Edge Turbulence Research Articles

Statistical Properties of Turbulence: A New Approach to Characterize Transport in Fusion Plasmas

A view of recent experimental results and progress in the characterization of the statistical properties of edge turbulence in fusion plasmas is given. The study of the dynamical interplay between fluctuations in gradients, turbulent transport and radial electric fields has shown that these parameters are strongly coupled both in tokamak and stellarator plasmas. The size of turbulent events increases when the plasma deviates from the average density gradient. The radial velocity of fluctuations is of the order of 20 m/s for transport events associated with a small deviation from the most probable gradient. On the contrary, the effective radial velocity increases up to 500 m/s for transport events in which the local gradient increases significantly above the most probable gradient. These results suggest a link between the size of transport events and the nature of transport (diffusive versus non-diffusive) in the plasma boundary region. The dynamical relationship between fluctuations in gradients and transport is strongly affected by the presence of sheared poloidal flows, heating power and the proximity to instability thresholds. There is also experimental evidence that the turbulent transport is strongly coupled with fluctuations in parallel flows, reflecting that parallel flows might, at least partially, be driven by turbulent mechanisms. Using the same methods developed for the study of turbulence, the statistical properties of the radial propagation of edge localized modes (ELMs) in the SOL of JET have also been investigated. ELM events propagate radially with effective velocities in the range of 1000 m/s, again showing a link between the radial velocity and the size of transport events. At such high velocities, the radial propagation competes strongly with parallel loss to the divertor plates and may therefore be an important mechanism transporting particles to the main chamber walls of fusion devices. This work emphasizes the importance of the statistical description of transport processes in fusion plasmas as an alternative approach to the traditional way of characterizing transport based on the computation of effective transport coefficients (i.e. diffusion coefficients) and on average quantities (i.e., average correlation lengths).

Experimental investigation of dynamical coupling between density gradients, radial electric fields and turbulent transport in the JET plasma boundary region

The dynamical interplay between turbulent transport, density gradients and radial electric fields has been investigated in the plasma boundary of magnetic confined plasmas. Experimental results show that there is a dynamical relationship between gradients and turbulent transport. Fluctuations on gradients, which turns out to have a rather Gaussian probability density function (PDF), and turbulent transport, which has a non-Gaussian PDF, are strongly coupled. Also, the size of turbulent events increases when the plasma deviates from the average gradient. This increase is particularly significant when the gradient increases above its average value. The system relaxes to the most probable state in a time comparable to the correlation time of turbulence. The present results emphasize the importance of the characterization of fluctuations in the terms of PDFs to test critically edge turbulence models.

The nonlinear drift wave instabilityand its role in tokamak edge turbulence

Drift wave turbulence, in general a balance between E×B drift turbulence in planes perpendicular to, anddissipative wave dynamics parallel to, a background magneticfield, is a hallmark example of nonlinearity in plasma physics. The turbulence generally has the same basic character in asheared magnetic field lying in closed surfaces whether linearinstabilities are present or not. Only when the linear forcingterms are dominant does this situation not prevail; it is notanalogous to neutral fluid turbulence where pure linear forcingis balanced by pure nonlinear mixing and decorrelation. Detailed computations show that two types of nonlinearity aresimultaneously present: advection of fluid vorticity by theE×Bflows, which tends to have a scattering character, andE×Badvection of pressure disturbances, which has the familiardiffusive mixing character. The vorticity nonlinearity excitesthe turbulence, acting against the mostly linear paralleldynamics which constrains it, while the pressure nonlinearityprovides dissipation via transfer to ever smaller scales. Thepractical result is that the saturated level of the turbulenceand the resulting averaged thermal energy transport arecontrolled principally by these nonlinear mechanisms even whenmoderate linear instabilities are present. The model is mostlyapplicable to tokamak edge turbulence, for which the linearforcing effects are sufficiently moderate that the nonlinearphysics is allowed to operate.

Initial studies of core and edge transport of NSTX plasmas

Rapidly developing diagnostic, operational, and analysis capability is enabling the first detailed local physics studies to begin in high β plasmas of the National Spherical Torus Experiment (NSTX). These studies are motivated in part by the observation of energy confinement times in neutral-beam-heated discharges that are favourable with respect to predictions from the ITER-89P scaling expression. For plasmas heated with neutral beaminjection (NBI), analysis based on profile measurements suggests that electron heat conductionis the dominant thermal loss channel. Cases where early analysis indicates that ionthermal conduction may be exceptionally low is motivating studies of possible sources of ion heating not presently accounted for by classical collisional processes. Gyrokinetic microstability studies indicate that long wavelength turbulence with kθρi~0.1-1 may be stable or suppressed by E×B shear in these plasmas, while modes with kθρi~50 may be robust. High harmonic fast wave (HHFW) heating efficiently heats electrons on NSTX, and studies have begun using it to assess transport in the electron channel. Regarding edge transport, H-mode transitions occur with either NBI or HHFW heating. The power required for L- to H-mode transitions far exceeds that expected from empirical ELM-free H-mode scaling laws derived from moderate aspect ratio devices. Finally, initial fluctuation measurements made with two techniques are permitting the first characterizations of edge turbulence.

Drift wave instability near a magnetic separatrix

It is well known that the pure drift-Alfvén wave (DW) (i.e., in the absence of curvature and toroidal coupling effects) is stabilized by magnetic shear in circular flux surface geometry when the drift frequency is constant radially [P. N. Guzdar, L. Chen, P. K. Kaw, and C. Oberman, Phys. Rev. Lett. 40, 1566 (1978)] as is implicit in a local ballooning analysis. In the edge plasma near a magnetic separatrix, X-point geometry is important and the circular flux surface model does not apply. Using several numerical codes and analytical models, it is found that the DW is robustly unstable in this case. Physically, instability is driven by wave reflection from the steep profile of k⊥ near the X-points, due to magnetic shear and the local minimum of the poloidal magnetic field. It is concluded that a complete set of dimensionless parameters describing edge turbulence must include DW parameters that embody the physics of X-point effects and plasma shaping.

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 model.

The Physics of E × B Shear, Zonal Flows and Streamers in Tokamak Edge Turbulence

The role of E × B flow shear in reducing turbulent transport in the edge region of a tokamak is investigated using 3D nonlinear global simulations. Transport reduction is found to be due to both a decrease of fluctuation amplitudes as well as a change in their relative phase. A scaling of the turbulent diffusivity with E × B flow shear has been deduced from these simulations. This scaling agrees with recent experimental observations as well as analytical models. Moreover these simulations allow us to examine the dynamics of anisotropic secondary flows such as zonal flows and streamers. These flows are found to regulate intermittent transport observed in flux driven simulations.

The Physics of E × B Shear, Zonal Flows and Streamers in Tokamak Edge Turbulence

The role of E × B flow shear in reducing turbulent transport in the edge region of a tokamak is investigated using 3D nonlinear global simulations. Transport reduction is found to be due to both a decrease of fluctuation amplitudes as well as a change in their relative phase. A scaling of the turbulent diffusivity with E × B flow shear has been deduced from these simulations. This scaling agrees with recent experimental observations as well as analytical models. Moreover these simulations allow us to examine the dynamics of anisotropic secondary flows such as zonal flows and streamers. These flows are found to regulate intermittent transport observed in flux driven simulations.

Coherent structures in the edge turbulence of the CASTOR tokamak

A two-dimensional array of electric probes placed on the poloidal plane has been inserted in the edge region of the CASTOR tokamak. The floating potential patterns measured by the probes show the presence of localized structures which are convected poloidally by the E×B plasma motion. The lifetime of these structures has been found to be large enough to allow them to complete several full poloidal rotations before dying away. Furthermore, the eddy turnover time of the plasma around the potential blobs is smaller than the lifetime, so that these structures can be called coherent.

Statistics of turbulence induced by magnetic field

Using the TCABR tokamak facility, we analyze turbulent electrostatic fluctuations in a stationary toroidal magnetoplasma, created by radio-frequency waves and confined by two different toroidal magnetic fields. The increase of toroidal magnetic field leads to gradients in the mean plasma radial profiles and the onset of electrostatic turbulence. For the turbulent fluctuations, we show that the statistics of data collected using fixed sampling time is the same than the statistics of the time in which measurements of the data return to a specified reference interval of values. With these statistical analyses we find special invariant probability distributions, power-scaling laws for some average quantities, and long-range correlation for their oscillations. These observations suggest that turbulence has recurrent properties, as those observed in recurrent fully chaotic low-dimensional systems. Therefore, evolution of measurements of low-dimensional dynamical systems can be used to describe the recurrence observed in the tokamak edge turbulence.

Direct Numerical Simulation of Turbulent Flow over a Rectangular Trailing Edge

This paper describes a direct numerical simulation (DNS) study of turbulent flow over a rectangular trailing edge at a Reynolds number of 1000, based on the freestream quantities and the trailing edge thickness h; the incoming boundary layer displacement thickness '* is approximately equal to h. The time-dependent inflow boundary condition is provided by a separate turbulent boundary layer simulation which is in good agreement with existing computational and experimental data. The turbulent trailing edge flow simulation is carried out using a parallel multi-block code based on finite difference methods and using a multi-grid Poisson solver. The turbulent flow in the near-wake region of the trailing edge has been studied first for the effects of domain size and grid resolution. Then two simulations with a total of 256 2 512 2 64 (~ 8.42106) and 512 2 1024 2 128 (~ 6.72107) grid points in the computational domain are carried out to investigate the key flow features. Visualization of the instantaneous flow field is used to investigate the complex fluid dynamics taking place in the near-wake region; of particular importance is the interaction between the large-scale spanwise, or Karman, vortices and the small-scale quasi-streamwise vortices contained within the inflow boundary layer. Comparisons of turbulence statistics including the mean flow quantities are presented, as well as the pressure distributions over the trailing edge. A spectral analysis applied to the force coefficient in the wall normal direction shows that the main shedding frequency is characterized by a Strouhal number based on h of approximately 0.118. Finally, the turbulence kinetic energy budget is analysed.

Visible imaging of turbulence in the SOL of the Alcator C-Mod tokamak

Measurements of fluctuations in the scrape-off layer (SOL) of Alcator C-Mod plasmas were made using visible emission from the plasma edge. Line emissions from a local gas jet of He atoms were imaged along radially separated, toroidally viewing chords and provided local measurements (AR, ΔZ = 3.4 mm, RΔO ∼ 20) mm) of density fluctuations. The RMS emission fluctuation amplitudes, normalized by the average emission, ranged from 10% to 60%, depending on distance from the separatrix, and increased sharply beyond ρ from LCFS = 20 mm. These intensity fluctuations imply that radial profile of the normalized RMS density fluctuations varies from ∼20% to 90%. Typical fluctuation spectra show turbulence out to frequencies of ∼ 150 kHz, although most of the spectral power is below 20 kHz. The radial correlation length for the <20 kHz fluctuations is ∼7 mm. No essential differences were seen in the SOL fluctuations when plasmas with Enhanced D α ' (EDA) H-mode confinement were compared with those having L-mode confinement. In addition, fluctuations in natural' D α light, due to recycling at an outboard poloidal limiter, were imaged by a gated fast-framing camera and provided measurements of the poloidal size scale of the SOL fluctuations. Snapshots of D α emission were obtained with exposures of 2 and 10 μs. Typical fluctuation size in the poloidal dimension was 0.01-0.03 m. These striations/fluctuations were randomly located in the successive gated frames taken at 1000 Hz, as expected for edge turbulence.

Direct Measurements of E × B Flow and Its Impact on Edge Turbulence in the CASTOR Tokamak Using an Optimized Gundestrup Probe

New experimental evidence of the correlation between edge sheared E×B flow and reduction of turbulence has been measured in the CASTOR tokamak (R = 0.4 m, a = 0.085 m, B T = 1 T). A biasing electrode is placed at the separatrix in a configuration which has demonstrated strongly sheared electric fields and consequent improvement of the global particle confinement. A set of movable electrostatic probes (rake, Langmuir, Gundestrup, and rotating Mach) provide redundant, simultaneous measurements of poloidal flow, toroidal flow, electron temperature, density, and radial electric field with high temporal resolution and at the same poloidal location. Particular effort has been made in the optimization of the Gundestrup probe collector geometry in order to reduce the relative uncertainty of Mach number measurements in plasmas with weak flow (M ∥, M ⊥ < 0.1). The measurements from the rake, Gundestrup, and rotating Mach probes give three independent radial profiles of E×B shear in ohmic and biased modes. Good agreement is obtained both for the profile shape and its absolute magnitude. The plasma flows, especially the poloidal E×B drift velocity, are strongly modified in the sheared region, reaching Mach numbers as high as half the sound speed. The corresponding shear rates (≈5×106 s-1) derived from both the flow and electric field profiles are in excellent agreement and are at least an order of magnitude higher than the growth rate of unstable turbulent modes as estimated from fluctuation measurements. In addition, we compare the measured E×B ion mass flow with the phase velocity of fluctuations moving poloidally across the Gundestrup collectors. Given the poloidal separation of the collecting plates and the sampling frequency (5 MHz), the maximum detectable phase velocity turns out to be rather modest compared to the measured bulk poloidal flow speed. Therefore the two quantities are only compared when the poloidal speed is low; in that case, they show similar behaviour in response to the applied bias.

Edge turbulence measurements in NSTX by gas puff imaging

Turbulent filaments in visible light emission corresponding mainly to density fluctuations at the edge have been observed in large aspect ratio tokamaks: TFTR, ASDEX, Alcator C-Mod, and DIII-D. This article reports on similar turbulent structures observed in the National Spherical Torus Experiment (NSTX) using a fast-framing, intensified, digital visible camera. These filaments were previously detected mainly in high recycling regions, such as at limiters or antennas, where the line emission from neutral atoms was modulated by the fluctuations in local plasma density. However, by introducing controlled edge gas puffs, i.e., gas puff imaging, we have increased the brightness and contrast in the fluctuation images and allowed the turbulent structure to be measured independently of the recycling. A set discrete fiber-optically coupled sight-lines also measured the frequency spectra of these light fluctuations with a 200 kHz bandwidth. Initial results in NSTX show that the turbulent filaments are well aligned with the magnetic field which can be up to 45° from the horizontal at the outer midplane of NSTX. The dominant wavelength perpendicular to the magnetic field is ∼7–11 cm, corresponding to a k⊥ ρs of ∼0.3 at an assumed Te=25 eV, and the frequency spectra has a typical broad shape characteristic of edge turbulence extending to about 100 kHz. By imaging a He gas puff along a magnetic field line the characteristic radial scalelength appears to be in the 3–5 cm range.

Visualization of plasma turbulence with laser-induced fluorescence (invited)

Turbulence is a key factor limiting the performance of fusion devices. Plasma edge turbulence determines the boundary values of the plasma density and temperature, which in turn determine the internal gradients and controls global plasma transport. In recent years, significant progress has been made in modeling turbulence behavior in plasmas and its effect on transport. Progress has also been made in diagnostics for turbulence measurement; however, there is still a large gap in our understanding of it. An approach to improve this situation is to experimentally visualize the turbulence, that is, a high resolution 2-D image of the plasma density. Visualization of turbulence can improve the connection to theory and help validate theoretical models. One method that has been successfully developed to visualize turbulence in gases and fluids is planar laser-induced fluorescence. We have recently applied this technique to visualize turbulence and structures in a plasma. This was accomplished using an Alexandrite laser that is tunable between 700 and 800 nm, and from 350 to 400 nm with second harmonic generation. The fluorescence light from an argon ion transition has been imaged onto an intensified charged coupled device camera that is gated in synchronization with the laser. Images from the plasma show a rotating structure at 30 kHz in addition to small scale turbulence.

Nonlocal simulation of the transition from ballooning to ion temperature gradient mode turbulence in the tokamak edge

The transition from resistive ballooning to ion temperature gradient (ITG) mode turbulence in the tokamak edge is studied in three dimensions using the electrostatic reduced Braginskii equations with ion temperature dynamics. In contrast to most previous simulations of plasma edge turbulence, which assume the parameters (density, temperature, collisionality, etc.) to be constant in space and time (local approximation), a realistic spatial variation and the nonlinear dependence of the parameters on the fluctuating quantities is taken into account. The influence of nonlocal effects is studied by a scan in the ratio of profile to turbulence scale length. For a large ratio, good agreement between local and nonlocal results on the ITG mode and ballooning turbulence is found. With increasing nonlocality, however, the anomalous transport is more and more suppressed. For the ITG mode, the turbulence quench is due to a decrease of the linear growth rate, while for the ballooning mode a novel, inherently nonlocal saturation mechanism is identified.

Effect of edge turbulence on threshold of multifaceted asymmetric radiation from the edge instability in tokamaks

The radiative condensation instability believed to be responsible for the occurrence of multifaceted asymmetric radiation from the edge (MARFE) in tokamaks has been investigated in the presence of a background turbulence of saturated drift resistive ballooning modes (DRBM). These modes are a natural source for edge fluctuations in tokamaks. For the m=1 MARFE, it has been shown that a modest level of DRBM turbulence can significantly lower the threshold radiation rate required for excitation of MARFEs, enhance its growth rate, and introduce a real part to the mode frequency. Some of these results are consistent with observations of onset of MARFEs in recent experiments on Joint European Torus (JET) [Proceedings of the 17th European Conference on Controlled Fusion and Plasma Heating, Amsterdam (European Physical Society, Petit-Lancy, 1990), Vol. 14b-1, p. 339] and Tokamak Experiment for Technology Oriented Research (TEXTOR) [Phys. Rev. Lett. 71, 1549 (1993)].

Condensation of Microturbulence-Generated Shear Flows into Global Modes

In full flux-surface computer studies of tokamak edge turbulence, a spectrum of shear flows is found to control the turbulence level and not just the conventional (0,0)-mode flows. Flux tube domains too small for the large poloidal scale lengths of the continuous spectrum tend to overestimate the flows and thus underestimate the transport. It is shown analytically and numerically that under certain conditions dominant (0,0)-mode flows independent of the domain size develop, essentially through an analog of Bose-Einstein condensation for the shear flows.

E×B shear flows and electromagnetic gyrofluid turbulence

Low frequency tokamak edge turbulence is modelled numerically using gyrofluid equations for electrons and ions on an equal footing. The electrons are electromagnetic, and arbitrarily strong finite gyroradius effects are included for the ions. Computations are in a globally consistent truncation of flux surface geometry arising from ideal tokamak equilibria. The turbulence is similar to that in the fluid model in steep gradient regimes, for which the electron transit frequency is comparable to that of the turbulence. The nonlinear drift wave instability is shown to be caused by E×B self-advection, and is similar for both two-and three-dimensional models. The turbulence always has drift wave mode character for the parameter regime of interest, except when the ideal ballooning threshold is reached. Turbulence interacts strongly with E×B shear flows, but does not build the flow shear to significant levels by itself. On the other hand, an imposed shear layer arising from the neoclassical equilibrium of the edge region does have the necessary properties and scaling to eventually result in a credible edge transport transition scenario.

Observation of radial propagation of electrostatic fluctuations on KT-C tokamak

The radial wavenumber spectra of electrostatic fluctuations measured by Langmuir probe arrays on the KT-5C tokamak show a quasimode-like structure which results in a net radial outward propagation of the turbulent fluctuations. The power-averaged radial wavenumber is approximately constant in the core region and increases near the limiter. The radial wavenumber spectral width stays nearly constant from core to edge and is about two times greater than the poloidal wavenumber spectral width. The measured fluctuation levels and wave action fluxes are in good agreement with model predictions (Mattor N and Diamond P H 1994 Phys. Plasmas 1 4002, Mattor N 1995 Phys. Plasmas 2 766) which suggest that drift wave propagation could be a source of edge turbulence.