Oscillations and instability of a weakly turbulent plasma

Vedenov, A. A.; Gordeev, A. V.; Rudakov, L. I.

doi:10.1088/0032-1028/9/6/305

Cited by 172 publications

(155 citation statements)

References 1 publication

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“…If we further approximate (k,k·v) ≈ 1, then we must assume that 2[ω pe /(kv T e )] 2 1. This assumption implies that for noneigenmode fluctuations, the wave number range should be restricted to short wavelength regime, k 2 λ 2 De 1.…”

Section: B Particle Kinetic Equation Including Collision Integralmentioning

confidence: 99%

“…, and the ion partial susceptibility for S mode, χ (2) i (k ,σ ω S k |k − k ,0), lend themselves to the well-known approximation, namely,…”

Section: Wave Kinetic Equation Including Collisional Damping and Ementioning

confidence: 99%

“…It is represented by a set of coupled equations that describe the time evolution of particle distribution functions and the time evolution of spectral intensities of the wave modes. The weak turbulence theory was largely developed between the late 1950s and the 1970s [1][2][3][4][5][6][7][8][9][10] and has been used since then in many studies of plasma phenomena, which are ongoing to this date [11][12][13][14][15]. The formal further development of weak turbulence theory was resumed by one of us (P.H.Y.)…”

Section: Introductionmentioning

confidence: 99%

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Weak turbulence theory for collisional plasmas

et al. 2016

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Plasma is an ionized gas in which the collective behavior dominates over the individual particle interactions. For this reason, plasma is often treated as collisionless or collision-free. However, the discrete nature of the particles can be important, and often, the description of plasmas is incomplete without properly taking the discrete particle effects into account. The weak turbulence theory is a perturbative nonlinear theory, whose essential formalism was developed in the late 1950s and 1960s and continued on through the early 1980s. However, the standard material found in the literature does not treat the discrete particle effects and the associated fluctuations emitted spontaneously by thermal particles completely. Plasma particles emit electromagnetic fluctuations in all frequencies and wave vectors, but in the standard literature, the fluctuations are approximately treated by considering only those frequency-wave number regimes corresponding to the eigenmodes (or normal modes) satisfying the dispersion relations, while ignoring contributions from noneigenmodes. The present paper shows that the noneigenmode fluctuations modify the particle kinetic equation so that the generalized equation includes the Balescu-Lénard-Landau collision integral and also modify the wave kinetic equation to include not only the collisional damping term but also a term that depicts the bremsstrahlung emission of plasma normal modes.

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Section: B Particle Kinetic Equation Including Collision Integralmentioning

confidence: 99%

“…, and the ion partial susceptibility for S mode, χ (2) i (k ,σ ω S k |k − k ,0), lend themselves to the well-known approximation, namely,…”

Section: Wave Kinetic Equation Including Collisional Damping and Ementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Weak turbulence theory for collisional plasmas

et al. 2016

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“…The equations describe the resonance (ω pe = kv) interaction of the electron beam with the surrounding plasma via the generation of plasma waves and include plasma inhomogeneity effects (see, e.g. Vedenov et al 1967;Ryutov 1969;Kontar & Pécseli 2002). When the plasma is uniform ∂ω pe (x) ∂x = 0, the stationary solution for the initially unstable beam distribution f (v, t = 0) = g 0 (v), v < v b of the coupled quasi-linear equations is well-known (Vedenov & Velikhov 1963).…”

Section: Quasi-linear Relaxation -Analytical Estimatesmentioning

confidence: 99%

Electron acceleration during three-dimensional relaxation of an electron beam-return current plasma system in a magnetic field

Karlický¹,

Kontar²

2012

A&A

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Aims. We investigate the effects of acceleration during non-linear electron-beam relaxation in magnetized plasma in the case of electron transport in solar flares. Methods. The evolution of electron distribution functions is computed using a three-dimensional particle-in-cell electromagnetic code. Analytical estimations under simplified assumptions are made to provide comparisons. Results. We show that, during the non-linear evolution of the beam-plasma system, the accelerated electron population appears. We found that, although the electron beam loses its energy efficiently to the thermal plasma, a noticeable part of the electron population is accelerated. For model cases with initially monoenergetic beams in uniform plasma, we found that the amount of energy in the accelerated electrons above the injected beam-electron energy varies depending the plasma conditions and could be around 10-30% of the initial beam energy.Conclusions. This type of acceleration could be important for the interpretation of non-thermal electron populations in solar flares. Its neglect could lead to the over-estimation of accelerated electron numbers. The results emphasize that collective plasma effects should not be treated simply as an additional energy-loss mechanism, when hard X-ray emission in solar flares is interpreted, notably in the case of RHESSI data.

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“…Through first order Eqs. Hence, the first order part of the distribution is given by ( 25) Finally, we calculate the current density and charge density. In particular, (29) where the angular brackets and the subscript t 2 denote an average, possibly local, over the variable t 2 .…”

Section: Another Object Of Importance To Hamiltonian Theory Is the Timentioning

confidence: 99%

Ponderomotive effects in collisionless plasma: A Lie transform approach

Cary¹,

Kaufman²

1981

The Physics of Fluids

139

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A new method for the kinetic analysis of ponderomotive effects in collisionless plasma is presented. This method involves the application of the Lie-transform perturbation technique to the Hamiltonian formulation of the Vlasov equation. Basically, a new system, in which the high frequency oscillations are absent, is found. In this system the distribution function evolves according to a ponderomotive Hamiltonian, which is the kinetic generalization of the ponderomotive potential. It is shown that the ponderomotive Hamiltonian can easily be determined from the well-known linear susceptibility. This formalism is used to calculate several new results. Among these results are the general formula for the quasi-static density perturbation produced by a hot magnetoplasma wave, a generalization of previous formulas for the laser-generated quasi-static magnetic field, and the general formula for the ponderomotive gyrofrequency shift produced by an electromagnetic wave propagating at an arbitrary angle.

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Oscillations and instability of a weakly turbulent plasma

Cited by 172 publications

References 1 publication

Weak turbulence theory for collisional plasmas

Weak turbulence theory for collisional plasmas

Electron acceleration during three-dimensional relaxation of an electron beam-return current plasma system in a magnetic field

Ponderomotive effects in collisionless plasma: A Lie transform approach

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