Bai, B.

Boedo, J.A.

Bombard, B.

Boswell, C.J.

Greenwald, M.

Hallatschek, K.

Kee, G.R.

Kopon, D.

Krasheninnikov, S.

Leonard, A.W.

Mahdavi, M.A.

Maqueda, R.J.

Moyer, R.A.

Nevins, W.M.

Rogers, B.N.

Rudakov, D.L.

Stangeby, P.C.

Terry, J.L.

Zweben, S.J.

DSpace@MIT

Experimental/Theoretical Comparisons of the Turbulence in the Scrape-Off-Layers of Alcator C-Mod, DIII-D, AND NSTX*J.L. Terry 1), S.J. Zweben 2), D.L. Rudakov 3), J.A. Boedo 3), K. Hallatschek 4),R.J. Maqueda 5), R.A. Moyer 3), B. Bai 1), C.J. Boswell 1), M. Greenwald 1),S. Krasheninnikov 3), B. LaBombard 1), D. Kopon 1), A.W. Leonard 6), M.A. Mahdavi 6),G.R. McKee 7), W.M. Nevins 8), B.N. Rogers 9), P.C Stangeby 10), D. Stotler 2),J.G. Watkins 11), W.P. West  6), D.G. Whyte 3), and X.Q. Xu 8)1) MIT Plasma Science and Fusion Center, Cambridge, MA, USA2) Princeton Plasma Physics Laboratory, Princeton, NJ, USA3) University of California, San Diego, CA, USA4) Max Planck Institute of Plasma Physics, Garching, Germany5) Los Alamos National Laboratories, Los Alamos, NM, USA6) General Atomics, San Diego, CA, USA7) University of Wisconsin, Madison, WI, USA8) Lawrence Livermore Laboratory, Livermore, CA, USA9) Dartmouth University, Hanover, NH, USA10) University of Toronto, Institute for Aerospace Studies, Toronto, Canada11) Sandia National Laboratories, Albuquerque, NM, USAe-mail contact of main author: terry@psfc.mit.eduAbstract: The intermittent turbulent transport in the scrape-off-layers of Alcator C-Mod, DIII-D, and NSTX isstudied experimentally. On DIII-D the fluctuations of both density and temperature have strongly non-Gaussianstatistics, and events with amplitudes above 10 times the mean level are responsible for large fractions of the netparticle and heat transport, indicating the importance of turbulence on the transport. In C-Mod and NSTX theturbulence is imaged with a very high density of spatial measurements. The 2-D structure and dynamics ofemission from a localized gas puff are observed, and intermittent features (also sometimes called “blobs”) aretypically seen. On DIII-D the turbulence is imaged using BES and similar intermittent features are seen. Thedynamics of these intermittent features are discussed. The experimental observations are compared withnumerical simulations of edge turbulence. The electromagnetic turbulence in a 3-D geometry is computed usingnon-linear plasma fluid equations. The wavenumber spectra in the poloidal dimension of the simulations are inreasonable agreement with those of the C-Mod experimental images once the response of the optical system isaccounted for. The resistive ballooning mode is the dominant linear instability in the simulations.1. IntroductonEvidence for intermittent convective radial transport in the Scrape-Off-Layers (SOL) oftokamaks has existed for a number of years [1]. Recently, studies aimed at investigating thisphenomenon have yielded a much clearer picture of the SOL transport and its implications ondivertor operation and possibly density limits [2]. Typically, detailed measurements of theturbulence have come from single or multi-point probe or optical measurements in theoutboard SOL, and they generally show very strong evidence for intermittent, convectiveparticle transport there. The physics of this intermittent transport is important since it maydominate the scrape-off-layer transport [2,3], carrying a large fraction of the net cross-fieldflux of particles and heat, and resulting in the flat or nearly flat density profiles observed in thefar-SOLs of many tokamaks. The three magnetic confinement devices reported on here,Alcator C-Mod, DIII-D, and NSTX, exhibit many qualitatively similar features, e.g. large,intermittent events, high levels of SOL turbulence, and poloidal and radial motion of localizedfeatures (“blobs”). Yet the SOL plasmas in these devices are different in many respects, e.g. B,IAEA-CN-94/EX/P5-10Fig. 1. Fraction of the total particle and heat flux in DIII-D carriedby transport events with relative amplitude Aevent greater than thecorresponding x-axis value. (Aevent is normalized to the mean flux.)Open circles are for L-mode; solid diamonds are for ELM-free H-mode. The measurements are made ~15 mm outside the separatrix.00.510 10 20 30 40 50 00.510 10 20 30 40 50Aevent=Γ event /< Γ>Γ>A/Γ  totQ>A/QtotHeat fluxParticle fluxAevent= Qevent /<Q>λei/Lc, ρs, gradient scale length. A SOLcomparison for moderate to high density L-mode discharges in each device is shown inTable 1. (Lpperp is the pressure scale length;Lc is the parallel connection length, Lo= Lc[ne e2 η! ρS/(R mi ωci)]0.5 (2R/Lp)0.25 is thecharacteristic size scale for the (linear)resistive ballooning mode [4]; Lturbpol is themeasured poloidal correlation length of theturbulence; τauto-cor is the FWHM of thefluctuation autocorrelation function at astationary point; λei is the electron-ion meanfree path.) It is the purpose of this paper toreport and compare observations from thesedevices, and to compare some of theexperimental results with simulations of theedge plasma in hopes of understanding theunderlying turbulence.2. Intermittent Fluctuation-Driven Transport FluxesIn the outboard SOL of DIII-D, the fluctuating components of the electron density, electrontemperature and poloidal electric field are simultaneously measured using a reciprocatingLangmuir probe array. Fromthese measurements thecross-field fluctuation-drivenparticle and heat fluxes arederived. The fluctuations ofboth density and temperaturehave strongly non-Gaussianstatistics characterized bypositive skewness andkurtosis. Conditionalaveraging was used tocharacterize typical events influctuations and fluxes. Theintermittent large-density events correlate with the occurrence of spikes in the poloidal electricfield and result in intermittent transport events carrying both particles and heat. Theintermittence has qualitatively similar character in L-mode and ELM-free H-mode. However,the absolute transport rates due to intermittence are much higher in L-mode. Figure 1 shows thecontribution of intermittent events to net particle and heat fluxes. Each point represents thefraction of the total flux carried by all events with relative amplitudes greater than the x-axisTABLE 1. Comparison of quantities characteriz-ing SOLs of specific L-mode plasmas in the threedevices, evaluated at the outboard midplane, ~1density e-folding length outside the separatrix.C-Mod DIII-D NSTXne 3x1019 m-3 5x1018 m-3 3x1018 m-3Te 25 eV 25 eV 20 eVLpperp 7 mm 20 mm 40 mmρs 0.18 mm 0.44 mm  3 mmLc 5 m 12 m  10 mLoresist. ball. ~1 mm ~1 mm ~10 mmLturbpol ~9 mm ~20 mm ~40 mmτauto-cor 20 µs 20 µs 40 µsIsatRMS/Isat ~40% ~40% ~40%λei/Lc 0.07 0.2 0.2β 3x10-5 4x10-5 8x10-4IAEA-CN-94/EX/P5-10Fig. 2. Sequences of experimental images from NSTX and C-Mod, showingspace and time evolution of turbulence at the outboard SOL. In 2b) the white-black line is the LCFS. In the last frame the lines track the motion of each blob.out10 cm10208070282 cm∆t=4 µs 2b) – C-Mod2a)        NSTXvalue. Events with amplitudes above 10 times the mean level are responsible for ~60% of thenet particle and heat transport in L-mode and for ~30% of the net transport in H-mode. Theseand other similar measurements on other devices demonstrate the importance of understandingthe turbulence that underlies this transport.3. “Imaging” the turbulenceThe turbulence that is presumably responsible for the transport documented above has beeninvestigated on all three devices. In Alcator C-Mod and in NSTX the edge/SOL turbulence isimaged with a very high density of high resolution spatial measurements [5,6] and studied withprobes. In DIII-D the density fluctuations are imaged directly with moderate spatial resolutionand coverage using BES [7] and studied with probes. As seen in Table 1, the size scales of theturbulent features, Lturb, as well as scales, Lp, ρs, and Lo vary by almost an order of magnitude.The imaging in C-Mod and NSTX is accomplished by viewing (parallel to the local field) lineemission from a localized gas puff [5,6]. The detailed 2-D structure and dynamics of theemission are measured using gated and high frame-rate (up to 1 MHz) cameras. Complexemission patterns are typically observed. Examples from NSTX and C-Mod are shown in Figure2. The larger sizescale in the NSTXimages is obvious.Often thelocalized,intermittentfeatures, as well as“wave-like”poloidal structuresare observed. OnC-Mod the largerfeatures move atspeeds up to ~0.5km/s. The atomicphysics that converts the density and temperature fluctuations into fluctuations in emissioncomplicates the quantitative interpretation and has been studied in [5,8]. The details will not berepeated here except to say that the atomic physics “windows” an observable region, limited onthe hot side by ionization and on the wall side by lack of excitation. Nonetheless, within this“window” the emission responds to the fluctuations approximately as neαTeβ, with α, β between0.3 and 1.4 [8]. Wavenumber spectra in the poloidal and radial planes are measured and used forquantitative comparison with the theoretical simulations (Section 4). In C-Mod there is no cleardifference in structure size between L- and H-mode plasmas [5]. In NSTX differences are seensince the emission “window” includes the H-mode pedestal. As evidenced in Figs 2b) and 3a),the turbulent features often appear to be formed near the LCFS [9] and propagate predominatelyoutward and poloidally at about Er x B velocity. Fig. 2b) shows a special case near the densityIAEA-CN-94/EX/P5-10Fig 3. Propagation of the intermittent eventsin DIII-D: (a) data from BES - the radialmotion of a positive density feature ofroughly 2 x 2 cm extent, marked by a dashedcircle, is indicated by vertical dashed lines:(b) data from midplane probe arrayLCFSRt0t0+5 µs6 cm5cm          ΘVf2Vf1E(kV/m)010100 µsa.u.(b)(a)limit (n/nGW≈0.7) in C-Mod, where a blob is seen on closed flux surfaces. As the blob crossesthe LCFS, it splits, and the portion on open field lines moves out radially. Fig. 3(a) shows twoframes of DIII-D BES data (2-D density plots). It isclear that the object is moving poloidally andradially with speeds that can be easily estimated tobe Vθ≈5 km/s and Vr≈1.5 km/s. The propagationvelocities can be estimated independently usingprobe data, such as shown in Fig. 3b). The tracesshown result from conditional averaging (over ~ 20events) at about 0.5 cm outside the LCFS. Apoloidal velocity of ≈4.5 km/s was estimated fromthe time delay between two floating potentials (toptraces) measured by two poloidally separated probetips. A radial velocity of ≈2.5 km/s was estimatedfrom the poloidal field inside the blob (bottomtrace) assuming the propagation is due to Eθ x Bdrift. Both velocities decrease with the distancefrom the LCFS in the SOL. The transverse objectsize, 1-3 cm near the LCFS, remains relatively unchanged between L and H-modes, althoughthe amplitude decreases [10]. As the objects move towards the wall, they shrink in size anddecay in amplitude [9].4. Comparisons with Simulations.In addition to the improvements in experimentally diagnosing the edge turbulence, recentadvances in the numerical modeling of edge turbulence now allow detailed comparison with theexperimental observations. In particular, we are able to compare directly the characteristics ofthe 2-D radial vs. poloidal turbulence calculated from 3-D non-linear drift-ballooning codes[4,11] with those of the experimental images. A simulation using time-averaged profilesmeasured in the outboard SOL of C-Mod has been done. The simulation solves the Braginskiifluid equations for electrons and ions in a 3-D geometry (note λei/Lc<0.1). It includesdiamagnetic, magnetic shear, and toroidal curvature effects, and mimics the effect of open fieldlines ending on outboard limiters located 1 and 2 m away. A separatrix and X-pt are notincluded. The inclusion of open lines ending at the divertor does not influence the results andindicates that the SOL turbulence field is not driven primarily by flute-like instabilities.Inclusion of open field lines ending on the outboard limiters does alter the shape of thesimulation's k-spectrum, indicating its importance in setting boundary conditions in thesimulation. The comparison of the simulation results with the measured edge turbulence in C-Mod shows that the average size-scales, fluctuation amplitudes, and particle fluxes agree towithin about a factor of two. A more rigorous test is to compare the kpol spectral shapes, as isdone in Figure 4, where an experimental NSTX k-spectrum is also shown. The simulation’sdensity fluctuation spectrum has relatively more structure between k=5 and 30 cm-1. However,Fig 4. Comparison of kpol spectrumfrom C-Mod with simulation andwith an experimental spectrum fromNSTX. The short dashed simulationspectrum has experimental time andspatial resolutions folded in.1 10kpoloidal (cm-1)0.1110100auto power S(k)C-Mod experimental          C-Mod simulation1020622006 frames 37-530.5<ρ <1.2 cmC-mod simulationne only  no compensationNSTXexperimental0.3including the effects of 1) the atomic physics “windowing”, 2) a 2 µs time-average, and 3) mostimportantly the measured spatial response of the experimental optical system (∆kHWHM~12 cm-1)results in the apparent suppression of the smaller-scale features and in the good match shown inFigure 4. Although the developed state of the turbulence is highly non-linear, the dominantlinear instability in the simulation is the resistiveballooning mode. Its scale size Lo is ~1 mm in C-Mod, ~10mm in NSTX, and ~1 mm in DIII-D, showing a scalingroughly consistent with the machines’ turbulence sizescales.An initial comparison with the C-Modobservations has also been done using another 3D non-local electromagnetic turbulence simulation code, BOUT[11], which models boundary-plasma turbulence with arealistic separatix and X-pt geometry. It also shows a goodmatch with the experimental k-spectrum, although thetime-averaged input profiles were somewhat differentfrom those measured. The dominant linear instability is theresistive X-pt mode, which is resistive ballooning in theproper X-pt geometry. The ballooning character of theturbulence in the simulations is also manifested in thepredictions of much reduced turbulence and transport at the inboard side of the plasma. This isseen in C-Mod where the normalized intensity fluctuation, as observed by a radial array ofviews just in front of an inboard midplane gas puff, is approximately a factor of ten smaller thanthat measured on the same flux surface at the outboard midplane. Inboard and outboard probemeasurements of IsatRMS/Isat give similar results.All three experiments show radial propagation of the turbulent structures, with speedsup to ~1.5 km/s. It has been proposed [12] that radial blob propagation on open field lines isdriven by ExB forces resulting from polarization within the blob’s flux tube. Many of theseobservations are consistent with this picture, e.g. the DIII-D measurements and the C-Modmovie of Figure 2b), where the radial speed changes as the blob “splits” at the LCFS.[1] M. ENDLER et al., Nucl. Fus. 35 (1995) 1307; also B. K. JOSEPH et al., Phys. Plasmas 4 (1997) 4292.[2] B. LABOMBARD et al., Phys. Plasmas 8 (2001) 2107; M. GREENWALD, Plasma Phys Cont Fusion 44 (2002) R27[3] Y. SARAZIN AND PH. GHENDRIH, Phys. Plasmas 5 (1998) 4214; also A. HUBER et al., J. Nucl. Mat. 266-269 (1999)546; also B.A. CARRERAS et al., Phys. Plasmas 8 (2001) 3702; also J.A. BOEDO et al., Phys. Plasmas 8 (2001) 4826.[4] B.N. ROGERS et al., PRL 81 (1998) 4396.[5] S.J. ZWEBEN et al., Phys. Plasmas 9 (2002) 1981.[6] R.J. MAQUEDA et al., to be published in Rev. Sci. Instrum. (2002); also S.J. ZWEBEN et al., EPS (2002)[7] G.R.MCKEE et al., Rev.Sci.Instrum. 70 (1999) 913.[8] D. STOTLER et al, to be published in J. Nucl. Mater. (2002)[9] J.A. BOEDO et al., to be published in in J. Nucl. Mater. (2002)[10] D.L. RUDAKOV et al., Plasma Phys. Cont. Fusion 44 (2002) 717.[11] X.Q. XU et al., Phys. Plasmas 7 (2000) 1951; also X.Q. XU et al., New Journal of Physics 4 (2002) 53.[12] S.I. KRASHENINNIKOV, Phys. Lett. A 283 (2001) 368; also D. D’IPPOLITO et al., Phys. Plasmas 9 (2002) 222.*Work supported by USDOE Cooperative Agreement DE-FC02-99ER54512, Contracts DE-AC02-76CHO3073, DE-AC03-99ER54463, W-7405-ENG-48 and DE-AC04-94AL85000, and Grants DE-FG03-95ER54294, and DE-FG03-96ER54373.IAEA-CN-94/EX/P5-10

Experimental/Theoretical Comparisons of the Turbulence in the Scrape-Off-Layers of Alcator C-Mod, DIII-D, AND NSTX

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Experimental/Theoretical Comparisons of the Turbulence in the Scrape-Off-Layers of Alcator C-Mod, DIII-D, AND NSTX

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