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.

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Zonal flows in plasma—a review

The understanding and predictive capability of transport physics and plasma confinement is reviewed from the perspective of achieving reactor-scale burning plasmas in the ITER tokamak, for both core and edge plasma regions. Very considerable progress has been made in understanding, controlling and predicting tokamak transport across a wide variety of plasma conditions and regimes since the publication of the ITER Physics Basis (IPB) document (1999 Nucl. Fusion 39 2137-2664). Major areas of progress considered here follow. (1) Substantial improvement in the physics content, capability and reliability of transport simulation and modelling codes, leading to much increased theory/experiment interaction as these codes are increasingly used to interpret and predict experiment. (2) Remarkable progress has been made in developing and understanding regimes of improved core confinement. Internal transport barriers and other forms of reduced core transport are now routinely obtained in all the leading tokamak devices worldwide. (3) The importance of controlling the H-mode edge pedestal is now generally recognized. Substantial progress has been made in extending high confinement H-mode operation to the Greenwald density, the demonstration of Type I ELM mitigation and control techniques and systematic explanation of Type I ELM stability. Theory-based predictive capability has also shown progress by integrating the plasma and neutral transport with MHD stability. (4) Transport projections to ITER are now made using three complementary approaches: empirical or global scaling, theory-based transport modelling and dimensionless parameter scaling (previously, empirical scaling was the dominant approach). For the ITER base case or the reference scenario of conventional ELMy H-mode operation, all three techniques predict that ITER will have sufficient confinement to meet its design target of Q = 10 operation, within similar uncertainties.

https://iopscience.iop.org/article/10.1088/0029-5515/47/6/S02/pdf

Chapter 2: Plasma confinement and transport

The use of the compressional hydromagnetic mode (also called the magnetosonic or, simply, the fast wave) is examined in some detail with respect to the heating of a tritium plasma containing a few percent deuterium. Efficient absorption of wave energy by the deuteron component is found when ω = ωC (deuterons), with Qwave 100. Reasonable efficiencies are found also for electron heating, but coherence effects between transit-time and Landau damping for electrons reduce the total absorption for both processes to one-half of the transit-time power, calculated separately.The fusion output of a two-component neutral-injected plasma can be enhanced by selective heating of the injected deuterons. Also, selective deuteron absorption may be used for ion-tail creation by radiofrequency excitation alone, as an alternative to neutral injection. The dominant behaviour of the high-energy deuteron distribution function is found to be f(v) ~ exp[(3/2)∫vdv / ], where is the Chandrasekhar-Spitzer drag coefficient, and is the Kennel-Engelmann quasi-linear diffusion coefficient for wave-particle interaction at the deuteron cyclotron frequency. An analytic solution to the one-dimensional Fokker-Planck equation, with r.f.-induced diffusion, is developed, and using this solution together with Duane's fit to the D-T fusion cross-section, it is found that the nuclear-fusion power output from an r.f.-produced two-component plasma can significantly exceed the incremental (radiofrequency) power input.

Fast-wave heating of a two-component plasma

In addition to the operational limits imposed by MHD stability on plasma current and pressure, an independent limit on plasma density is observed in confined toroidal plasmas. This review attempts to summarize recent work on the phenomenology and physics of the density limit. Perhaps the most surprising result is that all of the toroidal confinement devices considered operate in similar ranges of (suitably normalized) densities. The empirical scalings derived independently for tokamaks and reversed-field pinches are essentially identical, while stellarators appear to operate at somewhat higher densities with a different scaling. Dedicated density limit experiments have not been carried out for spheromaks and field-reversed configurations, however, `optimized' discharges in these devices are also well characterized by the same empirical law. In tokamaks, where the most extensive studies have been conducted, there is strong evidence linking the limit to physics near the plasma boundary: thus, it is possible to extend the operational range for line-averaged density by operating with peaked density profiles. Additional particles in the plasma core apparently have no effect on density limit physics. While there is no widely accepted, first principles model for the density limit, research in this area has focussed on mechanisms which lead to strong edge cooling. Theoretical work has concentrated on the consequences of increased impurity radiation which may dominate power balance at high densities and low temperatures. These theories are not entirely satisfactory as they require assumptions about edge transport and make predictions for power and impurity scaling that may not be consistent with experimental results. A separate thread of research looks for the cause in collisionality enhanced turbulent transport. While there is experimental and theoretical support for this approach, understanding of the underlying mechanisms is only at a rudimentary stage and no predictive capability is yet available.

https://iopscience.iop.org/article/10.1088/0741-3335/44/8/201/pdf

Density limits in toroidal plasmas

The paper is a review of investigations of the H-mode on ASDEX performed since its discovery in 1982. The topics discussed are: (1) the development of the plasma profiles, with steep gradients in the edge region and flat profiles in the bulk plasma, (2) the MHD properties resulting from the profile changes, including an extensive stability analysis, (3) the impurity development, with special emphasis on the MHD aspects and on neoclassical impurity transport effects in quiescent H-phases, and (4) the properties of the edge plasma, including the evidence of threedimensional distortions at the edge. The part on confinement includes scaling studies and the results of transport analysis. The power threshold of the H-mode is found to depend weakly on the density, but there is probably no dependence on the toroidal field or the current. For the operational range of the H-mode, new results for the limiter H-mode on ASDEX and the development of the H-mode under beam current drive conditions are included. A number of experiments are described which demonstrate the crucial role of the edge electron temperature in the L-H transition. New results of magnetic and density fluctuation studies at the plasma edge within the edge transport barrier are presented. Finally, the findings on ASDEX are compared with results obtained on other machines and are used to test various H-mode theories.

https://iopscience.iop.org/article/10.1088/0029-5515/29/11/010/pdf

The H-Mode of ASDEX

A new model of $L$- to $H$-mode transition in tokamak plasmas is presented. Nonambipolar particle losses determine the consistent radial electric field near plasma periphery. A "cusp-type catastrophe" among the radial electric field, particle flux, and edge gradients is found. At the transition, plasma loss can take multiple values for one profile of density and temperature near the edge. A critical edge condition for the transition is obtained.

Model of L- to H-mode transition in tokamak.

The paper presents a theoretical model of the H-mode in tokamaks which is based on the bifurcation of the radial electric field at the plasma edge. The electric field is determined by the balance of the non-ambipolar fluxes of ions and electrons at the edge. It is found that bifurcations of the radial electric field, the particle flux and the convective energy loss occur when the edge gradient reaches a critical value. This is attributed to L-H or H-L transition. The critical conditions are examined and the role of neutral particles as well as the effect of impurities are incorporated in the model. Combining the confinement scaling laws for both the core plasma and the scrape-off layer plasma, the threshold power for the transition is derived. The temporal evolution associated with the transition is studied.

https://iopscience.iop.org/article/10.1088/0029-5515/29/6/013/pdf

Model of the H-mode in tokamaks

Characteristics of MHD instabilities and their impacts on plasma confinement are studied in current free plasmas of the Large Helical Device. Spontaneous L?H transition is often observed in high beta plasmas close to 2% at low toroidal fields (Bt ? 0.75?T). The stored energy starts to rise rapidly just after the transition accompanying the clear rise in the electron density but quickly saturates due to the growth of the m = 2/n = 3 mode (m and n: poloidal and toroidal mode numbers), the rational surface of which is located in the edge barrier region, and edge localized mode (ELM) like activities having fairly small amplitude but high repetition frequency. Even in low beta plasmas without L?H transitions, ELM-like activities are sometimes induced in high performance plasmas with a steep edge pressure gradient and transiently reduce the stored energy up to 10%. Energetic ion driven MHD modes such as Alfv?n eigenmodes (AEs) are studied in a very wide range of characteristic parameters (the averaged beta of energetic ions, ?b?, and the ratio of energetic ion velocity to the Alfv?n velocity, Vb?/VA), of which range includes all tokamak data. In addition to the observation of toroidicity induced AEs (TAEs), coherent magnetic fluctuations of helicity induced AEs (HAEs) have been detected for the first time in NBI heated plasmas. The transition of a core-localized TAE to a global AE (GAE) is also observed in a discharge with temporal evolution of the rotational transform profile, having a similarity to the phenomenon observed in a reversed shear tokamak. At low magnetic fields, bursting TAEs transiently induce a significant loss of energetic ions, up to 40% of injected beams, but on the other hand play an important role in triggering the formation of transport barriers in the core and edge regions.

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MHD instabilities and their effects on plasma confinement in Large Helical Device plasmas

Propagation and absorption of waves in the ion cyclotron range of frequencies (ICRF) are investigated using the kinetic theory in a high-temperature plasma The wave equation which includes kinetic effects (such as finite-gyroradius effect and wave/particle interactions) is solved as a boundary-value problem for a two-ion-component plasma (majority deuterium and minority hydrogen) with one-dimensional inhomogeneities The global structure of the wave field and the absorption mechanism are explained The power deposition profile for each plasma species and the coupling to the antenna are obtained The mode conversion of the fast wave to the ion Bernstein wave is associated with the two-ion hybrid resonance, and the latter is absorbed by electrons and deuterons via Landau damping and collisional damping, respectively Protons absorb the wave which tunnels through the cut-off layer (for strong-field-side excitations) by cyclotron damping The existence of cavity resonances is also confirmed; these considerably influence the energy absorption

Kimitaka Itoh

Papers

Model of L- to H-mode transition in tokamak.

Model of the H-mode in tokamaks

MHD instabilities and their effects on plasma confinement in Large Helical Device plasmas

Kinetic description of propagation and absorption structures of icrf waves

Plasma and Fluid Turbulence: Theory and Modelling : Theory and Modelling