Edge Turbulence Research Articles

Edge turbulence and anomalous transport in fusion plasmas

A view of the latest experimental results and progress in the characterization and understanding of edge turbulence is given. The development of new fluctuation analysis techniques has provided a new bridge between experimental measurements and theoretical turbulence models. At the same time, the characterization of fluctuation and turbulent transport has stimulated new experimental developments in the measurement of electron temperature fluctuations; it has been shown that substantial levels of electron temperature fluctuations are present in the boundary region of magnetically confined plasmas. Several driving (curvature, atomic physics, .) and damping (electric field) mechanisms of the edge turbulence have been investigated. The development of methods to modify and control plasma turbulence and confinement appears as a very promising area of research. Recent results emphasize the importance of comparative studies between the structure of the turbulence in toroidal confinement systems to test critically edge turbulence models.

Bifurcated transition of radial transport in the HIEI tandem mirror

Transition to a high radial confinement mode in a mirror plasma is triggered by limiter biasing. Sheared plasma rotation is induced in the high confinement phase which is characterized by reduction of edge turbulence and a confinement enhancement factor of 2−4. Edge plasma parameters related to radial confinement show a hysteresis phenomenon as a function of bias voltage or bias current, leading to the fact that transition from low to high confinement mode occurs between the bifurcated states. A transition model based on azimuthal momentum balance is employed to clarify physics of the observed bifurcation.

Intermittency in tokamak edge turbulence: An artifact of kurtosis analysis

Kurtosis or flatness factor of an experimental time series is considered to be one of the important computed parameters in turbulence studies. The analysis itself is of a simple nature but like any other statistical analysis it demands extreme caution in the absence of which one is prone to draw false conclusions. An earlier kurtosis based statistical analysis [Phys. Rev. Lett. 69, 1375 (1992)] on the reported first measurement of intermittency in tokamak edge turbulence using density and potential fluctuation data has been found to be questionable on a number of counts (‘‘Comment’’ submitted to Phys. Rev. Lett.). This has necessitated a detailed reanalysis of the same data which has now been carried out and the results are presented in this paper. It is found that most of the density datasets and all the potential datasets exhibit a significant peak in their autospectra at about 4–6 kHz and all other datasets with significant non-Gaussianity are found to be either having plasma current associated high amplitude transients or are found to be nonstationary due to a trend in the variance. The datasets are close to Gaussian with kurtosis values approaching zero if these factors are properly taken care of.

Scaling study of edge plasma parameters using a multi-device database

A database consisting of edge equilibrium, turbulence and transport related plasma parameters has been compiled. Scaling laws for edge density, electron temperature, and radial particle flux are derived in an initial study using a subset of data obtained from tokamaks Phaedrus-T, Tokamak de Varennes, TEXT and TEXT-U. A comparison of edge particle transport in divertor and limiter plasmas shows that the magnetic topology of a separatrix or a divertor improves particle confinement. The particle diffusion coefficient varies radially in a manner opposite to that of Bohm diffusion.

Influence of Magnetic Configuration Properties and Methods of Plasma Heating on Divertor Flow Distribution in Stellarator Type Devices

Results of measurements of diverted plasma parameters in several stellarator type devices (Heliotron E, Saturn, Uragan-2, Uragan-3, Uragan-3M) are analyzed. a diverted plasma flow distribution appears to depend not only on the magnetic configuration properties but on confined plasma parameters, methods of plasma heating, the level of edge turbulence, etc. In some cases it becomes possible to elucidate the factors affecting strong inhomogeneity of diverted plasma flows. 12 refs., 4 figs., 1 tab.

Biased H mode experiments in Phaedrus-T

Inserting a positively biased electrode to just inside the Phaedrus-T tokamak limiter results in typical H mode behaviour (i.e. Hα or Dα drop, density rise, increase in stored energy, profile steepening, and reduction of edge turbulence and radial transport) in deuterium, hydrogen and helium discharges. Hα or Dα emission suggests that the improvement in particle confinement with H mode is poloidally asymmetric, with the greatest improvement occurring on the low field side. The radial conductivity is examined and measured values are compared with theory

Microwave scattering diagnostic on the Advanced Toroidal Facility torsatrona)

A 2 mm scattering diagnostic used to study density fluctuations of the electron cyclotron resonance heated plasma in the Advanced Toroidal Facility is described. A four‐channel flexible antenna design was chosen to monitor fluctuations within the wave number range of 3<k⊥<20 cm−1 and to locate the scattering volume anywhere in the stellarator minor cross section. Special attention was paid to the system calibration and to the normalization of the k spectra. Analysis of the diagnostic noise showed that the main source of spurious signal was a scattering from high‐level edge turbulence driven by the second‐harmonic radiation from the gyrotron used for plasma heating. This spurious signal was suppressed using waveguide filters and rearrangement of the microwave circuit elements. Evidence in support of direct scattering from a well‐defined plasma volume was found. Good correlation of the scattered waves’ intensity with the density scale length was observed. Use of a dual‐homodyne circuit configuration made is possible to determine that the plasma density fluctuations were propagating in the electron diamagnetic direction.

Edge turbulence spectrum alterations driven by resonant fields

An ergodic magnetic structure is generated in the TBR-1 Tokamak boundary to handle heat flux and minimize impurity generation. In this work, the effect of this structure on the plasma edge turbulence is investigated. Thus, spectral alterations driven by perturbing magnetic fields created by resonant helical windings are observed in the small Tokamak TBR-1. The investigated oscillations are detected with an array of Langmuir and magnetic probes. Spectral and bispectral analyses revealed significant changes induced by the resonant helical windings, mainly in the MHD frequency band. Thus, whereas the known Mimov oscillation amplitude reduction is observed, the density and potential oscillation spectra are slightly affected. However, the bispectral analysis shows a clear reduction of the wave-wave mode coupling in the MHD frequency range, while the high frequency turbulent coupling is steadily reduced

High-sensitivity, high-resolution measurements of radiated power on TEXT-U

Investigations of a possible radiation drive of edge turbulence in tokamaks require sensitive radiated power measurements having high temporal and spatial resolution. A commercially available 16-element X–UV-enhanced photodiode array having essentially 100% quantum efficiency from ∼25 to ≥6 keV is used. The frequency response is presently limited by the amplifiers to ∼50 kHz, although the ultimate response is expected to be much higher (≳200 kHz). Each element’s view is ∼0.4 cm wide along the major radius at the plasma midplane while the view of the entire array is ∼6.3 cm wide and is scannable over the entire plasma cross section. The details of the system as well as observations of fine spatial structures and fluctuations undetectable by conventional bolometers are presented.

Wave launching as a diagnostic tool to investigate plasma turbulence (abstract)

An experimental scheme to extend the investigation of plasma turbulence has been implemented. It involves driving waves into the plasma to modify the statistical properties of the fluctuations; the dynamical balance of the turbulence is perturbed via the injection of waves at selected spectral regions. New analysis techniques based on conditional sampling and high order correlation are developed for studying the wave launching and the wave-wave coupling processes. Experimental results from TEXT-U tokamak show that the launched waves interact with the intrinsic fluctuations both linearly and nonlinearly. The attainment of driven nonlinearity is necessary for this diagnostic scheme to work. It is also the key to an active modification and control of edge turbulence in tokamaks.

Microwave scattering diagnostic on the Advanced Toroidal Facility torsatron (abstract)a)

A 2 mm scattering diagnostic used to study density fluctuations of the electron cyclotron resonance heated plasma in the Advanced Toroidal Facility is described. A four-channel flexible antenna design was chosen to monitor fluctuations within the wave number range of 3&amp;lt;k⊥&amp;lt;20 cm−1 and to locate the scattering volume anywhere in the stellarator minor cross section. Special attention was paid to the system calibration and to the normalization of the k spectra. Analysis of the diagnostic noise showed that the main source of spurious signal was a scattering from high-level edge turbulence driven by the second-harmonic radiation from the gyrotron used for plasma heating. This spurious signal was suppressed using waveguide filters and rearrangement of the microwave circuit elements. Evidence in support of direct scattering from a well-defined plasma volume was found. Good correlation of the scattered waves’ intensity with the density scale length was observed. Use of a dual-homodyne circuit configuration made is possible to determine that the plasma density fluctuations were propagating in the electron diamagnetic direction.

Characterization of coherent structures in tokamak edge turbulence.

A statistical test for extracting and identifying coherent structures in the scrape-off layer turbulence is used to analyze Langmuir probe data from the ADITYA and ASDEX tokamaks. This method, the biorthogonal decomposition, allows one to characterize large-scale coherent structures in plasma turbulence in an unambiguous manner. It is shown that such structures effectively contribute to radial transport and to intermittency. Results from numerical simulations of turbulence driven by the resistive interchange instability in the scrape-off layer are compared to the observed statistical properties.

Drift wave propagation as a source of plasma edge turbulence: Toroidal theory

Recently [N. Mattor and P. H. Diamond, Phys. Rev. Lett. 72, 486 (1994)] it was suggested that large-amplitude turbulence in edge plasmas [ñ/n0∼O(1)] could originate from the core, propagating outward into the regions of low density and temperature. Here this theory is expanded, using a toroidal geometry. It is shown that a wave launched in the core region can propagate over a substantial portion of the radius, reaching the edge from the core. It is shown that a large increase of plasma flow from core to edge causes wave reflection, cutting off the source of edge turbulence. Experimental evidence is discussed, with particular attention to subtleties of global mode structure in a torus. Possible new experimental tests of this theory are discussed. Details are given of a new theory to explain the observed correlation between edge shear flows and improved confinement (‘‘H’’ modes), which are compared to experiment.

Drift wave propagation as a source of plasma edge turbulence: Slab theory

In a recent work [N. Mattor and P. H. Diamond, Phys. Rev. Lett. 62, 486 (1994)], it was suggested that large amplitude turbulence in edge plasmas [ñ/n0∼O(1)] could originate from the core, reaching large amplitude when encountering regions of low density and temperature. Here the slab model of that theory is elaborated on and generalized to the case of nonadiabatic electron dynamics. It is shown that a drift wave launched with ñ/n0≪1 in a dense region can propagate into a sparse region and amplify. It is shown that such waves cannot propagate into regions with a large increase of velocity, suggesting a simple explanation of the observed correlation between edge shear flows and high confinement (‘‘H’’ modes). It is shown that a wave launched in the adiabatic regime can become nonadiabatic when propagating into a low density and temperature edge region, suggesting a possible explanation for probe measurements.

Model on L- to H-Mode Transition Driven with Lower-Hybrid Wave

In this letter, a model for active suppressing tokamak edge turbulence and hence inducing the L-mode to H-mode transition with lower-hybrid wave (LHW) is proposed. The model includes the two contents: (a) The poloidal sheared flow of plasma is generated by the ponderomotive potential and induced magnetization acting on a tokamak plasma resulting from the oscillating electric field of the injected LHW. (b) During the time the LHW is injected into tokamak edge, the edge turbulence and the LHW-generated plasma poloidal flow compete with each other; if the shear of plasma poloidal flow is large enough to suppress the edge turbulence, the confinement will be remarkably improved and hence the system will enter the H operating mode. This model leads us to find that the threshold LHW power required for edge-turbulence suppression is proportional to A(ω) ≡ (ω/ωLH)2|(ω/ωLH)2 - 1|, which enables us to explain the experiment in the JT-60 tokamak with lower-hybrid current drive.

Turbulent edge transport in the Princeton Beta Experiment-Modified high confinement mode

The first probe measurements of edge turbulence and transport in a neutral beam induced high confinement mode (H-mode) are reported. A strong negative radial electric field is directly observed in H-mode. A transient suppression of normalized ion saturation and floating potential fluctuation levels occurs at the low confinement mode to high confinement mode (L–H) transition, followed by a recovery to near low mode (L-mode) levels. The average poloidal wave number and the poloidal wave-number spectral width are decreased, and the correlation between fluctuating density and potential is reduced. A large-amplitude coherent oscillation, localized to the strong radial electric field region, is observed in H-mode but does not cause transport. In H-mode the effective turbulent diffusion coefficient is reduced by an order of magnitude inside the last closed flux surface and in the scrape-off layer. The results are compared with a heuristic model of turbulence suppression by velocity-shear stabilization.

The H-mode in the ASDEX tokamak

The L-H transition in the ASDEX tokamak was investigated. The level of fluctuations both in the scrape-off layer and in a narrow region inside the separatrix drops on a 100 mu s timescale. Density turbulence coming from the edge and magnetic turbulence, as measured with magnetic probes, show a similar behavior. Before and during the transition no frequency shift in the fluctuation spectra could be detected which would indicate the rapid appearance of a radial E-field in the region of the H-mode barrier. Within milliseconds after the L-H transition new fluctuations propagating in the electron diamagnetic direction are destabilized which however exhibit no marked influence on transport across the barrier. In the bulk of the plasma fluctuation spectra show a frequency shift which is dominated by toroidal plasma rotation due to neutral beam injection. The initial transport barrier is deduced to lie inside the separatrix with a width of <or=3 cm.

The physics of transport barrier formation in the PBX-M H-mode

Measurements of edge profiles, turbulence, and turbulent-driven transport were made inside the last-closed flux surface (LCFS) and in the scrape-off layer (SOL) of PBX-M L-mode and H-mode plasmas using a fast reciprocating Langmuir probe diagnostic. Direct measurements of the potential profile confirm the generation of a strong inward radial electric field (Er approximately -100 V/cm) just inside the LCFS in H-mode. Density and potential fluctuation levels are reduced at the L-H transition, resulting in significantly lower turbulent transport. The edge density gradient then steepens in response to the reduced cross-field transport. After a stable H-mode edge equilibrium is formed, the fluctuation amplitudes recover back to nearly L-mode values. The poloidal wavenumber spectrum is narrowed in the transport barrier, and the density and potential fluctuations are decorrelated. The reduction in turbulent transport occurs across the LCFS and SOL regions and is not localized to the region of strong radial electric field.

H-mode of W7-AS stellarator

In W7-AS the H-mode has been observed for the first time in a currentless stellarator plasma. H-modes are achieved with 0.4 MW Electron Cyclotron Resonance Heating with 140 GHz at 2.5 T and high density, with 70 GHz at 1.25 T and lower density and with neutral beam injection. The H-phases display all characteristics known from tokamak H-modes including the development of an edge transport barrier, an increase of the poloidal impurity flow velocity at the edge, the reduction of edge turbulence and ELMs. The power threshold for the H-mode seems to be lower than that in tokamaks and is in agreement with an neBT scaling. Major differences to the divertor H-mode is the small increase in energy content of maximally 30%, the lack of a strong isotope effect both in threshold and in H-mode characteristics and a peculiarly narrow operational range in iota.

Drift wave propagation as a source of plasma edge turbulence.

It is suggested that large amplitude turbulence in edge plasmas could originate from core fluctuations propagating to the edge. It is shown that a drift wave launched with n\ifmmode \tilde{}\else \~{}\fi{}/${\mathit{n}}_{0}$\ensuremath{\ll}1 in a dense region can propagate into a sparse region and amplify, in both a slab and a torus. Propagation is cut off by a large velocity increase, suggesting a simple explanation of the observed correlation between edge shear flows and improved confinement (H modes). Evidence for such radial propagation might be found in asymmetries of fluctuations about the toroidal midplane.