Status of global energy confinement studies

Kaye, S. M.; Barnes, Cris W.; Bell, M.G.; DeBoo, J. C.; Greenwald, M.; Riedel, Kurt S.; Sigmar, D. J.; Uckan, N. A.; Waltz, R. E.

doi:10.1063/1.859578

Cited by 53 publications

(47 citation statements)

References 27 publications

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“…It has been recognized that the nature of the cross-field transport through the SOL is dominated by turbulence with a significant ballistic or non-local component where a diffusive description is improper [2]. Moreover, the scaling of the confinement time τ ∝ L α with α < 2 [3] is typical in low-confinement mode discharges, instead of the diffusion induced result…”

Section: Introductionmentioning

confidence: 99%

A theory of non-local linear drift wave transport

Moradi

Anderson²,

Weyssow³

2011

Physics of Plasmas

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Transport events in turbulent tokamak plasmas often exhibit non-local or non-diffusive action at a distance features that so far have eluded a conclusive theoretical description. In this paper a theory of non-local transport is investigated through a Fokker-Planck equation with fractional velocity derivatives. A dispersion relation for density gradient driven linear drift modes is derived including the effects of the fractional velocity derivative in the Fokker-Planck equation. It is found that a small deviation (a few percent) from the Maxwellian distribution function alters the dispersion relation such that the growth rates are substantially increased and thereby may cause enhanced levels of transport.

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Section: Introductionmentioning

confidence: 99%

A theory of non-local linear drift wave transport

Moradi

Anderson²,

Weyssow³

2011

Physics of Plasmas

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“…To date, the overwhelmingly dominant practical application of plasma physics has been controlled thermonuclear fusion research (CTR). The extreme practical complexity of magnetic confinement devices such as the tokamak (Sheffield, 1994) has inevitably led to a predominance of engineering ("mixinglength") estimates of "anomalous" 7 transport, confinement scaling laws based on statistical analyses of experimental data (Kaye, 1985;Kaye et al, 1990), etc. Many analogies can be drawn to practical applications of neutral-fluid turbulence-statistical closure theory is hopelessly inadequate for the detailed quantitative design of aircraft, for example.…”

Section: Fundamental Physics Vs Practical Engineeringmentioning

confidence: 99%

Fundamental statistical descriptions of plasma turbulence in magnetic fields

Krommes¹

2002

Physics Reports

261

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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“…(1) to convert expressions like the ones presented above into functions of _ and W_t. First, consider a single power law scaling Since scaling expressions are based upon nearly steady state data [18] for which dWu,Jdt << Pi,,, the energy and power forms fit the database equally well. Hence, there are no empirical reasons to choose one over the other.…”

Section: Energ3" Confinement Time Formulasmentioning

confidence: 99%

“…[17,18] Such expressions should be capable of describing the confinement behavior for all heating regimes. In this case, we take the minimum with "roll solely in order to obtain reasonable behavior in regimes where _e would not expect r_ to be accurate [for example, when the net input power P_ _ 0; P_,_is defined in Eq.…”

Section: Energ3" Confinement Time Formulasmentioning

confidence: 99%

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ASPECT: An advanced specified-profile evaluation code for tokamaks

Stotler¹,

Reiersen²,

Bateman³

1993

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•A specified-profile, global analysis code has been developed to evaluate the performance of fusion reactor designs. Both steady-state and time-dependent calculations are carried out; the results of the former can be used in defining the parameters of the latter, if desired. In the steady-state analysis, the performance is computed at a density and temperature chosen to be consistent with input limits (e.g., density and beta) of several varieties. The calculation can be made at either the intersection of the two limits or at the point of optimum performance as the density and temperature are varied along the limiting boundaries. Two measures of performance are available for this purpose: the ignition margin or the confinement level required to achieve a prescrib.ed ignition margin. The time-dependent calculation can be configured to yield either the evolution of plasma energy as a function of time or, via an iteration scheme, the amount of auxiliary power required to achieve a desired final plasma energy. Number of bits in a word: 64Number of processors used: 1 Peripheral used: disk Number of lines in distributed program: 7923Keywords: thermonuclear fusion, tokamak reactor, specified-profile transport Nature of physical problemThe purpose of this code is to provide a quick, if largely empirical, assessment of the performance of a tokamak fusion reactor [1,2]. ASPECT first performs a steady-state analysis at a point irl the density -temperature operating space determined according to a set of user-specified criteria. The code then carries out a time-dependent calculation which can be used to address, for example, auxiliary heating requirements and helium ash buildup. Method of solutionFor the steady-state portion of the calculation, the individual terms in the global power balance equation are estimated using user-specified radial plasmaprofiles. An expression for the energy confinement time is required; a number of popular forms are included in the code. The power balance equation is solved using a Brent algorithm subroutine [3]. The reactor performance is quantified using either the ignition margin parameter or the level of confinement required to achieve a specified ignition margin.For the time-.dependent calculation, the tempor__l variation of the device parameters, the relative plasma density, and the relative auxiliary power must be input. A feedback procedure for limiting the total heating power in the plasma is available. Helium ash accumulation can be included with an adjustable global confinement time. The time-dependent global plasma evolution equations are integrated using Hindmarsh's LSODE algorithm [4]; this yields the plasma energy as a function of time. The integration can be iterated (via the Brent algorithm subroutine [3]) to determine the level of auxiliary input power required to reach a specific plasma energy at a certain time.Restrictions on the complexity of the problem Although ASPECT is designed for use with tokamak reactors, it should be • applicable to any toroidal reactor dev...

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Status of global energy confinement studies

Cited by 53 publications

References 27 publications

A theory of non-local linear drift wave transport

A theory of non-local linear drift wave transport

Fundamental statistical descriptions of plasma turbulence in magnetic fields

ASPECT: An advanced specified-profile evaluation code for tokamaks

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