1 EX/11-2Ra The Isotope Effect in GAM – Turbulence Interplay and Anomalous Transport in Tokamak A.D. Gurchenko 1 , E.Z. Gusakov 1 , P. Niskala 2 , A.B. Altukhov 1 , L.A. Esipov 1 , D.V. Kouprienko 1 , M.Yu. Kantor 1 , S.I. Lashkul 1 , S. Leerink 2 , A.A. Perevalov 1 1 Ioffe Institute, St. Petersburg, Russia 2 Euratom-Tekes Association, Aalto University, Espoo, Finland E-mail contact of main author: aleksey.gurchenko@mail.ioffe.ru Abstract . It is demonstrated experimentally for the first time at the FT-2 tokamak that the theoretically predicted possibility of GAM control of the turbulence associated with the enhanced plasma rotation shearing manifests itself in modulation of the turbulence level at the GAM frequency. This observation is supported by ELMFIRE full-f global gyro-kinetic modeling demonstrating the modulation of density fluctuations as well as of the heat flux and diffusivity. The experimental effects were enhanced in deuterium discharges where GAM amplitude increased leading to the stronger fluctuation reflectometry signal suppression during the GAM bursts and to the decrease of the mean anomalous electron thermal diffusivity determined by the ASTRA modeling thus providing an explanation for the isotope effect in tokamak plasma anomalous transport. 1. Introduction The interaction between large-scale E×B flows, in particular geodesic acoustic modes (GAM), and small-scale drift-wave turbulence has been an important area of experimental research for anomalous transport of energy and particles in toroidal plasmas during the last decade utilizing more and more sophisticated tools. GAMs, which are, according to the present day understanding, excited in plasma due to nonlinear three-wave interaction of drift waves, in their turn can influence the turbulent fluctuations and anomalous transport. The mechanism GAMs control the turbulence could be associated with large inhomogeneity of poloidal rotation accompanying GAMs possessing small radial wavelength and huge radial electric field. Dependence of GAM excitation level and, more general, long-range correlations on ion mass could be responsible [1] for the isotope effect in tokamak anomalous transport [2] which is still unclear. The present paper is devoted to investigation of these effects in the FT-2 tokamak ( R = 55 cm, a = 7.9 cm) using a set of highly localized microwave backscattering diagnostics and the global gyro-kinetic (GK) modeling by ELMFIRE code [3]. 2. The turbulence and diffusivity modulation at GAM frequency as provided by ELMFIRE GK code The ELMFIRE simulations for ohmic 19 kA H-discharge ( B 2.1 T, n e (0) 4×10 13 cm -3 ; Z eff 3.5; T e (0) 470 eV, T i (0) 110 eV, see profiles in FIG. 1) were successfully validated against experimental data characterizing the FT-2 tokamak turbulent dynamics and transport phenomena including GAM temporal and spatial structure [3, 4]. Strong poloidal velocity

2 EX/11-2Ra 4 oscillations associated with GAMs and obtained in [3, 4] as a result of ELMFIRE radial electric 19 m -3 ) 2 n e (10 field E r simulation are shown in FIG. 2. The 0 GAM radial wave structure is located at small 450 T e (eV) radii r =4-6.5 cm. 300 T i (eV) 150 The mechanism GAMs control the turbulence 0 discussed in theory [5] is associated with large -6 -4 -2 0 2 4 6 inhomogeneity of poloidal rotation x (cm) accompanying GAMs possessing small radial FIG. 1. The density and temperature wavelength and huge radial electric field. The equatorial profiles in 19 kA H- stabilizing effect of strong GAM rotation shearing discharge. should be however reduced, according to theory 340 E r (kV/m) [6] by its quick temporal variation leading to the 320 -12 following modification of the drift-wave 300 -8 turbulence stabilization condition: t (mks) 280 -4 eff = | E×B H + 0 | > , where E×B and 0 are 260 0 240 poloidal rotation shearing rates corresponding to 220 4 GAM and mean flow correspondingly, is the 200 8 instability growth rate or the turbulence inverse 3 4 5 6 7 correlation time, parameter r (cm) 1/ 4 2 3 H (1 3 ) F 4 F (1 F ) 1 4 F is a FIG. 2. Temporal variation of the radial electric field spatial distribution reduction factor, F (2 F G / ) 2 and F G is the computed by ELMFIRE. GAM frequency. 4 r = 5.5 cm (a) V E x B (km/s) 0 The inward propagating intensive GAM waves -4 shown in FIG. 2 are sufficiently strong to -8 satisfy condition eff > . A comparison of the (b) eff 400 effective shearing and the growth rate (at eff , (kHz) F G r = 5.5 cm) is demonstrated in FIG. 3. The absolute value of the E×B shearing rate at this 200 0 radius composed of the mean shear 0 66 kHz and its fluctuating part reduced by 0 a factor H 0.2 is shown in FIG. 3b by red 210 240 270 300 330 curve. The turbulence growth rate, estimated t (mks) from the ELMFIRE data as 158 kHz is FIG. 3. The simulated E×B velocity (a) shown by blue line. The mean shear 0 and the and comparison of eff and (b). GAM frequency F G 53 kHz are shown in 340 2 /s) e (m FIG. 3b by black and green lines respectively. As 320 1.0 it is seen in FIG. 3, the effective shear eff 300 1.6 t (mks) 280 exceeds the turbulence growth rate level once or 2.2 260 even twice times per the GAM period depending 240 2.8 on the amplitude of the V E×B oscillations, which 220 3.4 is most likely the reason of the strong modulation 200 4.0 of the magnetic surface averaged electron 3 4 5 6 7 thermal diffusivity demonstrated in FIG. 4. The r (cm) similar phenomenon in ELMFIRE simulations FIG. 4. Temporal variation of the was also found for TEXTOR [7]. The influence of electron thermal diffusivity spatial the intensive GAM wave manifests itself initially distribution computed by ELMFIRE.

3 EX/11-2Ra in the turbulence level modulation. As it is seen in FIG. 5, the coherency spectrum of magnetic surface averaged radial electric field and density fluctuations squared in the vicinity of equatorial plane (where density component of the GAM is sin( ) suppressed in agreement with its FIG. 5. The spatial distribution of the symmetry, where is the poloidal angle) coherence spectrum between E r and possesses maximum at the GAM frequency n 2 computed by ELMFIRE. F G 53 kHz in the region where experimental measurement were performed (4.9 cm < r < 5.6 cm). In the next section of the paper we visualize this numerically predicted effect in the FT-2 tokamak experiment using complex approach utilizing microwave Doppler enhanced scattering (ES) and reflectometry diagnostics [8]. 3. Experimental investigation of GAM-turbulence interaction The theoretically predicted effect of turbulence control by GAMs was studied utilizing correlative Doppler microwave enhanced scattering (CDES) [9] (with X-mode out-off- equatorial plane microwave backscattering in the upper hybrid resonance off small-scale density fluctuations possessing radial wave numbers r S > 2) and reflectometry diagnostics. The medium-scale radial electric field GAM 20 f D (a.u.) (a) D oscillations are characterized in experiment by 15 H 10 the CDES technique using the backscattering 5 spectra Doppler frequency shift f D ( t ) 0 0 40 80 120 modulation [10], which is associated with F (kHz) oscillations of plasma poloidal rotation velocity ( f D ( t ) = V ( t )/2 where is the F (kHz) V , (b) 50 H turbulence wave number). The f D -signal power 40 30 D spectra measured in similar 19 kA H- and D- discharges at the same radial position are 5 6 7 8 r (cm) shown in FIG. 6a. GAM frequency radial profiles are shown in FIG. 6b. In accordance FIG. 6. (a) Power spectra of the f D -signal in D (red) and H (blue) discharges. (b) Radial with the theory predictions [11] (shown by solid profiles of the GAM frequency (blue triangles lines) they are determined by electron – for H, red circles – for D, solid curves – temperature behavior and the isotope mass. It is theoretical [11] estimation). important that a much larger level of the GAM H 19kA amplitude was observed in D-regime in 6 D 19kA comparison with hydrogen. The possible reason r (cm) H 32kA for this effect could be associated with the 4 D 32kA difference in ion collisionality in D- and H- r = G 2 discharges due to different mass and smaller atom density in deuterium. 0.8 1.2 The double-frequency probing correlative 2/3 L T 1/3 (cm) G = 4 i scheme was used for investigation of the GAM spatial structure [12] propagating inwards. The FIG. 7. Comparison of the GAM radial wave length measured experimentally r GAM wave length r and correlation length in D- with G in H- and D-discharges with regimes (with 19 kA and 32 kA plasma currents) plasma current 19 kA and 32 kA. have systematically larger values then in

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