Zonal flows in plasma—a review

TLDR: A comprehensive review of zonal flow phenomena in plasmas is presented in this article, where the focus is on zonal flows generated by drift waves and the back-interaction of ZF on the drift waves, and various feedback loops by which the system regulates and organizes itself.

Abstract: 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.

Figures

Table 3.4.3: Comparison of Stochastic Dynamics ______________________________________________________________________ Particles in Electrostatic Drift Wave in

Fig. 7.2 Spectra measured with the modified forked probe. Peaks of zonal flow and ambient turbulence (AT) are shown. (a) Auto power spectrum of V!1 ( !r = – 0.2 cm ). (b) Auto power spectrum of V!2 ( !r = – 1.2 cm ). (c) Cross power spectrum. (d) Coherency spectrum. (e) Wave number spectrum. (c), (d). and (e) were calculated from the long distance correlation between V!1 and V!2 . [7.19]

Fig. 3.4.1 The contrast of the linear view of the GKH modes (a) to a more general case where GKH modes are generated by both linear and nonlinear modulational instabilities (b). The linear view is hierarchical in that GKH is generated by the linear instability of zonal flows (ZF), which are already generated by DW. In general, GKH modes can, however, be generated directly from DW by modulational instability.

Table 3.4.3: Comparison of Stochastic Dynamics ______________________________________________________________________ Particles in Electrostatic Drift Wave in

Table B.1 Hierarchy of governing equations

Table 1.1. Comparison between zonal flow in plasmas, dynamo, electromagnetic (EM) flow generation and flow structure formation.

Frequently asked questions

Q1. What are the contributions in this paper?

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 implications of zonal flow phenomena for confinement in, and the phenomena of fusion devices are discussed. This review article is dedicated to the memory of Professor. 

Q2. What are the future works in this paper?

And theory After a summary ( not exhaustive ) of the recent experimental progress in pursuing the measurements of zonal flows, the authors discuss some future experimental plans and possibilities for further progress and list key physics information which future experiments will need from numerical simulations and theories for the identification of zonal flows. These difficulties must be overcome in the future, because the understanding of the drift wavezonal flow turbulence is a crucial element of the understanding of anomalous transport. Future progress on CHS experiments are promising, and will play a central role for the experimental study of zonal flow in core plasmas. This process can be extended to electromagnetic fluctuations in high ! 

Q3. Why are zonal flows not subject to Landau damping?

On account of their symmetry, zonal flows cannot access expansion free energy stored in temperature, density gradients, etc., and are not subject to Landau damping. 

Q4. What is the simplest way to describe the rate of amplification of zonal flows?

Considerations of energetics, in the quasi-linear approximation [2.12-2.13], are then used to describe and calculate the rate of amplification of zonal shears by turbulence. 

Q5. What mechanism can be used to stimulate the growth of sheared electric fields?

While many mechanism can act to trigger and stimulate the growth of sheared electric fields (i.e. profile evolution and transport bifurcation, neoclassical effects, external momentum injection, etc.) certainly one possibility is via the self-generation and amplification of E! 

Q6. What is the effect of the perturbation-driven torque on the flow velocity at the rational surface?

Wakatani showed that the perturbation-driven torque (divergence of the Reynolds-Maxwell stress) tends to decelerate the flow velocity at the rational surface. 

Q7. What is the effect of the collisional damping of zonal flows?

This is a simple consequence of self-regulation – flows damp the drift waves and collisions damp the flows, so collisions (more generally, zonal flow damping) ultimately regulate the turbulence. 

Q8. What is the relationship between zonal flow and the inverse transfer of fluid energy?

Zonal field generation is, simply put, related to the inverse transfer of magnetic flux while zonal flow generation is related to the inverse transfer of fluid energy. 

Q9. What is the rate of increment of the turbulence energy and that of flow energy?

As is explained in §3.5, the rate of increment of the turbulence energy and that of flow energy are dependent on the nonlinear saturation mechanism for the zonal flow. 

Q10. What is the difference between zonal flows and global gyrokinetic simulations?

Since the long wavelength components of zonal flows are more prominent in global gyrokinetic simulations, as compared to the flux-tube gyrofluid simulations, one can speculate that the higher value of steady state ion thermal diffusivity typically observed in gyrofluid simulation (in comparison to that seen in gyrokinetic simulation) is partially due to an underestimation of the low k r component of the zonal flows.