ASDEX-Upgrade-Team

Gude, A.

Günter, S.

Maraschek, M.

Sesnic, S.

English

MPG.PuRe

NEOCLASSICAL TEARING MODES AND THEIR INTERACTIONWITH FISHBONES AT ASDEX UPGRADEA. Gude, M. Maraschek, S. Günter, S. Sesnic, and the ASDEX Upgrade TeamMax-Planck-Institut für Plasmaphysik, EURATOM-AssociationD-85748 Garching, Germany1. IntroductionThe maximum achievable β in ASDEX Upgrade is often limited by neoclassical tearing modes(NTMs) [1,2]. The strongest restriction on stationary β is imposed by the coupled (3,2) and(2,2) NTM. However, for low enough collisionality the (2,1) NTM can be additionally excited,leading to further deterioration of the confinement. The interaction between the (3,2) NTMand MHD activity on the q = 1 surface, especially fishbones, has been studied. Theoreticalinvestigations (e.g., [3,4]) show that an NTM only grows if a minimum island size (seed island)is present in the plasma. To study the features and origin of the seed island, the early phase ofthe (3,2) NTM has been investigated using soft X-ray (SXR) and Mirnov diagnostics. Usually,the NTM begins with a finite amplitude, but in few cases no seed island has been observed [5].The collisionality dependence of NTMs according to the ion polarization current model [4] hasbeen examined.2. Interaction between (1,1) and NTMFig. 1 shows the evolution of an NTM.(1,1) activity, in many cases fishbonebursts, is always observed before theonset of the NTM. The early NTM fre-quency decay (of≈ 100 ms) reflects thereduction of the momentum and energyconfinement time due to the NTM. Thefrequency decrease is in agreement withthe experimentally observed reductionof the plasma rotation frequency. Thereduced energy confinement shows inthe decrease in βN (Fig. 1 c)) with con-stant heating power at the onset of theNTM.During the NTM phase, precedingMHD activity ((1,1) mode, sawteeth,and fishbones) is usually suppressed orweakened. In Fig. 1 a weak (1,1) modeis observed during the NTM phase,which is the subharmonic of the (2,2)component of the NTM.71428361020# 9865NTM (3,2) + (2,2)(1,1)(1,1)sawtooth crash1.9 2.0 2.1 2.32.2 2.4 2.6 2.72.5t (s)f (kHz)1.82.22.6even nodd n(a.u.)(a.u.)βNa)b)c)Figure 1. a) Wavelet plot [6] of an NTM. Dark areasrepresent mode activity. Before the onset of the NTM at2.126 s fishbone bursts are seen. b) Mirnov signals. Theeven n signal is dominated by the NTM, the odd n signalby (1,1) modes. c) βN = βtaB/I with βt = 2µ0p/B2t ;the arrow indicates the increase of neutral beam injectionpower from 5 to 7.5 MW.#9873STeven n odd n t = 2.002 s +10 ms +20 ms(a.u.)(a.u.)#9855 ELMseven n odd n (a.u.)(a.u.)t = 2.338 s +10 ms +20 msa) b)Figure 2. Mirnov signals for even and odd toroidal mode numbers. The spikes in the even n signal andthe corresponding fluctuations in the odd n signal indicate ELMs. The NTM begins at ≈ +10 ms in bothcases. a) NTM following a sawtooth crash b) NTM without trigger.The suppression of fishbones during the NTM can be understood in terms of the fishbonestability diagram [7,8]. The onset of the NTM flattens the plasma pressure between the q = 1.5and the q = 1 surface (coupled (3,2) and (2,2) mode). The reduction of the ion diamagneticdrift ω∗i can shift the plasma into the stable region. When the neoclassical mode disappears, thepressure partly recovers leading again to precessional fishbones and (1,1) sawtooth precursors.3. NTM after different trigger eventsThe NTM can be triggered by a sawtooth crash or by fishbone activity. In cases after a sawtoothcrash the initial mode amplitude is rather large (Fig. 2 a)), corresponding to a finite seed islandsize. If the NTM is preceded only by fishbones, several consecutive fishbones seem to be neededto increase the seed island size until it can grow on the neoclassical timescale. The mode startswith a weak amplitude and becomes stronger with a further fishbone. The amplitude directlyafter the last fishbone trigger is comparable with the mode amplitude directly after a sawtoothcrash. In few discharges the NTM begins spontaneously, without a clear trigger event, and growswithout a detectable seed island (Fig. 2 b)). In this case the mode amplitude at the beginningis at least ten times smaller than after a sawtooth crash, corresponding to a three times smallerseed island.In cases with sawtooth or fishbone triggered NTMs, the mode frequency sometimes beginsat the second harmonic of the preceding (1,1) mode (fishbones or sawtooth precursor), indicatingthat the NTM seed island might be produced by toroidal coupling of the preceding (2,2) modeto the q = 3/2 surface, as claimed in [1]. However, in many cases the NTM frequency risesduring the first 10 to 20 ms (Fig. 3) and stays well below the second harmonic of the preceding(1,1). For some sawtooth triggered NTMs with rising early frequency, a change in the modecharacter from a nearly pure (3,2) to a coupled (3,2) + (2,2) mode has been observed. Here, thesawtooth crash obviously has produced a (3,2) seed island directly.The scaling of βN at the time of the mode’s onset (βN,onset) after a sawtooth crash hasbeen investigated in [2]. For constant q95 and self-similar profiles βN,onset ∝ ρi has been found,where ρi ∝√Ti/Bt is the ion gyro radius, Ti the ion temperature at the rational surface, andBt the toroidal magnetic field. βN,onset values for NTMs without preceding sawtooth crash areadded to this scaling (Fig. 4).9183612152430t  = 2.035 sf (kHz)# 9600(1,1) (2,2)(1,1)fishbonesST(3,2) + (2,2)(3,2)+ 10 ms + 20 ms + 30 ms0. . . . .. . .Figure 3. Wavelet plot of an early NTM immedi-ately after a sawtooth crash. The NTM frequencyrises during the first 10 ms.✕✕✕1.0 2.0 3.0 4.0 5.01.01.52.02.53.0β           ⋅ I    / MAPN, onsetfishbone triggersawtooth trigger no triggerT  / keVi  ∝ √Tiq    = 4 ...4.595Figure 4. βN,onset · Ip vs. the ion temperatureat the (3, 2) radial position, Ti. Additionally thescaling, βN,onset · Ip ∝√Ti, is shown [2].For an NTM following fishbones, βN is higher than in cases with a sawtooth trigger,indicating that the seed island formation by fishbones is less efficient. This is plausible becauseon one hand, the fishbone frequency is determined by fast particles and thus strongly differentfrom the rotation frequency of a magnetic island, and, on the other hand, a sawtooth producesa stronger perturbation and thus more readily facilitates the formation of a (3,2) seed island. Ahigher β where the plasma is less stable against tearing is thus needed to produce a sufficientseed island size by fishbones.The highest βN,onset values correspond to cases where the NTM begins without a triggerevent, where no seed island is observed, indicating that with higher pressure the plasma be-comes more and more unstable against tearing. An island large enough for neoclassical growthis produced without a prominent MHD event. Therefore, it is not obvious, that to avoid NTMs,it is sufficient to prevent a q = 1 surface. To answer this question, one has to find out whetherthe coupling to the m = n mode, e.g. (2,2), is essential for the existence of NTMs.4. Collisionality dependence of NTMsAccording to the polarization current model [4], the minimum βp at which neoclassical growthis possible, βp,crit, and the necessary seed island size, Wseed, depend on the poloidal ion gyroradius, ρp, but also on the local collisionality at the resonant surface, νii/mεω∗e , through theparameter [4,1]g(ε, νii) ={ε3/2, νii/mεω∗e  C ≈ 11, νii/mεω∗e  C ≈ 1 .βp,crit and Wseed are both proportional to√g(ε, νii) · ρp. Considering this dependence, athreshold value for νii/mεω∗e is to be expected. For ASDEX Upgrade at the q = 1.5 surfaceit has been found to be νii/mεω∗e ≈ 0.03 for the (3,2)-mode [9]. At very low densities, andhence collisionalities, the (2,1)-mode can be additionally excited, leading to an H to L-transitionor even to disruptions. Both neoclassical modes have been avoided at ASDEX Upgrade byincreasing the collisionality (Fig. 5).5. SummaryThe neoclassical tearing mode (3,2) + (2,2) atASDEX Upgrade is often triggered by a saw-tooth crash or by fishbones. In few cases theNTM starts spontaneously.There is an interaction between NTMs andfishbones: NTMs can be triggered by fishbonesand sometimes they begin at the second fish-bone harmonic. On the other hand, an NTMsupresses fishbones.The β value at the NTM’s onset is higherfor modes triggered by a fishbone than by a saw-tooth and even higher for spontaneous NTMs.The fact that the NTM can grow spontaneously,indicates that to stabilize it, it might be not suf-ficient to avoid MHD activity that can producea seed island.The threshold character for the collision-ality dependence of the onset of the (3,2) andthe (2,1) neoclassical modes has been found.For the (3,2) mode the threshold has been de-termined as νii/mεω∗e ≈ 0.03. A scenariowith high density, and hence high collisional-ity, has been established, where NTMs could beavoided at ASDEX Upgrade.(3,2) NTM for low densityodd n[a.u.][10   m   ]19 -3en7891.8βN 2.22.6no (3,2) NTM for higher densityeven n[a.u.]2.5 2.7 2.9 3.1 t (s)[MW]NIpower# 10395 # 1039310150# 10393# 10395# 10395# 10393# 10395# 10393Figure 5. Comparison between two similar dis-charges (Bt = 2.0 T, Ip = 1.0 MA, q95 = 3.2)with only slightly different densities. For #10395with n̄e = 8 · 1019 m−3 the (3,2) mode appears,whereas for #10393 with n̄e = 8.5 · 1019 m−3there is no (3,2) mode.References[1] H. Zohm et al.: Plasma Phys. Control. Fusion 39, B237 (1997)[2] S. Günter et al.: “β scaling for the onset of neoclassical modes at ASDEX Upgrade.”Submitted to Nucl. Fusion[3] R. Fitzpatrick: Phys. Plasmas 2, 825 (1996)[4] H.R. Wilson et al.: Phys. Plasmas 3, 248 (1996)[5] A. Gude et al.: “Seed island of neoclassical tearing modes at ASDEX Upgrade.” Submittedto Nucl. Fusion[6] K. Hallatschek: PhD Thesis, Max-Planck-Institut für Plasmaphysik, Garching, IPP report5/78 (1998).[7] B. Coppi et al.: Phys. Rev. Lett. 63, 2733 (1989)[8] F. Porcelli: Plasma Phys. and Contr. Fusion 33, 1601 (1991)[9] M. Maraschek et al.: “Collisionality dependence of the neoclassical tearing mode inASDEX Upgrade.” Submitted to Plasma Phys. Controll. Fusion

Neoclassical Tearing Modes and their Interaction with Fishbones at ASDEX Upgrade

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Neoclassical Tearing Modes and their Interaction with Fishbones at ASDEX Upgrade

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