# 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, an analysis of non-linear three-wave interaction for propagation along a cylindrical plasma column surrounded either by a metallic boundary, or by an infinite dielectric, and immersed in an infinite, static, axial magnetic field is presented.

Abstract: The paper presents an analysis of non-linear three-wave interaction for propagation along a cylindrical plasma column surrounded either by a metallic boundary, or by an infinite dielectric, and immersed in an infinite, static, axial magnetic field. An averaged Lagrangian method is used and the results are specialized to parametric amplification and mode conversion, assuming an undepleted pump wave. Computations are presented for a magneto-plasma column surrounded by free space, indicating that parametric growth rates of the order of a fraction of a decibel per centimeter should be obtainable for plausible laboratory plasma parameters. In addition, experiments on non-linear mode conversion in a cylindrical magnetoplasma column are described. The results are compared with the theoretical predictions and good qualitative agreement is demonstrated.

7 citations

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TL;DR: In this article, the instability conditions of a uniform longitudinal plasma wave train including the effect of its interaction, both at resonance and nonresonance, with a long wavelength ion-acoustic wave were derived.

Abstract: Assuming amplitudes as slowly varying functions of space and time and using perturbation method three coupled nonlinear partial differential equations are obtained for the nonlinear evolution of a three dimensional longitudinal plasma wave packet in a hot plasma including the effect of its interaction with a long wavelength ion-acoustic wave. These equations are used to derive the instability conditions of a uniform longitudinal plasma wave train including the effect of its interaction, both at resonance and nonresonance, with a long wavelength ion-acoustic wave. At resonance, the threshold amplitude of the longitudinal plasma wave for the onset of instability is determined. At nonresonance, the plasma wave may become modulationally unstable if mod Vglx mod < omega L and if the difference mod omega L-Vglx mod is sufficiently small, where l is the wavenumber of perturbation and omega L is the frequency of the ion-acoustic wave having a wave-vector l. This effect vanishes completely when the ion motions are disregarded. Assuming the usual particular type of dependence of amplitudes on space and time the coupled equations are transformed into three other coupled equations which reduce to a single nonlinear Schrodinger equation when three dimensionality is disregarded.

7 citations

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TL;DR: In this paper, coupled-mode equations for three-mode interactions in a cylindrical medium are derived, taking account of non-resonant (virtual) wave-fields.

Abstract: The coupled-mode equations for three-mode interactions in a cylindrical medium are derived, taking account of non-resonant (virtual) wave-fields. Some important differences from the plane-wave case are found. There is no resonance condition in the radial mode-number, n. If there are many radial mode-numbers within one resonance width, i.e. if ∂ω/∂n , where is the nonlinear growth rate, each mode interacts with a large number of mode-pairs. In the limit n 1, the condition for this to happen is νr/ R, where νr is the average radial group velocity. It is not possible to reduce the number of waves by collecting the modes within one resonance width into one wave-packet whose envelope follows a simple evolution equation. Thus, under these conditions, the concept of an independent triplet of interacting modes has no meaning. One has to deal with a large number of inter-dependent triplets, wave-phases are easily randomized, and weak-turbulence description is adequate.

6 citations

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TL;DR: In this article, the authors investigated parametric instabilities in a bounded inhomogeneous plasma when the pump wave frequency is close to that of the Gould-Trivelpiece mode.

Abstract: We investigate parametric instabilities in a bounded inhomogeneous plasma when the pump wave frequency is close to that of the Gould-Trivelpiece mode. Using a suitable technique, we have obtained a dispersion relation in a radially inhomogeneous plasma column. The growth rates and threshold conditions for purely growing and four-phonon parametric instabilities are calculated. A comparison of these values with those for a homogeneous plasma shows that the plasma inhomogeneity enhances thresholds.

6 citations

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TL;DR: In this paper, the decay of electron plasma waves propagating in a cylindrical plasma column into well-defined modes is observed over a range of frequencies and shown to be a three-wave resonant process.

6 citations