On the route to a better understanding of the complex nonlinear dynamics of a plasma

Spatschek, K. H.

doi:10.1088/0741-3335/41/3a/007

Cited by 4 publications

(2 citation statements)

References 107 publications

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“…via terms ∼ (k 2 x − k 2 y ), etc. The system of equations (6.4.2a)-(6.4.2c) constitutes the set of envelope equations for the drift wave-zonal flow system, including the more general case of drift wave-convective cell systems [344][345][346][347][348][349].…”

Section: − 2iω Pementioning

confidence: 99%

Zonal flows in plasma—a review

Diamond

Itoh

et al. 2005

Plasma Phys. Control. Fusion

1,806

2,123

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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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Section: − 2iω Pementioning

confidence: 99%

Zonal flows in plasma—a review

Diamond

Itoh

et al. 2005

Plasma Phys. Control. Fusion

1,806

2,123

View full text Add to dashboard Cite

show abstract

“…Complex dynamics among fluctuations of different scale lengths is observed [516]. A survey of plasma turbulence from a complementary viewpoint is made in [517].…”

Section: System With Hysteresismentioning

confidence: 99%

Turbulence theories and modelling of fluids and plasmas

Yoshizawa

Itoh

et al. 2001

Plasma Phys. Control. Fusion

102

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Theoretical and heuristic modelling methods are reviewed for studying turbulence phenomena of fluids and plasmas. Emphasis is placed on understanding of effects on turbulence characteristics due to inhomogeneities of field and plasma parameters. The similarity and dissimilarity between the methods for fluids and plasmas are sought in order to shed light on the properties that are shared or not by fluid and plasma turbulence.

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Fundamental statistical descriptions of plasma turbulence in magnetic fields

Krommes¹

2002

Physics Reports

263

397

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A pedagogical review of the historical development and current status (as of early 2000) of systematic statistical theories of plasma turbulence is undertaken. Emphasis is on conceptual foundations and methodology, not practical applications. Particular attention is paid to equations and formalism appropriate to strongly magnetized, fully ionized plasmas. Extensive reference to the literature on neutral-fluid turbulence is made, but the unique properties and problems of plasmas are emphasized throughout. Discussions are given of quasilinear theory, weak-turbulence theory, resonance-broadening theory, and the clump algorithm. Those are developed independently, then shown to be special cases of the direct-interaction approximation (DIA), which provides a central focus for the article. Various methods of renormalized perturbation theory are described, then unified with the aid of the generating-functional formalism of Martin, Siggia, and Rose. A general expression for the renormalized dielectric function is deduced and discussed in detail. Modern approaches such as decimation and PDF methods are described. Derivations of DIA-based Markovian closures are discussed. The eddy-damped quasinormal Markovian closure is shown to be nonrealizable in the presence of waves, and a new realizable Markovian closure is presented. The test-field model and a realizable modification thereof are also summarized. Numerical solutions of various closures for some plasmaphysics paradigms are reviewed. The variational approach to bounds on transport is developed. Miscellaneous topics include Onsager symmetries for turbulence, the interpretation of entropy balances for both kinetic and fluid descriptions, self-organized criticality, statistical interactions between disparate scales, and the roles of both mean and random shear. Appendices are provided on Fourier transform conventions, dimensional and scaling analysis, the derivations of nonlinear gyrokinetic and gyrofluid equations, stochasticity criteria for quasilinear theory, formal aspects of resonance-broadening theory, Novikov's theorem, the treatment of weak inhomogeneity, the derivation of the Vlasov weak-turbulence wave kinetic equation from a fully renormalized description, some features of a code for solving the direct-interaction approximation and related Markovian closures, the details of the solution of the EDQNM closure for a solvable three-wave model, and the notation used in the article.

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On the route to a better understanding of the complex nonlinear dynamics of a plasma

Cited by 4 publications

References 107 publications

Zonal flows in plasma—a review

Zonal flows in plasma—a review

Turbulence theories and modelling of fluids and plasmas

Fundamental statistical descriptions of plasma turbulence in magnetic fields

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