Long-wavelength instability of periodic flows and helicon waves in electron magnetohydrodynamics

Lakhin, V. P.; Levchenko, V. D.

doi:10.1134/1.1568144

Cited by 3 publications

(19 citation statements)

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“…The dependence of ␣ on kd e , namely, a change of its sign when k crosses the value 1/d e is similar to the result found in Ref. 38, where in the framework of the dissipative EMHD stability of the helicon maintained by the external force with respect to the large-scale perturbations has been investigated. Equation ͑87͒ has a form which is similar to Eq.…”

Section: ͑86͒supporting

confidence: 59%

On the generation of mean fields by small-scale electron magnetohydrodynamic turbulence

Lakhin

Schep

2004

Physics of Plasmas

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The problem of the generation of mean magnetic fields by small-scale turbulence within the framework of electron magnetohydrodynamics (EMHD) is considered. Two EMHD models are investigated, a two and one-half dimensional (212D) model in which the magnetic field has all three spatial components but, due to a strong external field, depends only on two coordinates, and a fully three-dimensional (3D) model with an imposed stationary and homogeneous magnetic field. It is shown that in the case of 212D turbulence two possible mechanisms are responsible for the generation of mean magnetic fields. The first one is similar to the α-effect in the MHD dynamo problem and is due to a nonzero helicity of the turbulence. The second one is related to the anisotropy of the turbulence, which can give rise to negative dissipation (resistivity, viscosity) of the mean field. The influence of electron inertia on the above effects is analyzed. Inertia results in a qualitative modification of the helicity effects and may lead to a change in sign of the turbulent viscosity. The criteria for the generation of mean magnetic fields are obtained. In the case of the 3D model, the generation of large-scale helicons by the small-scale helicon turbulence is studied within the framework of the adiabatic approximation. A closed set of equations for the evolution of both the magnetic field of the large-scale helicon and of the generalized action of the small-scale turbulence is obtained. The criterion for the resonant instability of a large-scale helicon due to its interaction with small-scale helicon turbulence is obtained.

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Section: ͑86͒supporting

confidence: 59%

On the generation of mean fields by small-scale electron magnetohydrodynamic turbulence

Lakhin

Schep

2004

Physics of Plasmas

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“…Infrared catastrophes, or long-wavelength instabilities (LWI) as they are otherwise known, are ubiquitous in physical phenomena. From Magneto-Hydro-Dynamics [1] to chemical models [2], and from quantum systems [3] to fluid mechanics [4], polymer physics [5] and plasmas [6], large scale modulations may destabilize the system of interest. On the other hand, many of these instabilities (and their thresholds) have been quantified in the context of nonlinear models.…”

Section: Introduction and Setupmentioning

confidence: 99%

Avoiding infrared catastrophes in trapped Bose-Einstein condensates

et al. 2004

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This paper is concerned with the long wavelength instabilities (infrared catastrophes) occurring in Bose-Einstein condensates (BECs). We examine the modulational instability in "cigar-shaped" (1D) attractive BECs and the transverse instability of dark solitons in "pancake" (2D) repulsive BECs. We suggest mechanisms, and give explicit estimates, on how to "engineer" the trapping conditions of the condensate to avoid such instabilities: the main result being that a tight enough trapping potential suppresses the instabilities present in the homogeneous limit. We compare the obtained estimates with numerical results and we highlight the relevant regimes of dynamical behavior.

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“…where k is the component of the wavenumber of perturbation along the background magnetic field and ω i = −τ ω e is the ion drift frequency. In the cold-ion approximation, τ = 0, equation ( 6) describes the coupling between the electron drift-waves and Alfvén waves (Guzdar et al 2001, Lakhin 2003).…”

Section: Description Of Kinetic Drift-alfvén Turbulence With Length S...mentioning

confidence: 99%

“…In the range of plasma pressures by which modern tokamak facilities are characterized, β = 8πp/B 2 > m e /m i , the perturbations of the magnetic field start to play a significant role, and kinetic drift-Alfvén waves can be excited in plasma by some well-known linear mechanism. In previous studies of the generation of zonal flows by the oscillations of drift-Alfvén type, two limiting simplified models were used to describe the non-linear coupling between them: the model in which the ion-temperature effects were neglected and only the so-called finite ion Larmour radius effects in terms of the electron temperature were taken into account (Guzdar et al 2001, Smolyakov et al 2001, Lakhin 2003 and the model where both the zonal flow and the primary plasma oscillations were considered to have the scale lengths, which are small compared with the ion Larmour radius ρ i (ρ 2 i = T i /m i ω 2 Bi ) (Smolyakov et al 2002). The analysis of the first of these papers (Guzdar et al 2001) was based on the methods of the classical theory of coherent parametric instabilities.…”

Section: Introductionmentioning

confidence: 99%

“…It is based on the assumption of time-and space-scale separation of the turbulence and the zonal flow. In this approach, used in Smolyakov et al (2001), Smolyakov et al (2002), and Lakhin (2003), the drift-Alfvén turbulence (small-scale, fast process) is described by the evolution equation of the spectral function (the analogue of the wave kinetic equation), which takes into account the effect of zonal flow, while the zonal flow (large-scale, slow process)-is described by the hydrodynamic equations, in which the turbulence-related non-linear effects averaged over a fast scale are taken into account. Such an approach allows us to study the generation of a large-scale zonal flow by small-scale turbulence.…”

Section: Introductionmentioning

confidence: 99%

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Finite ion Larmour radius effects in the problem of zonal flow generation by kinetic drift-Alfvén turbulence

Lakhin

2004

Plasma Phys. Control. Fusion

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A theory of spontaneous generation of zonal flows by kinetic drift-Alfvén turbulence in the finite-pressure plasma (β > m e /m i ) is generalized to include the ion diamagnetic effects and the finite ion Larmour radius effects. In the framework of the corresponding set of generalized two-fluid magnetohydrodynamic equations and on the assumption of a distinct time-and space-scale separation between the turbulent oscillations and the zonal flow, a set of coupled equations is derived to describe the interaction between the turbulence and the flow, consisting of the evolution equation for the spectral function of turbulence and the mean-field equations for zonal flow. The possibility of spontaneous zonal flow generation by the kinetic drift-Alfvén turbulence is investigated in details in several cases. In the case of kinetic drift-Alfvén turbulence with the space scale of the order of the ion Larmour radius or below, the instability caused by the resonant interaction of the wave packet with the slow modulations of zonal flow has been analysed, and the criterion for the onset of the zonal flow instability has been derived. In the case of short-wavelength turbulence, two regimes are considered. It is shown, that, when the frequency of short-wavelength oscillations is close to the electrondrift frequency and the zonal perturbation of plasma density can be described by the Boltzmann Law, the instability criterion is a generalization of the previously obtained result to the case of non-equal temperatures of the ions and electrons. The new regime is found, in which the zonal perturbation of plasma density is negligible. The condition for the onset of resonant instability is obtained.

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Long-wavelength instability of periodic flows and helicon waves in electron magnetohydrodynamics

Cited by 3 publications

References 13 publications

On the generation of mean fields by small-scale electron magnetohydrodynamic turbulence

On the generation of mean fields by small-scale electron magnetohydrodynamic turbulence

Avoiding infrared catastrophes in trapped Bose-Einstein condensates

Finite ion Larmour radius effects in the problem of zonal flow generation by kinetic drift-Alfvén turbulence

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