Nonlinear wave effects in laboratory plasmas: A comparison between theory and experiment

Porkoláb, M.; Chang, Robert P. H.

doi:10.1103/revmodphys.50.745

Cited by 123 publications

(52 citation statements)

References 230 publications

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“…A very incomplete list of early references on weak plasma turbulence theory includes Rogister andOberman (1968, 1969), Sagdeev and Galeev (1969), Davidson (1972), Tsytovich (1977, and Galeev and Sagdeev (1979). The review by Porkolab and Chang (1978) of nonlinear plasma wave effects covers WTT, including experimental verifications. A recent treatise on the general weak-turbulence problem is by .…”

Section: Self-consistent Quasilinear Theorymentioning

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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Section: Self-consistent Quasilinear Theorymentioning

confidence: 99%

Fundamental statistical descriptions of plasma turbulence in magnetic fields

Krommes¹

2002

Physics Reports

260

397

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“…The daughter waves in the present work will either be hot ion plasma waves at the lower sideband ω 2 = (ω 0 -ω), (an ensemble of ion Bernstein waves propagating through high cyclotron harmonic frequencies nearly perpendicular to the weakly inhomogeneous magnetic field), and ion cyclotron quasi-modes (heavily cyclotron damped electrostatic response of the plasma near the beat frequency, (ω 0 -ω 2 ) = nΩ i , where n is an integer and Ω i is the angular ion cyclotron frequency ) [5,10]. The selection rules in the dipole approximation reduce to k 1 = -k 2 and this greatly simplifies the theory which then can be derived even for relatively large amplitude pump electric fields [ 5,6,11].…”

Section: Parametric Instabilities In the Lower Hybrid Range Of Frequementioning

confidence: 99%

Parametric Instabilities During High Power Helicon Wave Injection on DIII-D

Porkoláb

Pinsker

2017

EPJ Web Conf.

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Abstract. High power helicon (whistler) waves at a frequency of 0.47 GHz are being considered for efficient off-axis current generation in high performance DIII-D plasmas and in K-Star [3]. The need for deploying helicon waves for current profile control has been noted in previous publications since penetration to the core of reactor grade plasmas is easier than with lower hybrid slow waves (LHCD) which suffer from accessibility limitations and strong electron Landau absorption in fusion grade high temperature plasmas. In this work we show that under typical experimental conditions in present day tokamaks with 1 MW of RF power coupled per antenna, the associated perpendicular electric fields of the order of 40 kV/m can drive strong parametric decay instabilities near the lower hybrid layer. The EXB and polarization drift velocities which are the dominant driver of the PDI can be comparable to the speed of sound in the outer plasma layers, a key measure of driving PDI instabilities. Here we calculate growth rates and convective thresholds for PDIs, and we find that decay waves into hot ion lower hybrid waves and ion cyclotron quasi modes dominate in the vicinity of the lower hybrid layer, possibly leading to pump depletion. Such instabilities in future reactor grade high temperature plasmas are less likely.

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“…The accelerator physicists have pointed out the need of developing diagnostic tools to measure the noise level in the beam. The echo effect, first discovered in spin systems [1], and subsequently observed in solids [2] and in plasmas [3], [4], [5], [6] is a signature of coherence in a filamented phase space distribution and it is very sensitive to the noise. Therefore it can be used to detect the presence of noise in a beam and to measure its level if the relation with the echo amplitude is known.…”

Section: Introductionmentioning

confidence: 99%

Hamiltonian dynamics with a weak noise and the echo effect for the rotator model

Turchetti¹,

Bassi²,

Bazzani³

et al. 2006

J. Phys. A: Math. Gen.

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We analyze the effect of a weak noise on the Hamiltonian transport from the analytical and numerical viewpoint. A solvable model, the noisy rotator, is proposed to illustrate the basic phenomena. In the absence of noise, the phase space evolution is a shear flow, whose angular correlations decay following a power law, which depends on the smoothness of the initial action distribution. If the action has a fluctuating component, given by a Wiener process, then the angular correlations decay exponentially according to e − 2 t 3 /6 or faster, where is the noise amplitude. The echo effect is well suited to investigate the competition between the decorrelation due to filamentation and noise. The noisy rotator model allows an exhaustive analytical investigation of the process for a wide class of initial conditions and a generic disturbance. The echo time is proportional to the delay τ of the disturbance and its amplitude is proportional to λτ where λ is the amplitude of the disturbance. The noise reduces the echo amplitude by e −c 2 τ 3 , where c depends on the Fourier components of the initial angular distribution, and of the disturbance applied at time τ . The analytical results, derived in the limit λ → 0, τ → ∞, with λτ finite and sufficiently small to justify a first order expansion, are checked numerically. For more realistic models the analytical procedure would provide qualitative results and scaling laws. Quantitative results are obtained by solving the Fokker-Planck equation with a numerical scheme based on splitting: back propagation and biquadratic interpolation for the integrable part, implicit finite difference scheme for the noise component. The application to a noisy pendulum describing the longitudinal dynamics in a particle accelerator is considered, and we determine the value of the noise amplitude , below which the echo cannot be detected.

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Nonlinear wave effects in laboratory plasmas: A comparison between theory and experiment

Cited by 123 publications

References 230 publications

Fundamental statistical descriptions of plasma turbulence in magnetic fields

Fundamental statistical descriptions of plasma turbulence in magnetic fields

Parametric Instabilities During High Power Helicon Wave Injection on DIII-D

Hamiltonian dynamics with a weak noise and the echo effect for the rotator model

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