# Nonlinear evolution of a wave packet propagating along a hot magnetoplasma column

TL;DR: In this article, the methode des echelles multiples is used for etablir a non lineaire equation of Schrodinger non-lineaire, which decrit l'evolution non lineaires des ondes lentes du plasma electronique se propageant le long d'une colonne de plasma cylindrique chaud, entoure par un milieu dielectrique and immerge dans un champ magnetique axial infini.

Abstract: La methode des echelles multiples est utilisee pour etablir une equation de Schrodinger non lineaire, qui decrit l'evolution non lineaire des ondes lentes du plasma electronique se propageant le long d'une colonne de plasma cylindrique chaud, entoure par un milieu dielectrique et immerge dans un champ magnetique axial infini. Determination, depuis cette equation, de la condition pour l'instabilite de modulation pour un trait d'ondes de plasma non uniformes

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TL;DR: In this paper, the waveguiding properties of a homogeneous circular column of plasma imbedded in free space are examined in the two limits of zero and large axial magnetic field.

Abstract: Waveguiding properties of a homogeneous circular column of plasma imbedded in free space are examined in the two limits of zero and large axial magnetic field. The plasma is assumed to be cold and collisionless with ion motion neglected. The modes with azimuthal variation are included in the investigation, and dispersion curves are presented. For the zero field case the higher-order modes are found under certain conditions to exhibit backward-wave characteristics. For the case of large magnetic field, the occurrence of unique waveguiding features is discussed. The assumptions made are approximated by certain laboratory plasmas and hence the results may be of practical importance.

31 citations

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TL;DR: In this paper, the nonlinear behavior of the electron wave propagating in a cylindrical plasma waveguide immersed in an infinite axial magnetic field was investigated using the Krylov-Bogoliubov-Mitropolsky perturbation method.

Abstract: The nonlinear behaviour of the electron plasma wave propagating in a cylindrical plasma waveguide immersed in an infinite axial magnetic field is investigated using the Krylov-Bogoliubov-Mitropolsky perturbation method, by means of which is deduced the nonlinear Schrodinger equation governing the long-time slow modulation of the wave amplitude. From this equation the amplitude-dependent frequency and wavenumber shifts are calculated, and it is found that the electron waves with short wavelengths are modulationally unstable with respect to long-wavelength, low-frequency perturbations. It is further shown that an oscillatory solution of the Korteweg-de Vries equation, which is derived in the small wavenumber region, satisfies the small wavenumber limit of the nonlinear Schrodinger equation.

24 citations

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TL;DR: In this article, an electronic plasma wave disintegration was studied experimentally and theoretically in a strong magnetic field confined plasma, and the authors showed that it is possible to disintegrate an electronic wave in a magnetic field.

Abstract: An electronic plasma wave disintegration is studied experimentally and theoretically in a strong magnetic field confined plasma.

21 citations

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TL;DR: In this paper, an averaged-Lagrangian method was used to analyze the non-linear three-wave interaction for propagation along a cylindrical plasma column surrounded by an infinite dielectric, in the absence of a static magnetic field.

Abstract: Non-linear three-wave interaction is analysed for propagation along a cylindrical plasma column surrounded by an infinite dielectric, in the absence of a static magnetic field. An averaged-Lagrangian method is used, and the results are specialized to parametric interaction and mode conversion, assuming an undepleted pump wave. The theory for these two types of interactions is extended to include imperfect synchronism, and the effects of loss. Computations are presented indicating that parametric growth rates of the order of a fraction of a decibel per centimeter should be obtainable for plausible laboratory plasma column parameters.

15 citations

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TL;DR: In this paper, nonlinear effects in the propagation of longitudinal plasma waves due to trapped electrons are considered, and the importance of the instability in the development of strong turbulence is discussed.

Abstract: Nonlinear effects in the propagation of longitudinal plasma waves due to trapped electrons are considered. The spatial evolution of a stable, finite amplitude wave is compared with theory and shown to be characterized by the ratio of the trapped electron oscillation frequency to the linear Landau damping rate. The 'sideband' instability which develops at larger amplitudes is examined in considerable detail experimentally, and comparison with theory enables the conclusion to be reached that trapped particles are essential to the mechanism of the instability. Regimes are defined in which these types of nonlinear behaviour occur, and the importance of the instability in the development of strong turbulence is discussed.

14 citations