A review of theories of the L-H transition

Connor, J. W.; Wilson, H. R.

doi:10.1088/0741-3335/42/1/201

Cited by 310 publications

(346 citation statements)

References 186 publications

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“…The transition between states of low (L) plasma confinement to the high (H) confinement regime featuring such an edge transport barrier is up to now not satisfactorily described by any of the existing first-principle theories [36]. The notion that generation of zonal flows by direct drive of the turbulence can act to self-regulate by suppressing the driving turbulent vortices has lead to the development of predator-prey type bifurcation models that are able to describe specific characteristics of the L-H transition (see e.g.…”

Section: The Role Of Sheared Flows In Tokamak Turbulencementioning

confidence: 99%

Flux-surface shaping effects on tokamak edge turbulence and flows

Kendl

Scott

2006

Physics of Plasmas

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Shaping of magnetic flux surfaces is found to have a strong impact on turbulence and transport in tokamak edge plasmas. A series of axisymmetric equilibria with varying elongation and triangularity, and a divertor configuration are implemented into a computational gyrofluid turbulence model. The mechanisms of shaping effects on turbulence and flows are identified. Transport is mainly reduced by local magnetic shearing and an enhancement of zonal shear flows induced by elongation and X-point shaping.

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Section: The Role Of Sheared Flows In Tokamak Turbulencementioning

confidence: 99%

Flux-surface shaping effects on tokamak edge turbulence and flows

Kendl

Scott

2006

Physics of Plasmas

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“…introduced a particular system of two coupled ODE's for density fluctuation level and flow shear that exhibited a plausible bifurcation. Considerable research has been expended on the physics of the transition; recent reviews are by Burrell (1997) and Connor and Wilson (2000). Spatschek (1999) emphasized the general importance of low-dimensional descriptions and provided many references.…”

Section: L-h Transitionsmentioning

confidence: 99%

Fundamental statistical descriptions of plasma turbulence in magnetic fields

Krommes¹

2002

Physics Reports

260

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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“…Yet, the transition mechanism from the low ͑L͒ to high ͑H͒ confinement mode is not fully understood. [2][3][4][5][6] There are transport models, which are instrumental in furthering our understanding of the transition. However, because of the complexity of transition phenomenon, they tend to be increasingly, if not excessively, detailed.…”

Section: Introductionmentioning

confidence: 99%

Weak hysteresis in a simplified model of the L-H transition

Malkov

Diamond

2009

Physics of Plasmas

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A simple one-field L-H transition model is studied in detail, analytically and numerically. The dynamical system consists of three equations coupling the drift wave turbulence level, zonal flow speed, and the pressure gradient. The fourth component, i.e., the mean shear velocity, is slaved to the pressure gradient. Bursting behavior, characteristic for predator-prey models of the drift wavezonal flow interaction, is recovered near the transition to the quiescent H-mode ͑QH͒ and occurs as strongly nonlinear relaxation oscillations. The latter, in turn, arise as a result of Hopf bifurcation ͑limit cycle͒ of an intermediate fixed point ͑between the L-and H-modes͒. The system is shown to remain at the QH-mode fixed point even after the heating rate is decreased below the bifurcation point ͑i.e., hysteresis, subcritical bifurcation͒, but the basin of attraction of the QH-mode shrinks rapidly with decreasing power. This suggests that the hysteresis in the H-L transition may be less than that expected from S-curve models. Nevertheless, it is demonstrated that by shaping the heating rate temporal profile, one can reduce the average power required for the transition to the QH-mode.

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A review of theories of the L-H transition

Cited by 310 publications

References 186 publications

Flux-surface shaping effects on tokamak edge turbulence and flows

Flux-surface shaping effects on tokamak edge turbulence and flows

Fundamental statistical descriptions of plasma turbulence in magnetic fields

Weak hysteresis in a simplified model of the L-H transition

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