Spatially Resolved Measurements of Two-Dimensional Turbulent Structures in DIII-D Plasmas. Abstract

Spatially Resolved Measurements of Two-Dimensional Turbulent Structures in DIII-D Plasmas S.E. Zemedkun 1, S. Che 2, Y. Chen 1, C.W. Domier 2, N.C. Luhmann, Jr. 2, T. Munsat 1, S.E. Parker 1, B. Tobias 3, W. Wan 1, and L. Yu 2 1 Center for Integrated Plasma Studies, University of Colorado, Boulder, CO 80309 2 University of California at Davis, Davis, CA 95616 and 3 Princeton Plasma Physics Laboratory, Princeton, NJ 08543 Abstract Two-dimensional observations of spatially-coherent electron temperature fluctuations at driftwave scales (k 1 cm 1 ) have been made using the electron cyclotron emission imaging (ECEI) diagnostic on the DIII-D tokamak. These measurements enable the extraction of spectral properties, including poloidal dispersion relations. Temperature fluctuation levels are found to be T e / T e = 1.2%, and the phase velocity of the fluctuations is found to be constant across frequencies, consistent with modes having real frequencies low compared to the rotation-induced Doppler shifts. Comparisons with radially global linear gyrokinetic simulations suggest that the observed modes may be trapped electron modes (TEM). Electronic address: Samuel.Zemedkun@Colorado.EDU 1

I. INTRODUCTION AND BACKGROUND Trapped-electron modes (TEMs) [1 7] have been recognized as major contributors to the transport of energy and particles in magnetically confined plasmas in addition to ion temperature gradient (ITG) driven turbulence [8]. TEMs are driven by electron density or temperature gradients, and may be particularly important in scenarios with significant electron heating. Gyrokinetic simulations have demonstrated a number of key properties of the TEM, such as the spectral characteristics [4, 9], the interplay with zonal flows and transport barriers [5, 6], and their scalings with local plasma parameters [7]. Experimental studies have demonstrated evidence of TEMs consistent with measured temperature gradients and transport coefficients in various tokamaks [5, 10 13], and a number of diagnostics have provided frequency spectra and coherency data for both n e and T e fluctuations from TEMs. For example, the density fluctuation (ñ e ) wavenumber spectrum from nonlinear gyrokinetic simulations, in a TEM dominated case, matched the wavenumber spectrum from chord-integrated phase contrast imaging measurements in C-Mod, while also matching fluxes from transport analysis, using a synthetic diagnostic [14]. In a separate study, it was shown in both DIII-D and C-Mod that density-gradient driven TEMs dominate transport in the inner core of quiescent H-mode plasmas with moderately peaked density profiles [15]. In those studies, nonlinear gyrokinetic simulations using the GYRO code closely reproduced the ñ e frequency spectra from the Doppler backscattering diagnostic. Evidence has also been presented in which a threshold temperature gradient is observed in DIII-D plasmas, above which turbulence grows consistent with the T e -driven trapped electron mode [12, 13]. In these studies, multiple diagnostics were used to measure turbulence at multiple scales, and the cross-phase between T e and n e fluctuations was shown to be consistent with TEM predictions from the TGLF gyrofluid code. Contrary to the studies presented here, the radially-resolved instruments used in [12, 13] were not designed to detect extended coherent poloidal structures. Despite that difference, the general characteristics of the T e fluctuation spectra and coherency are qualitatively similar, despite a slight shift in the peak of the coherency spectrum ( 100 khz here, see fig. 3, and 75 khz in [12, fig. 4]). In addition, previous work has closely compared 2D radial and poloidal density fluctua- 2

tion wavelength spectra with gyrokinetic simulations in DIII-D and has shown the tilt of turbulent eddies in the poloidal plane is consistent with E B shear mechanisms [16]. The poloidal spatial structure of drift modes in the TEXT-U tokamak was characterized by using two-point correlation techniques on one-dimensional data from an early Electron Cyclotron Emission Imaging (ECEI) instrument [17, 18]. Additionally, substantial work has been done on a number of tokamaks using correlation electron cyclotron emission (CECE) techniques in the radial geometry. In these studies, pairs of ECE measurements are taken at closely spaced frequency intervals which represent highly correlated local temperature fluctuations but largely uncorrelated noise. In such systems, the signal-to-noise ratio can be greatly improved over single-signal measurements, which can be critical for fluctuation measurements. Early studies of this type include core electron temperature fluctuation measurements in the W7-AS stellarator [19] and studies of the relationship between core temperature fluctuations and heat transport in the TEXT-U tokamak [20]. Next-generation two-dimensional (2-D) ECEI systems on the DIII-D and TEXTOR tokamaks have already enabled imaging-based studies of magnetohydrodynamic (MHD) phenomena [21 24]. This work represents the first fully two-dimensional measurements of spatially coherent electron temperature fluctuations at drift-wave scales, including the radial and poloidal mode structure. Linear gyrokinetic simulations using the GEM code suggest the coherent structures observed may be TEMs. II. EXPERIMENTAL SETUP In this study, temperature fluctuation measurements were performed with an ECEI diagnostic [25, 26]. The instrument is based on a vertically distributed array of antennas which images the electron cyclotron layer with an optical system. As electrons undergo gyro-orbits in the magnetic field of the tokamak, they emit radiation at the electron cyclotron frequency (ω ce = eb/γm e ) and its harmonics, where e is the electron charge, B is the local magnetic field strength, γ is the relativistic factor, and m e is the electron rest mass [27 29]. Because the field strength falls off approximately as 1/R, where R is the major radius of the torus, each radius corresponds to a particular cyclotron frequency. Thus, frequency discrimination provides radial localization of the emitted radiation, with a channel width of 1 cm in these studies. Vertical localization is provided by the microwave imaging optics, with a spot-size 3

of 1 cm [25]. The sampling area of the 160-pixel image is 32 cm (vertical) 15 cm (radial), leading to a resolvable spatial frequency ranges of 0.2 cm 1 k θ 2.0 cm 1 and 0.4 cm 1 k r 1.7 cm 1 in the poloidal and radial directions, respectively. The instrument bandwidth, limited by the intermediate-frequency amplifiers, is 400 khz. The data shown in this study comes from the outboard (low-field side) ECEI array in DIII-D, with the plasma in low-confinement mode (L-mode) and I p = 0.8 MA, q 95 = 5.8, B T = 2 T (here the negative sign indicates the clockwise direction, as viewed from above). The low-field side array radial coverage for such discharges is from r/a = 0.5 to r/a = 0.8 (where r is the minor-radial coordinate and a is the plasma minor radius). The region of observation is detailed in Fig. 1. During the time period analyzed here, the plasma was heated by co-current neutral beam injection (2 MW) and by electron cyclotron heating (3 MW distributed between r/a = 0.2 and r/a = 0.3). Rotation due to the neutral beams leads to a Doppler shift of the lab-frame frequencies measured by the ECEI instrument, according to f lab = f r +(k θ /2π)(v θ v ϕ B θ /B ϕ ), where f r is the real frequency of the mode, k θ is the poloidal mode number, v ϕ and v θ are the plasma toroidal and poloidal rotation velocities, respectively, and f lab is the measured (Dopplershifted) frequency [30]. The ECRH systems on DIII-D operate at 110 GHz and heat in x-mode at the 2 nd harmonic resonance, as is standard on modern tokamaks having poor efficiency at the 3 rd harmonic. In a heating configuration, energy is damped equally on the perpendicular motion of co- and counter-propagating elections to raise the overall temperature while maintaining a thermal distribution. Production of a significant high-energy tail population is not common. In either case, the largely Maxwellian, isotropic population continues to act as an optically thick source, efficiently reabsorbing the downshifted emission of energetic electrons. Previous work has shown that the ECE radiation temperature for the 2 nd harmonic is effected only at very high temperatures, in regions of overlap with higher harmonic radiation at the same frequency, or in regions of dramatic inhomogeneity, such as at a strong transport barrier. Moreover, ECEI is used here as a fluctuation diagnostic and the data relevant to this work is not dependent on accurate measurement of the absolute electron temperature. To analyze the fluctuation data from the ECEI instrument, correlation techniques were applied to the waveforms for pixel pairs within the 2-D image. To reveal the 2-D structure of the coherent temperature fluctuation structures, we applied a two-point cross correlation 4

between a single reference channel and each other channel in the image. This effectively removes much of the uncorrelated thermal and instrument noise, enabling the resolution of correlated temperature fluctuations below the raw noise floor. Using this approach, the minimum detectable fluctuation level over an extended-duration sample is given by (T min e / T e ) 2 > (BW video /BW IF )/ N, where T min / T e is the minimum detectable relative fluctuation amplitude, BW video and BW IF e are the video and intermediate-frequency bandwidth values of the radiometers, respectively, and N is the number of samples in the correlated time series. For the study presented here, BW video = 400 khz, BW IF = 700 MHz, and N = 500,000, leading to Te min / T e of 0.1%. This technique has been used a number of times in previous correlation ECE studies with different instruments on the TEXT-U [20, 31], W7-AS [31], DIII-D [32, 33], and C-Mod [34] experiments. P xy = (x k x)(y k ȳ) N 1 k=0 [N 1 ] [ N 1 ] (1) (x k x) 2 (y k ȳ) 2 k=0 The central channel of the array (R = 2.12 m, Z = 0 m) is used as a reference channel for all analysis presented here. In this approach, each raw ECEI waveform was first filtered using a narrow-window Butterworth bandpass filter with width of 5 khz, over a series of center frequencies from 30-175 khz. response and linear phase [35]. k=0 The Butterworth filter was chosen for its flat frequency The two-point correlation values between the reference channel and each other channel were then calculated at zero lag and plotted versus position. The correlation value is defined in Eq. 1 for two discrete time series, x(t k ) and y(t k ), each containing N points [36]. For the analysis presented here, x and y represent the reference and second channel waveforms, respectively, after bandpass filtering, and the bar indicates a time average. A 0.5 s long signal was typically used (N = 500000), and the time windows were chosen during periods of stationary temperature behavior. An example of a resulting 2-D correlation map is shown in Fig. 1b. 5

III. EXPERIMENTAL RESULTS Figures 2a-c show the 2-D correlation maps for a series of three different frequency bands (f 52.5 khz, 107.5 khz, and 142.5 khz, respectively), illustrating the clarity of the poloidal mode structure, as well as the variation in k θ with f. As described later in the paper, this reflects an essentially linear relationship between k θ and f, resulting from the dominant Doppler shift in the lab-frame measurements. Figure 2d shows the same data as Fig. 2b, but with the color scale enhanced to show the radial and poloidal structure more clearly. In Fig. 2d a different reference channel (R=2.08 m, Z=0 m) was used and the intensity scale was renormalized row by row in the image. A similar analysis of turbulence structures using 2-D correlation maps was performed using the BES diagnostic on DIII-D, which measured density fluctuations (ñ e ) over a wide range of radii (0.45 < r/a < 0.9) [16]. While that data was not broken into narrow frequency bands, several notable similarities with this study were observed: the fluctuation level ñ e / n e = 1.5% in the region around r/a 0.65 0.75, and the turbulence group and phase velocities matched well with the observed Doppler shift of the rotating plasma. Also, tilted structures similar to those shown in Fig. 2 were observed, and shown to be consistent with E B shear effects. These are also similar to the structures visible in the simulation results shown in Fig. 5, below. Consistent with fluctuation spectra in previous TEM-dominated DIII-D cases (e.g. [12, 13]), the raw ECEI power spectrum (Fig. 3a) does not exhibit a clear signature of a dominant mode. Although the analyzed temperature waveforms are stationary in time, their spectral power is still far above the no-plasma system response, also shown in Fig. 3a. No distinct single mode peaks are identifiable in the power spectrum. The comparison of the 2-D map with the relatively featureless power spectrum illustrates the value of extended spatial coverage; modes which may be otherwise indistinguishable from background are made visible by the relative phase information across the diagnostic view. A quantitative spectral analysis of the observed modes (i.e. analysis of the relationships between the mode spectral power, phase, frequency and wavenumber) was performed using standard techniques [36]. The fluctuations exhibit non-negligible coherency only below around 200 khz, and the phase relationship between the channels is well-defined in the same 6

frequency range. As an example of this, Fig. 3b shows the coherency between two ECEI channels separated vertically by 3.2 cm. As evident from the red and black curves which show the response of the diagnostic in the presence and absence of a plasma signal, the signal to noise ratio falls off by roughly an order of magnitude between 100 and 200 khz. This is likely due to both the reduced amplitude of the underlying turbulence and limitations of diagnostic resolution. The effective spot size of an ECEI channel is of the order 1 cm 2, and so higher frequency fluctuations having similar dispersion characteristics are likely approaching the spatial Nyquist resolution. To explore these issues would be beyond the scope of the present work, which addresses fluctuations well diagnosed by mm-wave systems in the region 50-150 khz. Dispersion plots were constructed from the phase and spectral power using a procedure previously developed and applied to fixed probe pairs [37]. Taking two channels at the same radial location but poloidally separated by z, the local poloidal wavenumber k θ at each frequency f is given by k θ (f) = ϕ(f)/ z. Each spectral component of the cross-power between signal pairs thus has a unique f and k θ. The cross-power distribution is then binned and plotted against k θ and f. Spectral power from each combination of channel pairs can be similarly binned and summed into the map, providing an overall snapshot of dispersion behavior over an extended temporal and spatial window. It should be noted that a single pair cannot provide a fully two-dimensional spectral map [38]. The resulting plot for shot 144948 during t=2.8 3.3 s is shown in Fig. 4, illustrating the linear dispersion relationship of the mode. Also shown in Fig. 4 is a best-fit straight line through the maximum spectral power at each frequency, indicating the poloidal phase velocity of the mode in the lab frame of 10.8 km/s. While the emphasis of this paper is the poloidal structure of fluctuations diagnosed with the ECEI diagnostic, it is also useful to compare the amplitude of the T e fluctuations to similar measurements taken previously in DIII-D. In this study, the fluctuation level was found to be T e / T e = 1.2% (at ρ = 0.66). For comparison, several studies have published results for T e / T e values (integrated over all frequencies) from the CECE diagnostic in various DIII-D scenarios. In stationary L-mode discharges, measurements at ρ = 0.73 resulted in T e / T e = 1.5% [33]. Consistent with this, measurements from separate studies found T e / T e = 1.4% at ρ = 0.75 [39] and in a more comprehensive study T e / T e was found to range from 1.0% at ρ = 0.55 to 2.5% at ρ = 0.85, with an interpolated value of 1.3% at 7

ρ = 0.65 [40]. In a study of TEMs driven by critical temperature gradients, Te / T e values up to 2% were observed at the highest values of 1/L Te = 4.0 m 1, well above the critical gradient threshold [12, 13]. For comparison, 1/L Te = 5.3 m 1 in the cases presented here. IV. GEM SIMULATION SETUP Linear global electromagnetic simulations of these discharges were carried out for the DIII-D equilibrium at t=2.9 s using the gyrokinetic δf code GEM [41 43]. Global analysis is useful because variation of the equilibrium profile localizes the mode radially. Comparison of the linear two-dimensional eigenmode structure with ECEI is made assuming the plasma is in a weak turbulence regime where fluctuations are made up of a superposition of the dominant linear eigenmodes. GEM is a comprehensive particle-in-cell code with gyrokinetic ions and drift kinetic electrons, including electron-ion collisions. For particle species α = i, e, GEM solves the 5-dimensional distribution function f α (r, p α, t) from the gyrokinetic equation f α t + V Gα f α + ṗ α f α p α = C(f α ), (2) where p α = v α + q α m α A is the canonical momentum used as a coordinate, C(fα ) is the collision operator, and the guiding center velocity V Gα = v α b + Vdα + V E, (3) in which b = b + δb /B, V dα is the grad-b and curvature drift and V E = E b/b is the E B drift term. The ions are simulated using the δf-method, f i = f 0i + δf i with f 0α the shifted Maxwellian distribution for ions in v i u i0 (r) and Maxwellian distribution for electrons in v e, and the electrons are simulated using the split-weight scheme, for which f e = f 0e ϵ g ϕ f 0e ε e + h, so that the actual particle weights are corresponding to δf i and h. The simulation geometry was configured to match the center of the ECEI view at R = 2.12 m. Using a Miller parameterization of equilibrium [44], this corresponds to r/a = 0.726 where a = 0.621m is the minor radius and r is the radial Miller parameter that labels the flux surfaces. At this location q = 2.45, Ω i = 1.92 10 8 rad/s, ρ i = 1.35 10 3 m, v thi ρ i Ω i, c s /a = 1.60 10 3 Ω i, ν e = 0.14c s /a, ρ s /a = 3.20 10 3, k θ ρ i /n = 7.35 10 3, R maj = 1.67 m, and v E B = 4.85 km/s. The radial simulation domain L x covers 0.711 r/a 0.741. The simulation uses field-line-following coordinates where y is the toroidal direction and z is the 8

direction parallel to the magnetic field. There are 128, 32 and 48 grid points in L x, L y and L z, respectively, and the total number of particles is 6,291,456 per species. The magnetic equilibrium is provided by kinetic EFIT [45, 46]. The temperature and density profiles of all species including the carbon impurity are obtained from experimental data, and the experimental radial electric field E r is also used as input to the calculation. The simulation time step is t = 2Ω i, where Ω i is the proton gyro-frequency. The simulation parameters are presented in table I. Due to the characteristics of the frequency-wavenumber plot in Fig. 4, as well as the clear mode structure appearing in the bandpass filtered correlation images in Fig. 2, it is reasonable to suspect that what is observed is a series of excited linear eigenmodes. To support this hypothesis, linear gyrokinetic simulations were run for toroidal harmonics of n=10 40. The corresponding k θ was then measured in the same way as the experimental data in Fig. 4, but using the eigenmode structure from the simulation. Figure 5 shows the eigenmode structure of δt e for n = 20 (k θ =0.62 cm 1 ) from GEM. Both the full tokamak poloidal cross section and the diagnostic window are shown, to replicate the spatial window of the ECEI data shown in figs. 1 and 2. The raw GEM output has been convolved with a 2-D filter to replicate the spatial instrument response of the ECEI instrument. Specifically, the 2-D map was smoothed in the vertical direction with a 1-cm wide Gaussian filter to replicate the optical spot size, and smoothed in the horizontal direction with a 1-cm wide boxcar filter to approximate the frequency response function of the ECEI filters [25]. The instability is ballooning toward the outer side of the torus. The mode structures for other toroidal harmonics exhibit similar features. Additionally, nonlinear multi-mode simulations exhibit similar single structures. We note that the case shown is a collisionless result and adding the experimental collisionality makes n=20 marginally stable (discussed further below). The gyrokinetic simulation uses an externally imposed radial electric field taken as input obtained from DIII-D CER data and analysis [47 49]. To cancel the poloidal E B drift from E r, a parallel flow u i0 is added and a shifted Maxwellian distribution is used. This model is identical to previous core global gyrokinetic simulations modeling rotation [50, 51]. We find the gradient in the parallel flow is weakly destabilizing. The GEM simulation assumes no poloidal rotation. However, Ref. [52] shows that the poloidal rotation is significant. In future work we will implement an improved rotation model [53]. The best fit of GEM 9

n=10 to 40 (including Doppler shift) predicts a poloidal phase velocity of +7.2 km/s (where positive indicates the ion diamagnetic direction). V. COMPARISON BETWEEN GEM AND ECEI DATA Results from GEM indicate that the TEM, although weak, has the largest growth rate at the radius where the coherent structures are observed with ECEI. At r/a = 0.726, the pressure gradients are characterized by a/l n = 1.27, a/l Ti = 1.9 and a/l Te = 3.3, where L n = [ (ln n)/ r] 1 and L Tα = [ (ln T α )/ r] 1. The TEM is an important instability in core plasmas. Towards the outer core for this case, the TEM is the dominant linear mode. However, it is important to note that in the core of DIII-D L-mode plasmas, important instabilities include ITG, TEM as well as gradient-driven micro-tearing modes [54]. In fact it is not unusual for these modes to coexist in the turbulent state [54 56]. For large η i, where η i = L n /L Ti, the ITG mode dominates. For smaller η i ( 2), the TEM becomes dominant. At this radial location η i = 1.5, which is in the range where the TEM is the most unstable mode [4, 6, 7]. In fact, the ion temperature gradient has little effect on the growth rate of the instability within the uncertainties of the experimental measurement. We observe the same mode propagating in the electron diamagnetic direction of the plasma frame even when artificially increasing T i by 20%. This variation of the ion temperature gradient shows the robustness of the electron mode. Typical variation of R/L T is approximately 5% [39, Fig. 1] However, the variation of equilibrium parameters can be greater [57, 58]. For example, in the C-Mod L-mode case presented in [57, Fig. 1], the variation in R/L T can be 20% or higher approaching the edge. Figure 6 compares the linear growth rate γ and real frequency ω r of our collisionless simulations (with E r, full β) to simulations of varied scenarios. First, we find that taking the electrostatic limit (small β) has little effect on the growth rate or real frequency, consistent with TEM [4, 6, 7]. Secondly, in simulations without E r and hence no Doppler shift, the mode propagates in the electron diamagnetic drift direction, which is another characteristic of the TEM. (It should be mentioned, however, that there is some theoretical evidence that even marginally stable ion temperature-gradient modes can propagate in the electron diamagnetic direction [59].) Because the magnitude of the Doppler shift is large compared to the TEM propagation 10

velocity, it is important to clarify the various derived velocities (at the ECEI location). As shown in Fig. 6(b), the red dotted curve represents the GEM-simulated plasma-frame TEM real frequency which has a propagation velocity of -0.64 km/s. Also shown in Fig. 6 is the GEM-simulated lab-frame (i.e. Doppler-shifted) real frequency. The Doppler-shifted propagation velocity obtained by GEM using the simplified toroidal rotation model is +7.2 km/s, which is in disagreement with the ECEI prediction of +10.8 km/s. It is important to note that the plasma frame mode frequency is small compared to the Doppler shifted mode frequency, as can be seen in Fig. 6(b). The strong Doppler shift makes the precise determination of the relatively small plasma frame real frequency difficult using ECEI data. The inclusion of E r slightly reduces the linear growth rate. We have tested the drive of the instability by changing the density gradient and the electron temperature gradient with local flux tube simulations (not shown), and the results indicate that the electron temperature gradient provides the strongest drive. Finally, as expected by previous simulations [60, 61] and experimental studies [62], the TEM is significantly stabilized by finite collisionality. Our results show that the instability is marginally stable for n 20 when experimentally estimated electron-ion collision rates are applied. In reality, the marginally unstable TEM eigenmodes can be excited by other processes such as inverse cascade from higher n modes and non local turbulence spreading [63]. The radial location of this experimental observation is very close to the transport shortfall region, r/a = 0.8, of DIII-D L-mode plasmas, in which gyrokinetic simulations have shown turbulent saturation levels are low and do not agree with experiments [39, 40]. Recent global gyrokinetic simulations indicate that the turbulence spreading from the edge can increase the fluctuation intensity in this outer core region, although the increased ion heat flux transport level is still lower than the experimental value [63]. With the plasma parameters here, the growth rate is much less than the real frequency in the rotating frame and it is reasonable to assume the plasma is in a weak turbulence regime where fluctuations are made up of a superposition of linear eigenmodes with shearing due to equilibrium E r and self-generated zonal flows. In this study we simply compare the collisionless eigenmode which is robustly unstable and can be well modeled with an initial value particle code. We do not observe a sensitivity of the mode structure and real frequency as we vary the collisionality. 11

VI. SUMMARY In summary, broadband fluctuations displaying significant spatial coherence have been characterized by correlation techniques applied to 2-D imaging. Specifically, mode structures are revealed by applying narrow bandpass frequency filters to broadband ECEI data, which enables spectral analysis of the experimental data in both space and time. An analogous reduction of gyrokinetic simulation output was performed by looking at the unstable linear toroidal eigenmodes, and was compared to the ECEI data. Several aspects of this comparison suggest that the observed modes are TEM: the location of the experimentally observed modes (i.e. at the location where TEM is the most unstable in the simulations), their 2-D structure, and their relatively low propagation velocity. Evidence for the identification of this mode as TEM in the GEM simulations includes the experimental pressure gradients, the effect of β on the growth rate and real frequency, the mode propagation direction, and the modeled stabilization from increased collisionality. VII. ACKNOWLEDGMENTS The authors gratefully acknowledge Brian Grierson, Jon Hillesheim and James DeBoo for their help in this work. This work was supported by U.S. Department of Energy Contracts DE-SC0003913, DE-FG02-99ER54531, DE-AC02-09CH11466, DE-FG02-08ER54954, and DE-FC02-04ER54698. [1] Adam J C, Tang W M and Rutherford P H 1976 Physics of Fluids 19 561 [2] Coppi B and Rewoldt G 1974 Phys. Rev. Lett. 33 1329 [3] DeBoo J C, Cirant S, Luce T C, Manini A, Petty C C, Ryter F, Austin M E, Baker D R, Gentle K W, Greenfield C M, Kinsey J E and Staebler G M 2005 Nuclear Fusion 45 494 501 [4] Dannert T and Jenko F 2005 Phys. Plasmas 12 072309 [5] Ernst D R, Bonoli P T, Catto P J, Dorland W, Fiore C L, Granetz R S, Greenwald M, Hubbard A E, Porkolab M, Redi M H, Rice J E, Zhurovich K and Group A C M 2004 Phys. Plasmas 11 2637 12

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Figures 17

FIG. 1: (Color online). Temperature fluctuation map from the ECEI instrument, illustrating the poloidal structure of the drift mode. (a) Location of ECEI view within the flux-surface map of DIII-D. (b) 2-D correlation between the central ECEI channel and each other channel, in the 5 khz frequency window centered at f=107.5 khz. 18

FIG. 2: (Color online). (a-c) Correlation plot for 3 different frequency bins for shot 144948, t = 2.8 3.3 s. (n 10,20 and 25 respectively; see Fig. 4) (d) Data from correlation plot (b) renormalized row by row to enhance the contrast and expose the tilted structures. 19

FIG. 3: (Color online). (a) Spectral power density, summed over all ECEI channels, and (b) coherency between two ECEI channels separated by 3.2 cm. The black curves are for shot 144948 during t=2.8 3.3 s (during ECH and Co-NBI heating). The red curves are for the same shot at t=7.0 7.5 s (after the plasma has been quenched). The red curves thus represent the no-plasma system response. 20

FIG. 4: (Color online). Normalized spectral power map for shot 144948, t=2.8 3.3 s, during ECH and Co-NBI heating (Normalized cross-power suppressed to 0.1 for visualization). (Red solid line): Best fit line for the ECEI data. 21

FIG. 5: (Color online). (a) Poloidal mode structure for n = 20 from GEM simulation. (b) The n = 20 mode (from GEM) magnified to match the spatial window of the ECEI data shown in figs. 1 and 2. 22

FIG. 6: (Color online). Simulation results of a) linear growth rate and b) real frequency for n = 10 to 40. The collisionless simulations (solid lines) are compared to simulations with 10% of experimental β (dotted lines), simulations without the radial electric field E r (dashed lines) and simulations with collisions (dash-dotted lines). The ion diamagnetic direction is in the negative y-direction, and the electron diamagnetic direction is in the positive y-direction. 23

Tables 24

TABLE I: GEM simulation parameters r/a 0.726 ρ 0.657 n e (10 19 m 3 ) 1.548 T e (kev) 0.763 T e /T i 1.081 n i /n e 0.574 n imp /n e 7.103E-02 T imp /T i 1.0 c s /a (khz) 307.57 a/l ne 1.271 a/l ni 1.012 a/l Te 3.303 a/l Ti 1.901 a/l Timp 1.901 a/l nimp 1.620 γ E B (c s /a) -3.688E-02 ν ei (c s /a) 0.139 R 0 (r)/a 2.685 ρ* 3.200E-03 Z eff 1.3 q 2.453 ŝ = rd(ln(q))/dr 2.127 Shafranov shift -0.124 elongation, κ 1.223 s κ 0.177 triangularity, δ 0.153 s δ 0.223 β e 1.179E-03 25

S. Zemedkun Fig. 1 (a) 1.35 (b) 0.17 0.20 0.90 0.11 0.44 0.06 z (m) -0.01 z (m) 0.00 0.00-0.46-0.06-0.91-0.11-1.36 1.00 1.46 1.92 2.38 R (m) -0.17 2.04 2.09 2.14 2.19 R (m) -0.20

S. Zemedkun Fig. 2 (a) 0.17 50-55 khz (b) 105-110 khz (c) 140-145 khz 0.20 (d) 105-110 khz 0.11 0.06 Z (m) 0.00 0.00-0.06-0.11-0.17 2.04 2.12 2.19 2.04 2.12 2.19 2.04 2.12 2.19-0.20 2.04 2.12 2.19 R (m)

S. Zemedkun Fig. 3 (a) Power (V 2 Hz -1 ) (b) 10-4 10-5 10-6 10-7 10-8 0.3 Coherency 0.2 0.1 0.0 0 50 100 150 f (khz) 200 250

f [khz] 150 100 50 0 20 40 60 80 150 Slope = 10.8 km/s 10 50 Normalized Cross-Power 0.100 0.050 0 0 0 20 40 60 80 k θ [m -1 ] 0.000

1.50 0.11 0.50 0.06 z [m] z [m] 1.00 0.00 0.00 0.006 δ Te / Tio (b) 0.17 (a) -0.50-0.06-1.00-0.11-1.50 1.00-0.17 2.04 2.09 2.14 2.19 R [m] 1.50 2.00 R [m] 2.50 0.000-0.006

γ/ω 8 x i (a) 10 4 collisionless 7 10% β No E r 6 Collisional 5 4 3 2 1 (b) 3 x 10 3 2.5 2 1.5 1 0.5 0 ω r /Ω i 0 0 20 40 n 0.5 0 20 40 n