We present experimental results on edge turbulence and transport from the tokamak TEXT and the torsatron ATF. The measured electrostatic fluctuations can explain the edge transport of particles and energy. Certain drive (radiation) and stabilizing (velocity shear) terms are suggested by the results. The experimental fluctuation levels and spectral widths can be reproduced by considering the nonlinear evolution of the reduced MHD equations, incorporating a thermal drive from line radiation. In the tokamak limit (with toroidal electric field) the model corresponds to the resistivity gradient mode, while in the currentless torsatron or stellarator limit it corresponds to a thermally driven drift wave

Bell, J. D.

Bengtson, R.

Carreras, B. A.

Diamond, P. H.

Harris, J.

Hidalgo, C.

Holmes, J. A.

Isler, R.

Leboeuf, J. N.

Lee, D. K.

Lin, H.

Lynch, V. E.

Rhodes, T. L.

Ritz, C. P.

Rowan, W. L.

Thayer, D. R.

Uckan, T.

Ware, A. S.

Wootton, A. J.

UNT Digital Library

i WmXfK HB DMn•uttorwt tw • oormaoor uf *m U.£Gowrrwww undv oomiact fte. D£-AC06440A21400. Acncnir**/. « * U SrowHy km tonrn is i* • pubMa* form at *m I W I I or«kn» otfara » do to. tor US. Gu—nit«CONF-901025--6DE9C 017326S£F 1 8 {990EDGE TURBULENCE AND TRANSPORT: TEXTAND ATF MODELING*CH.P. RITZ, T.L. RHODES, H. LIN, W.L. ROWAN, R. BENGTSON,A.J. WOOTTONFusion Research Center, University of TexasAustin, Texas 78712B.A. CARRERAS, J.N. LEBOEUF, D.K. LEE, J. HARRIS,C. HIDALGO, J.D. BELL, J.A. HOLMES, R. ISLER, V.E. LYNCH,T. UCKANOak Ridge National LaboratoryOak Ridge, Tennessee 37831, U.S.A.P.H. DIAMOND, A.S. WAREUniversity of California at San DiegoLa Jolla, California 92093, U.S.A.D.R. THAYERScience Applications International CorporationSan Diego, California 92121, U.S.A.DISCLAIMERThis report was prepared as an account of work sponsored by an agency of the United StatesGovernment. Neither the United States Government nor any agency thereof, nor any of theiremployees, makes any warranty, express or implied, or assumes any legal liability or responsi-bility for the accuracy, completeness, or usefulness of any information, apparatus, product, orprocess disclosed, or represents that its use would not infringe privately owned rights. Refer-ence herein to any specific commercial product, process, or service by trade name, trademark,manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recom-mendation, or favoring by the United States Government or any agency thereof. The viewsand opinions of authors expressed herein do not necessarily state or reflect those of theUnited States Government or any agency thereof.Research sponsored by the Office of Fusion Energy, U.S. Departmentof Energy, under contract DE-AC05-84OR21400 with Martin MariettaEnergy Systems, Inc.DISIAEA-CN-53/C-3-4EDGE TURBULENCE AND TRANSPORT: TEXT AND ATFMODELINGABSTRACTWe present experimental results on edge turbulence and transportfrom the tokamak TEXT and the torsatron ATF. The measured electro-static fluctuations can explain the edge transport of particles and energy.Certain drive (radiation) and stabilizing (velocity shear) terms are sug-gested by the results. The experimental fluctuation levels and spectralwidths can be reproduced by considering the nonlinear evolution of thereduced MHD equations, incorporating a thermal drive from line radia-tion. In the tokamak limit (with toroidal electric field) the model corre-sponds to the resistivity gradient mode, while in the currentless torsatronor stellarator limit it corresponds to a thermally driven drift wave.1. Introduction.The motivation for studying the fluctuations and transport in theplasma edge is manifold; 1) experimental data exists which shows theelectrostatic fluctuations explain the total transport, 2) theories are betterdeveloped than for the core, and 3) modeling can be performed mainlyusing fluid equations. In an attempt to understand the edge turbulence acomparative study of the currentless torsatron ATF and tokamak TEXThas been initiated. We start by describing results from TEXT, notinghow experiment and theory have influenced each other. Next we presentresults from ATF, comparing them with those from TEXT. The finalsection provides both a historical perspective of the attempts to modelthe results, and a summary of the latest comparisons.2. TEXTTable 1 lists the edge equilibrium and fluctuating parameters for typ-ical TEXT discharges [1], and Fig. 1 shows the radial dependence of thenormalized density fluctuation level, fi/n. The turbulence is broadband,with frequency width oy % / % 150 kHz, and wave number (spectral)width <Tk0 « kg. Typically ks as 2 to 3 cm"1, so that kg ss 0.05, andcorrelation lengths ^ x l cm, ir x. 0.5 cm. Typically e^/Te > h/n andTg/Te < n/n are found. The small magnetic fluctuation level measured{b/Bj, < 10~5) at r > a is well correlated with the measured h at r < a,suggesting that b is the result of a perturbed current density at r < a [2].The fluctuation levels are determined primarily by material probes.In the usual technique [3] the plasma potential <f> and its fluctuation levelare determined by assuming 4>fioat = 4> — 6Te. Uncertainties in 8 translatedirectly to uncertainties in <f>, Te, iji, and Te. However, the important resultthat (ne^)/(Ten) > 1 is confirmed by a heavy ion beam probe.Initial modeling [5] showed that resistivity gradient driven turbulence,rather than collisional drift waves which are stable due to the electrontemperature gradient, could explain the measured correlation lengths (inMacrotor), and predicted fluctuation levels were ~10 to 15%. The re-sult [ne^>)/{Ten) > 1 motivated the inclusion of thermal and condensa-tion drives for the resistivity gradient mode [6]. In turn, the modellingsuggested that controlled impurity injection should be performed. Ex-periments with purposely added impurities in TEXT show that e0/Tecan be strongly modified in the edge. Assuming the probe technique isunaffected by the impurities, î 2 puffing increases <f> but not n in regionswhere Te % 20 ev. The electrostatic fluctuation driven flux T? increases.The results suggest a thermal drive in the region where the cooling rcte de-creases with increasing Te. Rapidly decreasing the applied toroidal electricfield Ej, by 90% has no significant effect on the edge turbulence proper-ties. The local parameters T, n, n, 0, and b remain practically unchangedfor several confinement times. This excludes Ej, as the sole driving term,again suggesting that resistivity gradient driven turbulence is not a com-plete explanation for the observations.The measured ensemble averages (n^) and (Te<j>) account for thetotal particle and energy fluxes. Regression analysis of the electro-static fluctuation driven flux F ' for r =s a shows the results are fit byF^ oc n f l^ 2 ± 1 . The density gradient scale length Ln behind the singlepoloidal ring limiter is well fit by balancing F^ with flow at 0.5 c, alongfield lines. The measured fluctuation amplitudes and correlations predictthe measured ratio LTe/Ln, but the result is very sensitive to the sec-ondary electron coefficient which determines the parallel heat flux to thelimiter.While the equilibrium density and temperature fall smoothly withincreasing minor radius, there is a mass velocity shear layer near the out-ermost closed flux surface (at r = a). Here the radial electric field ETchanges sign; the fluctuation phase velocity vph ss v^t — ErjB^ % 0 (vdeis the electron diamagnetic velocity) at the shear layer radius r = a,. Inthis shear layer the turbulence correlation time in the rotating frame isreduced from > 10/xa to % 1 to Zfis, tr is reduced, and the fluctuationamplitudes reduced. These features are in agreement with theoretical pre-dictions [7]. These radially localized effects can be displaced by purposelymodifying Er, either by using biased limiters or external windings to cre-ate a stochastic magnetic field. These results support the notion that amass velocity shear is a strong stabilizing influence.3. ATFATF is an £ — 2, 12—field period torsatron with major radius R =2.10m, average minor radius d = 0.27m, magnetic field on axis B <2 Tcentral rotational transform -t0 = 1/efo ~ 0-3, and edge transform*a = l/<?o ~ 1- Typical edge equilibrium and fluctuating parameters aresimilar to TEXT, as seen from Table 1. The majority of ATF data for thisstudy were taken at B = 0.95 T in currentless plasmas produced with 200to 400kW of 53GHz second harmonic electron cyclotron heating (ECH)power. This explains the lower operating density.Like TEXT, ATF has a shear layer where ET and vpk change sign.When the radial profiles of h/n are plotted with the radius normalizedto the radius of the shear layer, the resulting dependence is very similarto that seen in TEXT (Fig. 1). This suggests that the shear layer is thefunctional boundary of the plasma.In ATF, the location of the shear layer shifts with the vacuum magneticconfiguration when the externally imposed vertical field is varied. Theshear layer also moves inward when the rail limiter (toroidal extent as 9°)is moved inside the nominal last closed magnetic surface where t s; 1.The shear layer is also affected by the main plasma parameters: it movesradially outward by 2-3 cm as the plasma stored energy increases in bothECH and neutral beam injection heated plasmas.As in TEXT, the n and <̂  frequency spectra are broad, and domi-nated by fluctuations at frequencies < 200 kHz. The values of T* arecomparable to those estimated from global particle balance measurements[8]; as in TEXT T* increases with increasing n at a fixed radius. Theperpendicular wave number spectra are also broad, with o"fc/fc = 0.5 — 1.Figure 2 shows that 0-jtfl(<x l/^e) varies systematically with the poloidalphase velocity of the fluctuations both in TEXT and in ATF. In bothmachines a maximum value is reached at the shear layer itself (wherevph = 0): typically, <rM(ATF)/<rM(TEXT) « [?a(ATF)/g.(TEXT)]-1, inaccordance with expectations for fluctuations resonant with the pitch ofthe magnetic field.Under some conditions a highly coherent peak is found [9] with probesand reflectometer at / % 50 kHz with lg > 2 cm % Ln. While thefluctuation is large {n/n ~ 10~2) it does not contribute appreciably (<10%) to Tf at the edge.4. Modelling.Modelling started with resistivity gradient driven turbulence [5]. Fail-ure to account for (ne(f>)/(Teh) > 1 and a^e ~ 2 —3 cm""1, led to thermallydriven convective cell turbulence [6], where the desired enhancement isprovided by radiation through thermal and condensation [10] drives. Wehave since shown condensation to be not only unimportant but invalid[11]. Since TEXT and ATF results have shown that E^ is not the impor-tant drive, we are investigating thermally driven drift waves [12] as limitsof thermally driven convective cells when the loop voltage fades away anddiamagnetic effects take over. The basic equations are Ohm's law,^ ^ ^ (1)the moment m balance equation,S J i(Vi^) (2)the electron temperature equation,f f ^ . V l l J B (3)Here rj denotes the resistivity, fi the viscosity, \\\ and x± ^ e parallel andperpendicular thermal conductivities, and J|| the parallel current. Theradiation drive fR = — 2/3ntdIz(Te)/dTe, where nx is the impurity densityand the intensity of the cooling is given by Iz(Te).Analytical theory [12] shows that the turbulence saturation conditionis the result of the enhanced parallel diffusion by the radial turbulenttransport balancing the resistivity gradient (when E$ ^ 0) and/or thermalinstability drives. The predicted potential saturation level, in the radiationdominated regime, can be expressed as= )Te ( x A f ) W C V 'where k'., = kg/L,, and a = 1.71 for thermal drift waves or a = 0 forresistivity gradient driven turbulence.The computations are performed in cylindrical geometry using our 3Dnonlinear, initial value, reduced MHD code KITE [13]. They are carriedout with TEXT edge parameters and profiles in a region where q as 2.8,Te % 15 eV, n % 4.5 x 1012 cm"3 and nz as 8.0 x 1010cm"3. The radiationfunction Iz(Te) is based on a shifted coronal equilibrium. While the modelI?.(Te) is in agreement with TEXT bolometric data, recent TEXT and ATFmeasurements indicate that the radiated power for a single line is peakedat smaller radii than we have used. This discrepancy suggests not onlythat the choice of the functions Iz(Te), nz(r) and Zts{r) are critical tothe results, but other drives such as ionization (an electron thermal energysink and density drive) and charge exchange (momentum and ion thermalsink).Nonlinear calculations in the resistivity gradient driven turbulencelimit with radiation drive, applicable to Ohmic TEXT discharges, showthat the fluctuation levels are in good agreement with the theoreticalpredictions. They are also in reasonable agreement with experimentalmeasurements at the edge of TEXT in both their magnitude and radialdistribution. Figure 3a shows ecj>/Te (most accurately modelled, althoughh/n is the most accurately measured) from the experiment, computationand analytic theory (Eq. (4)). The model can explain both the mea-sured e<j>/Te > 40%, and the measured e0/Te > n/n. It yields a magneticfluctuations level 5 times higher than the experiment but with a radialdependence consistent with the experimental one.The calculated akg values range from 1 to 2 cm 1 as compared toexperimental values of 2 to 3 cm""1. The calculations show there is astrong dependence of akg % kg on radius, therefore on the q profile, with<Tk6 scaling as q in a radially averaged sense. Since qa ~ 3 in TEXT andqa ~ 1 in ATF, we predict akg for ATF to be about a factor of 3 lowerthan for TEXT. This was confirmed in Fig. 2.The calculations also yield Te/Te > h/n. This result has beenconfirmed theoretically [11] and agrees with preliminary upper estimatesin ATF with r < a,, but disagrees with TEXT measurements which wereperformed for r > a where the model may be invalid. Calculations in thethermally driven drift wave limit, applicable to edge current free TEXTdischarges and the currentless ATF, have also been performed with TEXTparameters. Thermal drift waves are stabilized by electron temperaturegradients. Instability with growth rates comparable with the ripplingmode with radiation drive growth rates can be recovered using the exper-imental radiation strength (Iz(Te) amplitude). As illustrated in Fig. 3b,saturation levels of e^/Te ss 50%, comparable to those obtained with theresistivity gradient turbulence with radiation drive, can be achieved. Thecalculations also yield akg values between 0.75 and 1.5 cm"1. These re-sults might explain the similarities observed between TEXT with E$ ^ 0(resistivity gradient with radiation?), TEXT with £ ^ 0 (thermal driftwave?), and ATF (thermal drift wave?). An important feature of the cal-culations is the self-generation, through the nonlinear couplings betweenunstable propagating modes, of a dc potential and hence of a sheared elec-tric field by the drift wave turbulence. This dc potential helps saturatethe instability and quench the turbulence.Ongoing work includes 1) obtaining and using more realistic estimatesIz{Te), nz(r), and Ze//(r), 2) applying the thermal drift wave model toATF parameters, 3) the incorporation of the ionization term in the ripplingplus radiation model, 4) the inclusion of the ionization and radiation termsin the collisional drift wave model, and 5) the inclusion of limiter effects.The importance of ionization is already recognized; it destabilizes thecollisional drift wave and provides a purely inward particle flux, offering acandidate to explain the inward pinch term required in tokamak modeling.In the future all the above aspects will be inc rporated in a single model.Work supported by the U.S. Department of Energy.REFERENCES[1] RITZ, CH.P., BROWER, D.L., RHODES, T.L., BENGTSON, R.D.,et al., Nucl. Fusion 27, (1987) 1125.[2] KIM, Y.J., GENTLE, K.W., RITZ, C.P., RHODES, T.L., andBENGTSON, R.D., Nucl. Fusion 29, (1989) 99.[3] RITZ, CH.P., POWERS, E.J., RHODES, T.L., BENGTSON, R.D.,et al., Rev. Sci. Instrum. 9, (1988) 1739.[4] ROBINSON, D.C., and RUSBRIDGE, M.G., Plasma Physics 11,(1969) 73.[5] GARCIA, L., DIAMOND. P.H., CARRERAS, B., and CALLEN, J.,Phys. Fluids 28 (1985) 2147; HAHM, S., DIAMOND, P.H.,TERRY, P.W., GARCIA, L., CARRERAS, B.A., Phys. Fluids 30,(1987) 1452.[6] THAYER, D.R., AND DIAMOND, P.H., Phys. Fluids 30, (1987)3724.[7] CHIUEH, T., TERRY, P.W., DIAMOND, P.H., and SEDLAK, J.E.,Phys. Fluids 29, (1986) 231; BIGLARI, H., et al., IAEA-CN-53/D-3-5-3, this meeting.[8] UCKAN, T., BELL, J.D., HARRIS, J.H., CARRERAS, B.A.,DUNLAP, J.L., DYER, G.R., RITZ, CH.P., WOOTTON, A.J.,RHODES, T.L., and CARTER, K., J. Nucl. Mater, accepted forpublication (1990).HARRIS, J., et a l , IAEA-CN-53/C-4-7, this meeting.DRAKE, J.F., Phys. Fluids 30, (1987) 2429.THAYER, D.R., and DIAMOND, P.H., SAIC Technical Report#SAIC-90/1207:APPAT-130, SAIC, La Jolla, CA, (1990).[12] WARE, A.S., DIAMOND, P.H., THAYER, D.R., CARRERAS, B.A.,and LEBOEUF, J.N., Paper 1C13,1990 Sherwood Theory Conference,Williamsburg, VA, April 23-25, (1990).[13] GARCIA, L., HICKS, H.R., CARRERAS, B.A., CHARLTON, L.A.,and HOLMES, J.A., Journ. Comp. Phys. 65, (1986) 253.Table I. Equilibrium and turbulence characteristicsn(cm~3)Te(ev)qn/nTEXT2T4 x 10~123030.1 - 0.20.05 - 0.1(for r > a)0.15-0.33ATFIT1 x 10~122010.05 - 0.10.1(upper limit)0.1-0.21Resistivity DriftGradient WaveLimit Limit0.10.20.41 - 20.30.50.75-1.5FIGURE CAPTIONSFig. 1. The radial dependence of normalized density fluctuation levels.The radial coordinate is normalized to the minor radius a, of theshear layer itself. Results for TEXT (solid triangles) and ATF(open circles) are shown.Fig. 2. The radial dependence of the width <Tkg of the fluctuation kgspectrum. The radial coordinate is normalized to the shear layerminor radius a,. Results for TEXT (open circles) and ATF (solidsquares) are shown.Fig. 3. Radial dependence of normalized potential fluctuation levelsmeasured and predicted for TEXT. 3a) resistivity gradientdriven model with radiation: experiment (solid circles), analytictheory (solid squares) and computational model (open squares)values. 3b) thermally driven drift wave model: resistivity gradi-ent with radiation (open squares) and thermal drift wave (solidtriangles) computational model values .0.4 -0.2 -0I A- O-•-" oTEXTATF0 6• i 1 i iA8O4£>AO°AAo-° °:gA °AAA,A•--0.9 0.95 1 1.05 1.1Fig. 1s8High Te and typical TEXT shot:O TEXTlm ATFi • • • • 1 1 • • i p io• . . . i . . . . i . . . . i . . . . i0-4 105 -2 105 0 2 105 4 105velocity (cm/sec)e-0)0.90-0.70"0.50"0.30-0.100.90 1.050.5b)a>0)0.4-0.3"0.2-aD resistivity gradientA drift waves•••A0.10.90 0.95 1.00r/a1.05

Edge turbulence and transport: Text and ATF modeling

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Edge turbulence and transport: Text and ATF modeling

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