Nonlinear evolution of whistler wave modulational instability

1995 ◽  
Vol 2 (9) ◽  
pp. 3302-3319 ◽  
Author(s):  
V. I. Karpman ◽  
J. P. Lynov ◽  
P. K. Michelsen ◽  
J. Juul Rasmussen
Keyword(s):  
Nonlinear Evolution ◽  
Modulational Instability ◽  
Whistler Wave

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

1987 ◽  
Vol 37 (1) ◽  
pp. 107-115
Author(s):  
B. Ghosh ◽  
K. P. Das
Keyword(s):  
Magnetic Field ◽  
Multiple Scales ◽  
Nonlinear Evolution ◽  
Axial Magnetic Field ◽  
Modulational Instability ◽  
Wave Train ◽  
Dielectric Medium ◽  
Ion Effects ◽  
The Magnetic Field ◽  
Uniform Plasma

The method of multiple scales is used to derive a nonlinear Schrödinger equation, which describes the nonlinear evolution of electron plasma ‘slow waves’ propagating along a hot cylindrical plasma column, surrounded by a dielectric medium and immersed in an essentially infinite axial magnetic field. The temperature is included as well as mobile ion effects for ail possible modes of propagation along the magnetic field. From this equation the condition for modulational instability for a uniform plasma wave train is determined.

scholarly journals Nonlinear evolution of Langmuir and electromagnetic pulses in a warm, unmagnetized plasma: modulational instability, integrability and self-focusing in 2 + 1 dimensions

1994 ◽  
Vol 52 (1) ◽  
pp. 75-90
Author(s):  
Ronald E. Kates ◽  
D. J. Kaup
Keyword(s):  
Nonlinear Evolution ◽  
Modulational Instability ◽  
Soliton Solutions ◽  
Integrable Case ◽  
Regime Parameter ◽  
Self Focusing ◽  
Long Time ◽  
Unmagnetized Plasma ◽  
Modulational Instabilities ◽  
Parameter Values

The nonlinear dynamics of wave envelopes modulated in 2 + 1 dimensions is considered for two systems in plasma physics: (i) Langmuir pulses and (ii) intense (but weakly relativistic) electromagnetic (EM) pulses. Using singular perturbation techniques applied to an envelope approximation, both problems are reduced to the two-dimensional nonlinear Schrödinger (2DNLS) system, which describes the dynamics of two coupled slowly varying potentials. The general 2DNLS system exhibits a rich variety of phenomena, including enhanced (compared with ‘longitudinal’ propagation) modulational stability and (1D) soliton formation; decay of 1D solitons over long time scales; self- focusing regimes (determined by a virial-type condition); as well as integrability and 2D solitons. Applying our recent results on the 2DNLS system, we determine which of these phenomena can actually occur here and compute the parameter regimes. (i) The 2DNLS system for the Zakharov equations is modulationally unstable for all parameter values. It also has an integrable sector and a self-focusing regime. (ii) The 2DNLS system describes coupled ‘longitudinal’ and ‘transverse’ modulations of linearly or circularly polarized EM pulses propagating through a warm unmagnetized two-component neutral plasma with arbitrary masses (i.e. electron—positron or electron—ion). The pulse can accelerate particles to weakly (but not fully) relativistic velocities; relativistic, ponderomotive and harmonic effects all contribute to the nonlinear terms. The resulting 2DNLS system does not admit a self-focusing regime. Parameter values leading to an integrable case (the so-called ‘Davey—Stewartson I’ equations, which admit 2D soliton solutions) are computed; however, the required values would not be attainable in a laboratory or astrophysical setting. None the less, the existence of new nonlinear modulational instabilities associated with the second spatial degree of freedom already represents an important potential limitation on any (1 + 1)-dimensional approach to nonlinear evolution and modulational instability of plasma EM waves.

Influence of dispersion on the modulational instability of a whistler wave

1989 ◽  
Vol 41 (2) ◽  
pp. 289-300 ◽  
Author(s):  
V. I. Karpman ◽  
A. G. Shagalov
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Growth Rates ◽  
Cyclotron Frequency ◽  
Modulational Instability ◽  
Low Frequency ◽  
Whistler Wave ◽  
Long Wave ◽  
Frequency Modulations ◽  
Magnetic Sound

The modulational instability of a whistler wave propagating along an external magnetic field is investigated, taking into account the dispersion of the low-frequency modulations. The dispersive effects are significant if the modulation frequencies Ω are comparable to or greater than the ion cyclotron frequency ωci. It is shown that in this case there are four unstable branches: the long-wave modulational instability and three others with much larger growth rates. At Ω≪ωci the latter correspond to fast magnetic sound, Alfvén and slow magnetic sound branches.

Self-interaction of Alfvén waves in a cylindrical waveguide filled with an ideally conducting compressible plasma

1991 ◽  
Vol 45 (1) ◽  
pp. 89-101
Author(s):  
Nagendra Kumar ◽  
Krishna M. Srivastava
Keyword(s):  
Compressible Fluid ◽  
Nonlinear Evolution ◽  
Modulational Instability ◽  
Alfven Waves ◽  
Cylindrical Waveguide ◽  
Radial Mode ◽  
Alfvén Waves ◽  
Nonlinear Behaviour ◽  
Compressible Plasma ◽  
Dependent Frequency

The nonlinear behaviour of azimuthally symmetric Alfvén waves propagating along the axis of a cylindrical ideally conducting compressible fluid-filled waveguide is investigated. It is shown that the nonlinear evolution of such waves is governed by the nonlinear Schrödinger equation. Modulational instability for fundamental (m = 1) radial mode is discussed for α2 = 0·1,0·2, 0·3 and different values of k. The amplitude-dependent frequency and wavenumber shifts are calculated and their variations with wavenumber are shown graphically.

Nonlinear evolution of the modulational instability of whistler waves

1990 ◽  
Vol 64 (8) ◽  
pp. 890-893 ◽  
Author(s):  
V. Karpman ◽  
F. Hansen ◽  
T. Huld ◽  
J. Lynov ◽  
H. Pécseli ◽  
...  
Keyword(s):  
Nonlinear Evolution ◽  
Modulational Instability ◽  
Whistler Waves

scholarly journals How electron two-stream instability drives cyclic Langmuir collapse and continuous coherent emission

2017 ◽  
Vol 114 (7) ◽  
pp. 1502-1507 ◽  
Author(s):  
Haihong Che ◽  
Melvyn L. Goldstein ◽  
Patrick H. Diamond ◽  
Roald Z. Sagdeev
Keyword(s):  
Feedback Loop ◽  
Nonlinear Evolution ◽  
Modulational Instability ◽  
Acoustic Mode ◽  
Small Scale ◽  
Linear Stage ◽  
Strong Electron ◽  
Langmuir Waves ◽  
Coherent Emission ◽  
Stream Instability

Continuous plasma coherent emission is maintained by repetitive Langmuir collapse driven by the nonlinear evolution of a strong electron two-stream instability. The Langmuir waves are modulated by solitary waves in the linear stage and electrostatic whistler waves in the nonlinear stage. Modulational instability leads to Langmuir collapse and electron heating that fills in cavitons. The high pressure is released via excitation of a short-wavelength ion acoustic mode that is damped by electrons and reexcites small-scale Langmuir waves; this process closes a feedback loop that maintains the continuous coherent emission.

scholarly journals Nonlinear Evolution Equations for Broader Bandwidth Wave Packets in Crossing Sea States

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
S. Debsarma ◽  
S. Senapati ◽  
K. P. Das
Keyword(s):  
Growth Rate ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Modulational Instability ◽  
Wave Packets ◽  
Nonlinear Evolution Equations ◽  
Wave Spectra ◽  
Surface Gravity Wave ◽  
Freak Waves ◽  
Wave Trains

Two coupled nonlinear equations are derived describing the evolution of two broader bandwidth surface gravity wave packets propagating in two different directions in deep water. The equations, being derived for broader bandwidth wave packets, are applicable to more realistic ocean wave spectra in crossing sea states. The two coupled evolution equations derived here have been used to investigate the instability of two uniform wave trains propagating in two different directions. We have shown in figures the behaviour of the growth rate of instability of these uniform wave trains for unidirectional as well as for bidirectional perturbations. The figures drawn here confirm the fact that modulational instability in crossing sea states with broader bandwidth wave packets can lead to the formation of freak waves.

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