Analytic solution of the Vlasov equation and closed fluid equations

Bendib, K.; Bendib, A.

doi:10.1063/1.873402

Cited by 18 publications

(13 citation statements)

References 14 publications

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“…3 extend those of Ref. 9 to the whole collisionality range. Note that in this work, we have limited our theory to the radiative effects in the motion equation.…”

Section: The Collisionless Contributionsupporting

confidence: 69%

“…9, since we can define the temperature as ␦Tϭ␦T ϩ 1 6 m e (␦v 0 ) 2 , which includes the contribution of the hf field. Thus, the results displayed in Fig.…”

Section: The Collisionless Contributionmentioning

confidence: 99%

“…͑28͒ and ͑29͒, and using the conservative properties of the Krook operator, 9 it results the relations …”

Section: Appendix A: Computation Of the Isotropic Moments V And Wmentioning

confidence: 99%

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Nonlocal radiative forces in fully-ionized plasmas

Tahraoui

Bendib

2000

Physics of Plasmas

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The solution of the Fokker-Planck equation which contains the contribution of high-frequency electric fields is presented. For this, the projection operators of the Krook collision operator and the semicollisional propagator computed with the continued fractions were used. Both elastic and inelastic momentum transfer from the high-frequency electric field to electrons have been considered. The contributions of such high-frequency electric fields to the stress tensor and to the mean change of momentum due to electron-ion collisions are derived in the whole collisionality range. As a result, in the collisionless range, these contributions led to a new force which is 1.6 ͑instead of 4/3͒ more important than the Miller force. In the collisional range, the radiative force due to the inverse bremsstrahlung absorption is recovered and a new contribution which arises from the mean change of momentum due to collisions is found.

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“…3 extend those of Ref. 9 to the whole collisionality range. Note that in this work, we have limited our theory to the radiative effects in the motion equation.…”

Section: The Collisionless Contributionsupporting

confidence: 69%

“…9, since we can define the temperature as ␦Tϭ␦T ϩ 1 6 m e (␦v 0 ) 2 , which includes the contribution of the hf field. Thus, the results displayed in Fig.…”

Section: The Collisionless Contributionmentioning

confidence: 99%

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Nonlocal radiative forces in fully-ionized plasmas

Tahraoui

Bendib

2000

Physics of Plasmas

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“…Our Letter presents the generalization of nonlocal transport theory [1] to time-dependent problems. The published results regarding high-frequency collisional electrostatic perturbations [4][5][6] and the transport formulation of the collisionless plasmas [7] have already used a similar approach in a limited regime of parameters. From transport relations and specifically from the generalized Ohm's law, one finds the plasma dielectric function as shown for different regimes of parameters in Refs.…”

mentioning

confidence: 98%

“…From transport relations and specifically from the generalized Ohm's law, one finds the plasma dielectric function as shown for different regimes of parameters in Refs. [1,[7][8][9]. The dielectric properties of the collisional plasma are constantly being examined [10,11] in the transition region between weakly collisional and Vlasov limits.…”

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confidence: 99%

Kinetic Susceptibility and Transport Theory of Collisional Plasmas

et al. 2004

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A system of nonlocal electron transport equations for electrostatic perturbations in (omega,k) space in a high-Z plasma is derived from the Fokker-Planck equation for arbitrary relations between the time, space, and collisionality scales. The closed scheme for obtaining the longitudinal plasma susceptibility epsilon(omega,k) in the entire (omega,k) plane is proposed. Regions in the (omega,k) plane have been mapped for problems such as the relaxation of the local temperature enhancement with a time-dependent heat conductivity. The electron dielectric permittivity has been calculated over the entire range of parameters, including the transition region between Vlasov and Fokker-Planck equation solutions.

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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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Analytic solution of the Vlasov equation and closed fluid equations

Cited by 18 publications

References 14 publications

Nonlocal radiative forces in fully-ionized plasmas

Nonlocal radiative forces in fully-ionized plasmas

Kinetic Susceptibility and Transport Theory of Collisional Plasmas

Fundamental statistical descriptions of plasma turbulence in magnetic fields

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