A comprehensive review of zonal flow phenomena in plasmas is presented. While the emphasis is on zonal flows in laboratory plasmas, planetary zonal flows are discussed as well. The review presents the status of theory, numerical simulation and experiments relevant to zonal flows. The emphasis is on developing an integrated understanding of the dynamics of drift wave–zonal flow turbulence by combining detailed studies of the generation of zonal flows by drift waves, the back-interaction of zonal flows on the drift waves, and the various feedback loops by which the system regulates and organizes itself. The implications of zonal flow phenomena for confinement in, and the phenomena of fusion devices are discussed. Special attention is given to the comparison of experiment with theory and to identifying directions for progress in future research.

/pdf/zonal-flows-in-plasma-a-review-3byloag115.pdf

Zonal flows in plasma—a review

The present status of zonal flow experiments is reviewed with the historical process to attain the concept of zonal flows, which provides a new framework for understanding turbulence and transport in toroidal plasmas. The existence of zonal flows is experimentally confirmed to present a new paradigm of plasma turbulence. The paper presents contemporary experiments on zonal flows as major topics with a brief presentation of the zonal flow theories, the diagnostics and data processing techniques for turbulence and zonal flows and the peripheral issues of zonal flow physics. The accumulated experimental results introduced in this review include identification of zonal flows (both stationary zonal flows and geodesic acoustic modes), nonlinear interactions between zonal flows and turbulence, quantification of turbulent Reynolds stress, flow dynamics, energy transfer dynamics between turbulent wave components and the effects of zonal flows on plasma transport. These results have given rise to a new paradigm, namely, that the plasma turbulence is a system of zonal flows and drift waves, with an emphasis on the interaction between the disparate scale structures, e.g. zonal flows (mesoscale) and turbulence (micro-scale).

https://iopscience.iop.org/article/10.1088/0029-5515/49/1/013001/pdf

A review of zonal flow experiments

The structure of the edge radial electric field {ital E}{sub {ital r}} inferred from the poloidal rotation velocity is compared with that of the particle and thermal transport barrier for {ital H}-mode plasmas in JFT-2M. Both {ital E}{sub {ital r}} and its gradient {partial derivative}{ital E}{sub {ital r}}/{partial derivative}{ital r} in the thermal transport barrier are found to become more negative at the {ital L}-{ital H} transition. On the other hand, {partial derivative}{ital E}{sub {ital r}}/{partial derivative}{ital r} is more positive outside of the separatrix. The shear of the radial electric field and poloidal rotation velocity in the {ital H} mode is localized within the order of an ion poloidal gyroradius near the separatrix, in the region of ion collisionality {nu}{sub *{ital i}}{approx}20--40.

Edge electric field profiles of H-mode plasmas in JFT-2M tokamak

Radial profiles of ion temperature and plasma flow are measured at the n/m = 1/1 magnetic island produced by external perturbation coils in the Large Helical Device. The sheared poloidal flows and sheared radial electric field are observed at the boundaries of the magnetic island, because the poloidal flow vanishes inside the static magnetic island. When the width of the magnetic island becomes large, the flow along the magnetic flux surface inside the magnetic island appears around the O point in the direction which reduces the shear of the poloidal flow at the boundary of the magnetic island.

https://nifs-repository.repo.nii.ac.jp/?action=repository_action_common_download&item_id=460&item_no=1&attribute_id=22&file_no=1

Observation of plasma flow at the magnetic island in the large helical device.

The differences and similarities between the internal transport barriers (ITBs) of tokamak and helical plasmas are reviewed. By comparing the characteristics of the ITBs in tokamak and helical plasmas, the mechanisms of the physics for the formation and dynamics of the ITB are clarified. The ITB is defined as the appearance of discontinuity of temperature, flow velocity, or density gradient in the radius. From the radial profiles of temperature, flow velocity, and density the ITB is characterized by the three parameters of normalized temperature gradient, R / L T , the location, ρ ITB , and the width, W/a, and can be expressed by ‘weak’ ITB (small R / L T ) or ‘strong’ (large R / L T ), ‘small’ ITB (small ρ ITB ) or ‘large’ ITB (large ρ ITB ), and ‘narrow’ (small W/a) or ‘wide’ (large W/a). Three key physics elements for the ITB formation, radial electric field shear, magnetic shear, and rational surface (and/or magnetic island) are described. The characteristics of electron and ion heat transport and electron and impurity transport are reviewed. There are significant differences in ion heat transport and electron heat transport. The dynamics of ITB formation and termination is also discussed. The emergence of the location of the ITB is sometimes far inside the ITB foot in the steady-state phase and the ITB region shows radial propagation during the formation of the ITB. The non-diffusive terms in momentum transport and impurity transport become more dominant in the plasma with the ITB. The reversal of the sign of non-diffusive terms in momentum transport and impurity transport associated with the formation of the ITB reported in helical plasma is described. Non-local transport plays an important role in determining the radial profile of temperature and density. The spontaneous change in temperature curvature (second radial derivative of temperature) in the ITB region is described. In addition, the key parameters of the control of the ITB and future prospects are discussed.

/pdf/internal-transport-barrier-in-tokamak-and-helical-plasmas-re1lp8qp3n.pdf

Internal transport barrier in tokamak and helical plasmas

The bifurcation nature of the electrostatic structure is studied in the toroidal helical plasma of the Compact Helical System (CHS) [K. Matsuoka et al., Proceedings of the 12th International Conference on Plasma Physics and Controlled Nuclear Fusion Research, Nice, 1988 (International Atomic Energy Agency, Vienna, 1989), Vol. 2, p. 411]. Observation of bifurcation-related phenomena is introduced, such as characteristic patterns of discrete potential profiles, and various patterns of self-sustained oscillations termed electric pulsation. Some patterns of the electrostatic structure are found to be quite important for fusion application owing to their association with transport barrier formation. It is confirmed, as is shown in several tokamak experiments, that the thermal transport barrier is linked with electrostatic structure through the radial electric field shear that can reduce the fluctuation resulting in anomalous transport. This article describes in detail spatio-temporal evolution during self-sust...

/pdf/experimental-study-of-the-bifurcation-nature-of-the-2qb5stw53x.pdf

Experimental study of the bifurcation nature of the electrostatic potential of a toroidal helical plasma

Turbulence and zonal flow at a transport barrier are studied with twin heavy ion beam probes in a toroidal helical plasma. A wavelet analysis is used to extract turbulence properties, e.g. spectra of both density and potential fluctuations, the coherence and the phase between them and the dispersion relation. Particle transport estimated from the fundamental characteristics is found to clearly rise with their intermittent activities after the barrier is broken down. Time-dependent analysis reveals that the intermittency of turbulence is correlated with the evolution of the stationary zonal flow.

Turbulence and Transport Characteristics of a Barrier in a Toroidal Plasma

A. Fujisawa, K. Itoh, H. Iguchi, K. Matsuoka, S. Okamura, A. Shimizu, T. Minami, Y. Yoshimura, K. Nagaoka, C. Takahashi, M. Kojima, H. Nakano, S. Ohshima, S. Nishimura, M. Isobe, C. Suzuki, T. Akiyama, K. Ida, K. Toi, S.-I. Itoh and P. H. Diamond National Institute for Fusion Science, Oroshi-cho Toki, Japan RIAM, Kyushu University, Kasuga 816-8580 Japan University of California, San Diego, La Jolla, California, 92093-0319 USA

Experimental Identification of Zonal Flows in CHS

A new kind of oscillatory steady state is discovered in observation of potential with a heavy ion beam probe in Compact Helical System Heliotron/Torsatron. Bulk plasma parameters, such as electron temperature and density profile, change being synchronized with the pulsation of potential. The phenomenon can be regarded as successive transitions between two bifurcative states of the plasma. The pulsation can be self-sustained and create a dynamic steady state in low density plasma with electron cyclotron heating. The cause of phenomenon is associated with the bifurcation nature of radial electric field, that is inherent with toroidal helical plasmas. This paper presents two examples of the phenomenon in different density regimes. Dependence of pulsation characteristics on several parameters is described. The bifurcation property predicted by a neoclassical theory is presented for comparison with the experimental observations.

/pdf/dynamic-behavior-associated-with-electric-field-transitions-28u8i1uwc1.pdf

Dynamic Behavior Associated with Electric Field Transitions in CHS Heliotron/Torsatron

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Papers

Experimental study of the bifurcation nature of the electrostatic potential of a toroidal helical plasma

Turbulence and Transport Characteristics of a Barrier in a Toroidal Plasma

Experimental Identification of Zonal Flows in CHS

Dynamic Behavior Associated with Electric Field Transitions in CHS Heliotron/Torsatron