Plasma Edge Turbulence

Hasegawa, Akira; Wakatani, Masahiro

doi:10.1103/physrevlett.50.682

Cited by 423 publications

(386 citation statements)

References 11 publications

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“…Moreover, the calculation in Ref. 6 has indicated that the steadystate particle flux is linearly proportional to ion viscosity. Thus, the particle flux vanishes when ion viscosity is absent.…”

Section: Discussionmentioning

confidence: 99%

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Nonlinear evolution of drift instabilities in the presence of collisions

Federici

Lee

Tang

1987

The Physics of Fluids

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PPPL-2354 DE86 013642Nonlinear evolution of drift instabilities in the presence of electron-ion collisions in a shear-free slab has been studied by using gyrokinetic particle simulation tech niques as well as by solving, both numerically and analytically, model mode-coupling equations. The purpose of the investigation is to determine the mechanisms respon sible for the nonlinear saturation of the instability and for the ensuing steady-state transport. Such an insight is very valuable for understanding drift wave problems in more complicated geometries. The results indicate that the electron E x B convection is the dominant mechanism for saturation. It is also found that the saturation amplitude and the associated quasilinear diffusion are greatly enhanced over their collisionless values as a result of weak collisions. In the highly collisional (fluid) limit, there is an upper bound for saturation with e/T e ~ (<^i/tti)/(k±p,) 2 .The associated quasilinear diffusion, which increases with collisionality, takes the form of D q i ~ -yi/k±, where u>; and 7; are the linear frequency and growth rate, re spectively. In the steady state, the diffusion process becomes stochastic in nature.The relevant mechanisms here are related to the velocity-space nonlinearities and DISTRIBUTION OF THIS DOCUMENT IS UNLIMITED background fluctuations. The magnitude of the diffusion at this stage can be com parable to that of quasilinear diffision in the presance of collisions, and it remains finite even in the collisionless limit.

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Section: Discussionmentioning

confidence: 99%

“…These potentially important nonlinear mechanisms have generally been ignored in tlie confinement studies for tokamaks. The recent progress made in modelling microinstabilities in the edge region 6 '" affords us an opportunity to assess the relevancy of these nonlinear interactions when the collisions are present.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear evolution of drift instabilities in the presence of collisions

Federici

Lee

Tang

1987

The Physics of Fluids

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“…In more sophisticated fluid models, dissipative processes enter more naturally. One such model was developed by Hasegawa and Wakatani (1983) and Wakatani and Hasegawa (1984), who considered nonadiabatic response due to electron-ion collisions.…”

Section: Hasegawa-wakatani Equationsmentioning

confidence: 99%

Fundamental statistical descriptions of plasma turbulence in magnetic fields

Krommes¹

2002

Physics Reports

266

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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“…To understand the characteristics of the nonlinear interactions in our MEDV turbulence model, it is interesting to compare it with that of the Hasegawa-MimaWakatani (HMW) model [14,15,16,17] describing the electrostatic drift waves in an inhomogeneous magnetoplasma. For instance, the generalized magnetic field vorticity is driven byẑ × ∇B · ∇∇ 2 B nonlinearity.…”

Section: Simulation Resultsmentioning

confidence: 99%

Simulations of two-dimensional magnetic electron drift vortex mode turbulence in plasmas

Shaikh¹,

Shukła²

2009

J. Plasma Phys.

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Abstract. Simulations are performed to investigate turbulent properties of nonlinearly interacting two-dimensional (2D) magnetic electron drift vortex (MEDV) modes in a nonuniform unmagnetized plasma. The relevant nonlinear equations governing the dynamics of the MEDV modes are the wave magnetic field and electron temperature perturbations in the presence of the equilibrium density and temperature gradients. The important nonlinearities come from the advection of the electron fluid velocity perturbation and the electron temperature, as well as from the nonlinear electron Lorentz force. Computer simulations of the governing equations for the nonlinear MEDV modes reveal the generation of streamer-like electron flows, such that the corresponding gradients in the direction of the inhomogeneities tend to flatten out. By contrast, the gradients in an orthogonal direction vary rapidly. Consequently, the inertial range energy spectrum in decaying MEDV mode turbulence exhibits a much steeper anisotropic spectral index. The magnetic structures in the MEDV mode turbulence produce nonthermal electron transport in our nonuniform plasma.

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Plasma Edge Turbulence

Cited by 423 publications

References 11 publications

Nonlinear evolution of drift instabilities in the presence of collisions

Nonlinear evolution of drift instabilities in the presence of collisions

Fundamental statistical descriptions of plasma turbulence in magnetic fields

Simulations of two-dimensional magnetic electron drift vortex mode turbulence in plasmas

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