Strong ExB shear flows in the transport barrier region in H mode plasma H. Xia,∗ M. G. Shats,† and H. Punzmann‡ Plasma Research Laboratory, Research School of Physical Sciences and Engineering, Australian National University, Canberra ACT 0200, Australia (Dated: February 2, 2008) Wereportthefirstexperimentalobservationofstationaryzonalflowinthetransportbarrierregion 7 of theH mode plasma. Strong peaks in Er shear mark thewidth of this region. Strongm=n=0 0 low-frequency(f <0.6kHz)zonalflowisobservedinregionsofincreasedEr,suggestingsubstantial 0 contributionof zonal flow tothespatial modulation ofEr radial profiles. Radiallocalization of the 2 zonal flow is correlated with a region of zero magnetic shear and low-order (7/5) rational surfaces. n PACSnumbers: 52.25.Fi,52.25.Gj,52.55.s a J 3 Transportbarriers(TBs)are radiallylocalizedregions strong zonal flows developing near rational surfaces can in toroidal plasma where radial transport of particles or provide a trigger for the TB formation [9]. ] h energy is drastically reduced. In the high confinement We present results obtained in the H-1 toroidal heliac p mode (H mode) [1], the presence of a TB is manifested [10] (major radius of R = 1 m and mean minor plasma - m as a steep density (or temperature) gradient near the radiusofabouthai≈0.2 m)underthefollowingplasma plasma boundary. The top of this region is sometimes conditions(see,forexample,[11]andreferencestherein): s a referred to as a pedestal. ne = 1×1018 m−3, Te ∼ 10 eV, Ti ∼ 40 eV in argon at pl Characteristics of the H mode edge TBs are impor- fillingpressureof(1−4)×10−5 Torrandatlowmagnetic . tant. Spatial structure of a TB is closely related to the fields, B =(0.05−0.12) T. Such plasma is produced by s c globalstability,confinementandtheplasmaperformance ∼80kWoftheradio-frequencywavesat7MHz. Several si (for a review see, for example, [2]). Understanding and combinations of Langmuir probes (single, triple probes) y predicting characteristicsof the TBs has become a focus are used to characterize plasma parameters, such as the h of the international fusion community (see, e.g., [3, 4]). electron density, electron temperature, and electrostatic p potential, as described in [12]. Probes are also used to The ultimate goal of these studies is the optimization of [ the radialprofilesoftheplasmaparametersinthefuture characterize poloidal and toroidal wave numbers of tur- 2 fusion reactor [5]. bulent fluctuations [13]. v ThehighconfinementmodeobservedinH-1[14]issim- 6 The formation of a TB has been ascribed to the gen- ilartoHmodeintokamaks. Typicalelectrondensityand 5 eration of a sheared radial electric field (or E × B flow, 2 where E is the electric field and B is the magnetic field) plasma potential profiles are illustrated in Fig. 1 for low 7 (L) and H modes. L and H modes are achieved respec- whichleadstothe reductioninturbulenceandtransport 0 tivelyaboveandbelowcriticalmagneticfield[14]. When 6 [6,7,8]. However,thephysicsoftheTBformationisnot the magnetic field is close to the critical value, sponta- 0 yetwellunderstood. ExperimentalstudiesofTBsarere- neous L-H transitions are observed. In these discharges, / stricted due to difficulties in measuringradialparameter s atripleprobeisusedtomeasuretheelectrondensityand c profiles with sufficient spatial and temporal resolution. i potentialonashot-to-shotbasis. Excellentreproducibil- s In this Letter we report detailed experimental studies ity of the measurements allows reliable determination of y h of the TB structure in H mode of the H-1 heliac. It is profiles without perturbing plasma by the probe arrays. p shownforthefirsttime,thatdistinctfeaturesintheelec- Despite largedifferences in electrontemperature,den- v: tron density profile, marking the pedestal and the foot sity,andmagneticfield,plasmasinH-1andintheTBre- of TB, spatially coincide with radially localized strongly i gions of large tokamaks, are dimensionally similar. This X shearedE × B flows. These radialregionsarealsoiden- dimensional similarity has been discussed in [15], where r tifiedasregionswherestrongstationarym=n=0zonal it has been shown that the width of TB measured in ion a flows are localized in H mode. The radial localization gyroradii is very similar to that in, for example, DIII- of zonal flows also coincides with the position of a low- D tokamak. However in absolute units, the TB width order rational surface and a minimum in the magnetic in H-1 is substantially broader (30-40 mm) than that shear. These results confirm, to some extent, a hypoth- in larger experiments with stronger magnetic fields and esis based on results of the gyrokinetic simulations that lighterions. This,incombinationwithlowelectrontem- peratureinH-1,opensanopportunitytostudystructure of the TB using probes with sufficiently high spatialres- olution. ∗Electronicaddress: [email protected] †Electronicaddress: [email protected] The development of the TB in H mode plasma in H- ‡Electronicaddress: [email protected] 1 is illustrated in Fig. 1. Radial profiles of the electron 2 2 (a) I II 2 (a) I II Lmode 1.5 0 -3m) ( c ) m) 180 1.0 kV/ -2 1 H mode ( n(e0.5 Er -4 0 100 (b) Lmode (d) 0.-56 80 H mode (b) V) 60 2m) f( 40 V/ 0.0 60 1 20 ( ,Er-0.5 0 0.2 0.4 0.6 0.8r 1 0.2 0.4 0.6 0.8r 1 -1.0 0.2 0.4 0.6 0.8 r 1 FIG.1: Radialprofilesof(a)electrondensity,(b)plasmapo- tentialinLmode,and(c)electrondensity,(d)plasmapoten- tial in H mode, respectively. Dashed guide lines and shading FIG.2: Radialprofilesof(a)radialelectricfieldand(d)shear are used to mark two radial regions in the transport barrier in the radial electric field, computed using plasma potential (I and II). profile of Fig. 1(d). frequency (f < 0.6 kHz) spectral feature increases in density and the plasma potential in L mode are rather some radial regions, which will be discussed later. The featureless as seen in Fig. 1(a,b). In H mode, the cen- powerspectraofthefluctuationsintheplasmapotential, tral density doubles while the plasma potential becomes P(φ), atvariousradialpositionsinHmode areshownin more negative in the central regionand more positive at Fig. 3(a). The low-frequency feature (0.1−0.6 kHz) is the edge (Fig. 1(c,d)). The increase in the density co- incides with the formation of the characteristic kink in dominantinHmode. Poloidalwavenumberkθofthislow frequency component is measured using two poloidally the density profile at about ρ=r/a≈0.6, referredto as separated probes. Measured poloidal wave number of the pedestal. The ne profile outside the pedestal can be approximated by a straight line (Fig. 1(c)). The profile kθ = (2−5) m−1 at f = (0.1−0.6) kHz is indicative of the mode number m = 0. The toroidal mode num- of the plasma potential φ also shows two characteristic berisestimatedusingtoroidallyseparatedprobes,asde- kinks: oneatthetopoftheTB,andtheotheratρ=0.8, scribed in [13], and shows n = 0. Hence the strong low which we will refer to as the foot of the TB. The third frequencyfluctuationsintheplasmapotentialareidenti- kink in the plasma potential is seen near the last closed fied as stationary zonal flows. It should be noted that it flux surface (ρ = 1.0) and is due to the reversal of the isusuallydifficult toaligntoroidallyseparatedprobesto radialelectricfieldfromnegative(inside)topositive(out- exactly the same poloidal position. As a result, a phase side). Weusedashedguidelinesandshadingthroughout shift between toroidally separated probes will occur due the paper to mark two radial regions of interest: (I) - a totheuncertaintyinthepoloidalseparationbetweenthe region between the top and foot of the TB, and (II) - a probes, ∆y: region between the foot and the last closed flux surface. Profilesof the radialelectric field Er and its shearEr′, ∆ϕ(f)=kk(f)∆Lk+kθ(f)∆y, (1) derivedfromtheradialprofileoftheplasmapotentialare shown in Fig. 2. Since Er is computed by differentiat- where ∆L and ∆y are toroidal and poloidal separa- k ing radial profile of the plasma potential, the (negative) tionbetweenthe probesrespectively,andkθ(f)isknown maximaofthe radialelectricfieldcannotbedetermined from the phase difference between the probes which are exactly. Three Er regions are seen: slightly positive Er poloidally separated. In case of a zonal flow, m=0, the inside the top of the transport barrier, substantial nega- second term on the right-hand side becomes zero (since tive Er ≈ -1 kV/m in region I, and even more negative kθ = 0), such that the poloidal uncertainty ∆y becomes Er ≈ -4 kV/m in region II. Correspondingly,the Er′ has unimportant and the toroidal wave number can be reli- distinctpeakatthetop,atthefootofthe transportbar- ably estimated by measuring ∆ϕ. rier and at the last closed flux surface. Spectra similar to those in Fig. 3(a) have also been Fluctuations in the electron density and potential are observed in the Compact Helical System (CHS) using strongly reduced in a broad range of frequencies from heavy-ion-beam probe [17]. In that experiment, low fre- L to H mode as discussed in [16]. However, the low quency potential structures were also identified as sta- 3 0.3 1.44 i (a) I II r=0.85 ) r=0.9 1.42 z H r=0.65 k 0.03 2V/ r=0.95 ) ( 1.4 7/5 f ( P r=0.6 0.003 1.38 0.2 0.4 0.6 0.8 r 1 m=0, n=0 stationary FIG. 4: Radial profile of rotational transform in magnetic zonal flow f(kHz) 0.0003 configuration discussed in thispaper. 0.01 0.1 1 10 100 2V)0.02 (b) I II existenceofthe7/5rationalsurfacesisalsoconfirmedby ( stationary z] the observation of the m = 5 chain of magnetic islands H zonal flow k inthe regionofρ≈(0.83−0.87). The plasma currentin 0.6 0.01 the H-1 heliac is negligibly small (∼10 A) and does not 1- affect the vacuum magnetic structure. 0. [ A possible role of low-order rational surfaces in the ) f formation of H mode has been recognized since the first ( P 0 observation of H mode in stellarators [18, 20]. Spatial 0.2 0.4 0.6 0.8 r 1 correlation of the rational surfaces with the stationary zonalflows,seeninFig.3(b)andFig.4,maybeindicative FIG.3: (a)Powerspectraoftheplasmapotentialindifferent of the generation of stationary zonal flows due to the radial regions; (b)radialprofileofthespectralpowerdensity of stationary zonal flows (0.1 ∼ 0.6 kHz). Hatched boxes influence of the rational surfaces, as suggested in [21]. indicate radial positions of the Er maxima in regions I and Formation of the TB and strong stationary zonal flow II. is also observed during spontaneous L-H transitions in H-1, described in [15]. Fig. 5(a) shows temporal evolu- tionofthemeanplasmadensityduringspontaneousL-H tionary zonal flows. transition. In this discharge the mean electron density The spectral power density of the zonal flow (shaded jumps from about 0.6×1018 m−3 to almost 1.2×1018 spectralregionoff =(0.1−0.6)kHz inFig.3(a))varies m−3 in about one millisecond. Similarly to stationary H alongtheradius. Radialprofileofthespectralpowerden- modedischargesdescribedabove,strongzonalflowinthe sityofthezonalflowinHmodeispresentedinFig.3(b). TB region is observedin the H mode stage of discharges Stationaryzonalflowisaband-likestructurelocalizedin with spontaneous transitions. The spatial correlation of radial region of 0.6<ρ<1.0. the TB regions and stationary zonal flow in the sponta- Two hatched boxes drawn in Fig. 3(b) indicate the neous transitions is also observed. uncertainty in the radial positions of the (negative) Er In Fig.5(b), the changeof the fluctuation powerspec- maxima in regions I and II ( Fig. 2(a)). It can be seen tra across the L-H transition at the radial position of thatthezonalflowmaximumspatiallycoincideswiththe ρ = 0.65 is illustrated. It can be seen that across the maximumin(negative)Er. Thissuggeststhatstationary transition, fluctuations in the broad spectral range from zonal flow directly contributes to mean Er and may be 0.6 to 100 kHz are reduced, while the spectral power responsible for the ”corrugation” of the Er profile seen of low-frequency zonal flow, f = (0.1−0.6) kHz, is in- in Fig. 2(a). creased. The list of spatially coinciding phenomena in this ManyoftheingredientsoftheTBphysicspresentedin plasma is complemented by the observationthat the TB thispaperhavebeendiscussedwithregardtoHmodesin regionappears in the vicinity of the zero magnetic shear tokamaks and stellarators. For example, the role of the inthismagneticconfiguration. Thecomputedradialpro- low-orderrationalsurfaces [8, 22], the role of zonalflows file of the rotational transform ι = 1/q (where q is the in L-H transition [23], modification of the Er profiles by safetyfactor)isshowninFig.4. Inadditiontozeroshear non-neoclassical(turbulence-driven) effects [6, 24, 25]. at ρ ≈ 0.75, ι = 1.4 = n/m = 7/5 rational surfaces are Here we present for the first time experimental evi- present in both zones I (at ρ ≈ 0.65) and II (at ρ ≈ dence that zonal flow, which develop near the n/m = 0.85). The accuracy of the ι computation has been veri- 7/5rationalsurfaces,is spatiallycorrelatedwithdistinct fiedusingexperimentalelectronbeammapping[19]. The regions of the radial electric field inside the TB region 4 1.2 waveisresponsibleforthesustainmentofzonalflowinH H mode (a) mode, as has been proposed in [26]. 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