On the Stability of a Magnetized Plasma in a Large Amplitude Circularly Polarized Wave

1980 ◽  
Vol 21 (6) ◽  
pp. 831-835 ◽  
Author(s):  
L Stenflo
Keyword(s):  
Large Amplitude ◽  
Magnetized Plasma ◽  
Circularly Polarized ◽  
The Stability

Large-amplitude circularly polarized electromagnetic waves in magnetized plasma

2014 ◽  
Vol 21 (5) ◽  
pp. 054501 ◽  
Author(s):  
I. Y. Vasko ◽  
A. V. Artemyev ◽  
L. M. Zelenyi
Keyword(s):  
Large Amplitude ◽  
Electromagnetic Waves ◽  
Magnetized Plasma ◽  
Circularly Polarized

On the stability of self-consistent large-amplitude waves in a cold plasma. Part 3. Transverse circularly polarized waves in the presence of a large-scale magnetic field

1979 ◽  
Vol 21 (1) ◽  
pp. 43-50 ◽  
Author(s):  
M. A. Lee ◽  
I. Lerche
Keyword(s):  
Magnetic Field ◽  
Large Amplitude ◽  
Cold Plasma ◽  
Large Scale ◽  
Circularly Polarized ◽  
Polarized Waves ◽  
Large Scale Magnetic Field ◽  
Self Consistent ◽  
Instability Rate ◽  
The Stability

We demonstrate that a self-consistent large-amplitude circularly polarized wave, propagating in a cold plasma in the presence of a large-scale magnetic field, is unstable if the constant bulk streaming speed of the plasma is zero in the frame in which the wave depends oniy on time. The growth rate is of the order of the plasma frequency or the gyrofrequency at short perturbation wavelengths, and is proportional to the perturbation wave vector at long wavelengths. For nonzero but small streaming the instability rate increases for one streaming direction and decreases for the other. We conclude that instability is the rule rather than the exception for large-amplitude waves in a cold plasma.

scholarly journals Anomalous width variation of rarefactive ion acoustic solitary waves in the context of auroral plasmas

2004 ◽  
Vol 11 (2) ◽  
pp. 219-228 ◽  
Author(s):  
S. S. Ghosh ◽  
G. S. Lakhina
Keyword(s):  
Solitary Waves ◽  
Nonlinear Theory ◽  
Acoustic Waves ◽  
Large Amplitude ◽  
Magnetized Plasma ◽  
Amplitude Variation ◽  
Fully Nonlinear ◽  
Weakly Nonlinear ◽  
Ion Acoustic Solitary Waves ◽  
Ion Acoustic

Abstract. The presence of dynamic, large amplitude solitary waves in the auroral regions of space is well known. Since their velocities are of the order of the ion acoustic speed, they may well be considered as being generated from the nonlinear evolution of ion acoustic waves. However, they do not show the expected width-amplitude correlation for K-dV solitons. Recent POLAR observations have actually revealed that the low altitude rarefactive ion acoustic solitary waves are associated with an increase in the width with increasing amplitude. This indicates that a weakly nonlinear theory is not appropriate to describe the solitary structures in the auroral regions. In the present work, a fully nonlinear analysis based on Sagdeev pseudopotential technique has been adopted for both parallel and oblique propagation of rarefactive solitary waves in a two electron temperature multi-ion plasma. The large amplitude solutions have consistently shown an increase in the width with increasing amplitude. The width-amplitude variation profile of obliquely propagating rarefactive solitary waves in a magnetized plasma have been compared with the recent POLAR observations. The width-amplitude variation pattern is found to fit well with the analytical results. It indicates that a fully nonlinear theory of ion acoustic solitary waves may well explain the observed anomalous width variations of large amplitude structures in the auroral region.

scholarly journals Corrigendum

1979 ◽  
Vol 22 (3) ◽  
pp. 571-572
Author(s):  
E. Infeld ◽  
G. Rowlands
Keyword(s):  
Large Amplitude ◽  
Plasma Waves ◽  
Relativistic Plasma ◽  
Small Perturbations ◽  
Transverse Waves ◽  
The Stability

In this note we investigate the stability of large-amplitude longitudinal relativistic plasma waves. We find that they are secularly stable, that is, small perturbations grow in time proportional to time but not exponentially with time. Similar results have recently been obtained for transverse waves by Romeiras (1978)

Finite-amplitude internal wavepacket dispersion and breaking

2001 ◽  
Vol 429 ◽  
pp. 343-380 ◽  
Author(s):  
BRUCE R. SUTHERLAND
Keyword(s):  
Numerical Simulations ◽  
Internal Waves ◽  
Large Amplitude ◽  
Finite Amplitude ◽  
Critical Amplitude ◽  
Fully Nonlinear ◽  
Weakly Nonlinear ◽  
The Stability ◽  
The Waves ◽  
Horizontal Wavelength

The evolution and stability of two-dimensional, large-amplitude, non-hydrostatic internal wavepackets are examined analytically and by numerical simulations. The weakly nonlinear dispersion relation for horizontally periodic, vertically compact internal waves is derived and the results are applied to assess the stability of weakly nonlinear wavepackets to vertical modulations. In terms of Θ, the angle that lines of constant phase make with the vertical, the wavepackets are predicted to be unstable if [mid ]Θ[mid ] < Θc, where Θc = cos−1 (2/3)1/2 ≃ 35.3° is the angle corresponding to internal waves with the fastest vertical group velocity. Fully nonlinear numerical simulations of finite-amplitude wavepackets confirm this prediction: the amplitude of wavepackets with [mid ]Θ[mid ] > Θc decreases over time; the amplitude of wavepackets with [mid ]Θ[mid ] < Θc increases initially, but then decreases as the wavepacket subdivides into a wave train, following the well-known Fermi–Pasta–Ulam recurrence phenomenon.If the initial wavepacket is of sufficiently large amplitude, it becomes unstable in the sense that eventually it convectively overturns. Two new analytic conditions for the stability of quasi-plane large-amplitude internal waves are proposed. These are qualitatively and quantitatively different from the parametric instability of plane periodic internal waves. The ‘breaking condition’ requires not only that the wave is statically unstable but that the convective instability growth rate is greater than the frequency of the waves. The critical amplitude for breaking to occur is found to be ACV = cot Θ (1 + cos2 Θ)/2π, where ACV is the ratio of the maximum vertical displacement of the wave to its horizontal wavelength. A second instability condition proposes that a statically stable wavepacket may evolve so that it becomes convectively unstable due to resonant interactions between the waves and the wave-induced mean flow. This hypothesis is based on the assumption that the resonant long wave–short wave interaction, which Grimshaw (1977) has shown amplifies the waves linearly in time, continues to amplify the waves in the fully nonlinear regime. Using linear theory estimates, the critical amplitude for instability is ASA = sin 2Θ/(8π2)1/2. The results of numerical simulations of horizontally periodic, vertically compact wavepackets show excellent agreement with this latter stability condition. However, for wavepackets with horizontal extent comparable with the horizontal wavelength, the wavepacket is found to be stable at larger amplitudes than predicted if Θ [lsim ] 45°. It is proposed that these results may explain why internal waves generated by turbulence in laboratory experiments are often observed to be excited within a narrow frequency band corresponding to Θ less than approximately 45°.

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