing. In order to measure the toroidal velocity with CXRS, short NBI blips (≈ 50ms) areintroduced. Figure (4) shows the frequency spectrogram frothe magnetic pick-up coilsof a TAE mode with different n numbers and the frequenciesfo calculated at 4.65s, at thetime of an NBI blip, and atρpol ≈ 0.53. There is good agreement between the theoreticalequation forfo and assumptions (3) and (4). Thefo calculated by assumptions (3) and (4)show no dependence on the n number, being constant at roughly134kHz. On the other hand,assumptions (1) and (2) have poorer agreement, indicating that the diamagnetic velocity isnot negligible. A possible explanation for the poor agreement might be the underestimationof vtor. A q=1 mode withflab ≈ ftor ≈ 4kHz is observed before and immediately after theNBI blip. Taking this extra rotation into account decreasesthe fo calculated by assumptions(1) and (2) to frequencies closer to the theoretical frequencies.Case Study 3 - Disruptions by (2,1) NTMsA plasma disruption can be preceded by the growth of a tearinginstability resonant at theq = 2 surface. Figure (5) shows plasma parameters during discharge # 21363, in which34th EPS 2007; J.Schirmer et al. : Rotation Frequencies of MHD Modes in ASDEX Upgrade 3 of 4   Shot 17758: MTR:B31-144.0 4.5 5.0 5.5Time (Seconds)050100150200250Frequency (kHz)n=6n=5n=4n=3nfo (kHz)f o =flab -nftor -mfpol +mfdiaf o =flab -nf torf o =flab -nftor +mfdiaf o =flab -nftor -mfpoltheoretical f o2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7050100150200Figure 4:Frequencies of TAE modes in discharge #17758.a (2,1) NTM mode grows, locks and causes a plasma disruption a4.2s. The frequenciesfo are calculated at the onset of the mode at 1.1s and right before the disruption at 4.1s.For all fo assumptions, the frequency drops before the disruption andin some cases themode rotation changes from the ion to the electron diamagnetic direction. For example,fo =flab−n ftor −m fpol + m fdia =2.6kHz at 1.1s and -3.6kHz at 4.1s. Likewise,flab decreasesfrom 15.4kHz to 2.7kHz andftor decreases from 3.3kHz to -0.9kHz. This implies that toavoid a disruption, an increase in the plasma toroidal velocity is necessary. On other fusiondevices, this technique has proven to work [8, 9].Summary Several assumptions forfo have been tested        km/s        arb. units      10   m     MJ, arb. units     MW19    -30246810122.50.01.02.002468NBIICRHECRHH98βNStored Energyedge necore ne                             1.50.510201 2 3 4 5Time (s)40300-1050vtor        0-202-201-1Magnetic ProbeSignalsFigure 5: Time traces of plasma pa-rameters in discharge #21363.for NTM and TAE modes in co-NBI injected discharges.The rest frame frequencies during an NTM are small andthe rotation is in the ion diamagnetic direction when con-sidering only toroidal and poloidal fluid velocities. How-ever, with the inclusion of the diamagnetic velocity as re-quired [2], fo decreases to roughly 0kHz, indicating thatNTMs have no intrinsic rotation. Assumption (3) is iden-tical to assumptions (4) and (5) when the poloidal velocityis small, which is typically the case in the plasma core. Inthe case of TAE modes, when comparing thefo assump-tions with fo predicted from theory, assumptions (3) and(4) agree best. Hence, the diamagnetic velocity is not neg-ligible and should be included info calculations.References[1] O.Klüber et al., Nuclear Fusion31, 907 (1991)[2] B.Scott et al., Phys. Rev. Lett.54, 1027 (1985)[3] A.G.Peeters et al., Phys. Plasmas7, 268 (2000)[4] G.D.Conway et al., Plasma Phys. Control. Fusion46, 951 (2004)[5] E.J.Strait et al., Plasma Phys. Control. Fusion36, 1211 (1994)[6] R.J.LaHaye et al., Phys. Plasmas10, 3644 (2003)[7] A.Scarabosio et al., 33rd EPS Conference on Plasma Phys., ECA 30I, P-1.151 (2006)[8] H.Zohm et al., Plasma Phys. Control. Fusion33, 1423 (1991)[9] P.C.de Vries et al., Plasma Phys. Control. Fusion38, 467 (1996)34th EPS 2007; J.Schirmer et al. : Rotation Frequencies of MHD Modes in ASDEX Upgrade 4 of 4

Rotation frequencies of MHD modes in ASDEX Upgrade

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Rotation frequencies of MHD modes in ASDEX Upgrade

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