# 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

##### References

More filters

••

TL;DR: In this article, the authors used the method of multiple scales to derive the two coupled nonlinear partial differential equations which describe the evolution of a three-dimensional wavepacket of wavenumber k on water of finite depth.

Abstract: In this note we use the method of multiple scales to derive the two coupled nonlinear partial differential equations which describe the evolution of a three-dimensional wave-packet of wavenumber k on water of finite depth. The equations are used to study the stability of the uniform Stokes wavetrain to small disturbances whose length scale is large compared with 2π/ k . The stability criterion obtained is identical with that derived by Hayes under the more restrictive requirement that the disturbances are oblique plane waves in which the amplitude variation is much smaller than the phase variation.

1,021 citations

••

TL;DR: In this article, a linear stability analysis of the Laminar flow of air over water confined between two infinite parallel plates was made and the conditions at which small amplitude surface waves first begin to grow were determined.

Abstract: The fully developed laminar flow of air over water confined between two infinite parallel plates was used to study nonlinear effects in the generation of surface waves. A linear stability analysis of the basic flow was made and the conditions at which small amplitude surface waves first begin to grow were determined. Then, following Stewartson & Stuart (1971), the nonlinear stability of the flow was examined and the usual parabolic equation with cubic nonlinearity obtained for the amplitude of the disturbances. The calculation of the linear stability characteristics and the coefficients appearing in the amplitude equation was a lengthy computational task, with most interest centred on the coefficient of the nonlinear terms in the amplitude equation. In two profiles, used as crude models of a boundary layer flow of air over water, the calculations indicated that, over a range of parameters, the non-linear effects would reduce the growth rate of the surface waves and hence lead to equilibrium amplitude waves.

126 citations

••

TL;DR: In this paper, the cyclotron modes were found to be purely transverse electric at cut-off, gradually changing in character along their propagation curves through hybrid to purely transversal magnetic modes at cyclotic resonance.

Abstract: In the analysis of the waves which propagate in a waveguide completely or partially filled with a stationary plasma column or an electron beam drifting with a uniform velocity and collimated with a magnetic field of finite magnitude, it is necessary to include the effects of the rotation of the electric field in order to treat the waves which have phase velocities comparable to or greater than the velocity of light. Certain interesting features of perturbed waveguide modes and cyclotron modes become apparent only when the dynamic nature of the electric field is recognized in the analysis. These features are the influence of cyclotron frequency and the polarization of waves on the propagation characteristics. The cyclotron modes are found to be purely transverse electric at cut-off, gradually changing in character along their propagation curves through hybrid to purely transverse magnetic modes at cyclotron resonance. A classification of modes of propagation is proposed, and formulae for cut-off f...

86 citations

••

TL;DR: In this paper, a non-linear Schrodinger equation for Langmuir waves is derived by using a fluid model for the electrons, while both a fluid and a Vlasov formulation are considered for the ion dynamics.

Abstract: A non-linear Schrodinger equation for Langmuir waves is presented. The equation is derived by using a fluid model for the electrons, while both a fluid and a Vlasov formulation are considered for the ion dynamics. The two formulations lead to significant differences in the final results, especially in the expressions concerning the modulation instability of a plane Langmuir wave. When the Vlasov equation for the ions is applied, a Langmuir wave is modulationally unstable for arbitrary perturbations independent of the unperturbed wave amplitude, in contrast to what is found for fluid ions. A simple analogy with negative energy waves explaining the different features of the two cases is outlined.

42 citations