K. Hallatschek

Edge turbulence imaging in the Alcator C-Mod tokamak

The two-dimensional (2D) radial vs poloidal structure of edge turbulence in the Alcator C-Mod tokamak [I. H. Hutchinson, R. Boivin, P. T. Bonoli et al., Nucl. Fusion 41, 1391 (2001)] was measured using fast cameras and compared with three-dimensional numerical simulations of edge plasma turbulence. The main diagnostic is gas puff imaging, in which the visible Dα emission from a localized D2 gas puff is viewed along a local magnetic field line. The observed Dα fluctuations have a typical radial and poloidal scale of ≈1 cm, and often have strong local maxima (“blobs”) in the scrape-off layer. The motion of this 2D structure motion has also been measured using an ultrafast framing camera with 12 frames taken at 250 000 frames/s. Numerical simulations produce turbulent structures with roughly similar spatial and temporal scales and transport levels as that observed in the experiment; however, some differences are also noted, perhaps requiring diagnostic improvement and/or additional physics in the numerical m...

Observations of the turbulence in the scrape-off-layer of Alcator C-Mod and comparisons with simulation

The intermittent turbulent transport in the scrape-off-layer (SOL) of Alcator C-Mod [I.H. Hutchinson, R. Boivin, P.T. Bonoli et al., Nucl. Fusion 41, 1391 (2001)] is studied experimentally by imaging with a very high density of spatial measurements. The two-dimensional structure and dynamics of emission from a localized gas puff are observed, and intermittent features (also sometimes called “filaments” or “blobs”) are typically seen. The characteristics of the spatial structure of the turbulence and their relationship to the time-averaged SOL profiles are discussed and compared with those measured on the National Spherical Torus Experiment [M. Ono, S. M. Kaye, Y.-K. M. Pong et al., Nucl. Fusion 40, 557 (2000)]. The experimental observations are compared also with three-dimensional nonlinear numerical simulations of edge turbulence. Radial profiles of the poloidal wave number spectra and the poloidal scale length from the simulations are in reasonable agreement with those obtained from the experimental ima...

Experimental characterization of coherent, radially-sheared zonal flows in the DIII-D tokamak

A271 EXPERIMENTAL CHARACTERIZATION OF COHERENT, RADIALLY-SHEARED ZONAL FLOWS IN THE DIII-D TOKAMAK. Application of time-delay-estimation techniques to two-dimensional measurements of density fluctuations, obtained with beam emission spectroscopy in DIII-D plasmas, has provided temporally and spatially resolved measurements of the turbulence flow-field. Features that are characteristic of self-generated zonal flows are observed in the radial region near 0.85 {<=} r/a {<=} 1.0. These features include a coherent oscillation (approximately 15 kHz) in the poloidal flow of density fluctuations that has a long poloidal wavelength, possibly m = 0, narrow radial extent (k{sub r}{rho}{sub I} < 0.2), and whose frequency varies monotonically with the local temperature. The approximate effective shearing rate, dv{sub {theta}}/dr, of the flow is of the same order of magnitude as the measured nonlinear decorrelation rate of the turbulence, and the density fluctuation amplitude is modulated at the frequency of the observed flow oscillation. Some phase coherence is observed between the higher wavenumber density fluctuations and low frequency poloidal flow fluctuations, suggesting a Reynolds stress contribution. These characteristics are consistent with predicted features of zonal flows, specifically identified as geodesic acoustic modes, observed in 3-D Braginskii simulations of core/edge turbulence.

Excitation of geodesic acoustic mode in toroidal plasmas

The instability of the geodesic acoustic mode (GAM) in tokamak turbulence is analysed. It can be caused by dynamic shearing of the ambient turbulence by GAMs combined with the poloidal inhomogeneity of the turbulent flux. The dispersion relation is derived. The competition between the drive mechanism and the damping by turbulence viscosity is discussed. GAMs are more unstable for high safety factors.

Frequency scaling and localization of geodesic acoustic modes in ASDEX Upgrade

The frequency behaviour and localization of the geodesic acoustic mode (GAM), believed to be a coherent plasma turbulence-generated Er × B zonal flow (ZF) oscillation, is studied in the ASDEX Upgrade tokamak using Doppler reflectometry. In typical elongated (1.4 < κ < 1.75) plasmas with an X-point divertor configuration the GAM is observed only in the edge density gradient region 0.95 < ρpol < 1.0 between the density pedestal top and the flux surface boundary. The GAM frequency (5–25 kHz) is found to scale linearly as ω = G cs/Ro (sound speed over major radius) but with an inverse dependence on the plasma elongation κ and a weak direct dependence on the safety factor q. The lower the GAM frequency the more important it is expected to become in moderating the turbulence via shear decorrelation. A heuristic scaling law for the frequency scale factor involving κ and finite aspect ratio terms has been obtained from dedicated parameter scans. For circular plasmas κ ~ 1 touching the limiter the density pedestal is weakened and the GAM is seen to reach in radially as far as ρpol ~ 0.75, depending on the q profile, with a frequency scale consistent with theoretical predictions. Radially the GAM frequency is not a smooth function but displays a series of plateaus a few centimetres wide coinciding with peaks in the GAM amplitude, suggesting several ZF layers. At the plateau edges the GAM spectral peak splits into two frequency branches.

Quiet periods in edge turbulence preceding the L-H transition in the National Spherical Torus Experiment

This paper describes the first observations in the National Spherical Torus Experiment (NSTX) [S. M. Kaye et al., Phys. Plasmas 8, 1977 (2001)] of “quiet periods” in the edge turbulence preceding the low-to-high (L-H) mode transition, as diagnosed by the gas puff imaging (GPI) diagnostic near the outer midplane separatrix. During these quiet periods the GPI Dα light emission pattern was transiently similar to that seen during H-mode, i.e., with a relatively small fraction of the GPI light emission located outside the separatrix. These quiet periods had a frequency of ∼3 kHz for at least 30 ms before the L-H transition, and were correlated with changes in the direction of the local poloidal velocity. The GPI turbulence images were also analyzed to obtain an estimate for the dimensionless poloidal shearing S=(dVp/dr)(Lr/Lp)τ. The values of S were strongly modulated by the quiet periods but did not significantly vary during the ∼30 ms preceding the L-H transition. Since neither the quiet periods nor the shea...

Observation and characterization of radially sheared zonal flows in DIII-D

Zonal flows, thought crucial to the saturation and self-regulation of turbulence and turbulent transport in magnetically confined plasmas, have been observed and characterized in the edge region of DIII-D plasmas. These flows exhibit temperature scaling characteristics and spatial features predicted for geodesic acoustic modes (GAMs), a class of higher-frequency zonal flows seen in nonlinear simulations of plasma turbulence. The zonal flows (GAMs) have been observed in the turbulence flow-field in the radial region 0.85 ≤ r/a ≤ 1.0 via application of time-delay-estimation techniques to two-dimensional measurements of density fluctuations, obtained with beam emission spectroscopy. Spatial and temporal analysis of the resulting flow-field demonstrates the existence of a coherent oscillation (approximately 15 kHz) in the poloidal flow of density fluctuations that has a long poloidal wavelength, possibly m = 0, narrow radial extent (krρi < 0.2), and a frequency that varies monotonically with the local temperature. The approximate effective shearing rate, dvθ/d r, of the flow is of the same order of magnitude as the measured nonlinear decorrelation rate of the turbulence. These characteristics are consistent with predicted features of zonal flows, specifically identified as GAMs, observed in three-dimensional Braginskii simulations of core/edge turbulence.

Coherent structure of zonal flow and onset of turbulent transport

Excitation of the turbulence in the range of drift wave frequency and zonal flow in magnetized plasmas is analyzed. Nonlinear stabilization effect on zonal flow drive is introduced, and the steady state solution is obtained. The condition for the onset of turbulent transport is obtained and partition ratio of fluctuation energy into turbulence and zonal flows is derived. The turbulent transport coefficient, which includes the effect of zonal flow, is also obtained. Analytic result and direct numerical simulation show a good agreement.

Physics of Zonal Flows

Zonal flows, by which we mean azimuthally symmetric band‐like shear flows, are ubiquitous phenomena in nature and the laboratory. It is now widely recognized that zonal flows are a key constituent in virtually all cases and regimes of drift wave turbulence, indeed, so much so that this classic problem is now frequently referred to as “drift wave‐zonal flow turbulence.” In this lecture note, we present new viewpoints and unifying concepts which facilitate understanding of zonal flow physics, via theory, computation and their confrontation with the results of laboratory experiment. Special emphasis is placed on identifying avenues for further progress. We briefly survey issues such as (i) mechanism of zonal flows excitation, (ii) back interaction on turbulence, (iii) saturation mechanism of zonal flows, (iv) energy partition between fluctuations and flows, (v) turbulent transport coefficient dressed by zonal flows, and (vi) experimental efforts to verify these fundamental processes.

Observation of geodesic acoustic modes (GAMs) and their radial propagation at the edge of the TEXTOR tokamak

The electrostatic potential and density fluctuations have been measured at the edge of the TEXTOR tokamak by two toroidally distant Langmuir probe arrays. The geodesic acoustic mode (GAM) zonal flows (ZFs) are observed in potential fluctuations with a toroidal and poloidal symmetric structure. The GAM frequency, fGAM, changes monotonically with the local temperature and is close to the frequency-dispersion predicted by theories. Bispectral analysis shows clear nonlinear coupling between the GAM and broadband ambient turbulence. The GAM packet has a narrow radial extent with kr 0.5–0.7 cm−1 and exhibits explicitly a radially outward propagation. Furthermore, the radial correlation structure of GAMs and their radial propagation have been investigated in a wide range of parameters by varying plasma density and edge safety factor (5.0 ≤ q(a) ≤ 5.9). It is found that the magnitude of the GAM correlations reduces remarkably with the increase in the plasma density approaching the density limit, while the radial wavelength of GAMs only decreases slightly in higher density and larger q(a) discharges. With increasing plasma density, the radial propagating phase speed of GAMs is strongly reduced along with the drop in the local temperature. The results provide new evidence on the propagation properties of GAM ZFs.