scholarly journals Modulational instability and nonlinear evolution of two-dimensional electrostatic wave packets in ultra-relativistic degenerate dense plasmas

2011 ◽  
Vol 18 (4) ◽  
pp. 042308 ◽  
Author(s):  
Amar Prasad Misra ◽  
Padma Kant Shukla
Keyword(s):  
Nonlinear Evolution ◽  
Modulational Instability ◽  
Wave Packets ◽  
Two Dimensional ◽  
Electrostatic Wave ◽  
Dense Plasmas

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.

scholarly journals Evolution and Stability of Two-Dimensional Anelastic Internal Gravity Wave Packets

2018 ◽  
Vol 75 (10) ◽  
pp. 3703-3724 ◽  
Author(s):  
Alain D. Gervais ◽  
Gordon E. Swaters ◽  
Ton S. van den Bremer ◽  
Bruce R. Sutherland
Keyword(s):  
Wave Packet ◽  
Gravity Wave ◽  
Linear Theory ◽  
Nonlinear Evolution ◽  
Wave Packets ◽  
Internal Gravity Wave ◽  
Two Dimensional ◽  
Fully Nonlinear ◽  
Weakly Nonlinear ◽  
Nonlinear Simulations

The weakly nonlinear evolution, stability, and overturning of horizontally and vertically localized internal gravity wave packets is examined for a nonrotating, anelastic atmosphere that is stationary in the absence of waves. The weakly nonlinear evolution is examined through the derivation of their wave-induced mean flow, which is used to formulate a nonlinear Schrödinger equation. The induced flow is manifest as a long, hydrostatic, bow wake-like disturbance, whose flow direction transitions from positive on the leading flank of the wave packet to negative on the trailing flank of the wave packet. As such, two-dimensional wave packets are always modulationally unstable. This instability results in enhanced amplitude growth confined to either the leading or trailing flank. Hence, when combined with anelastic growth predicted by linear theory, we anticipate two-dimensional waves will overturn either somewhat below or just above the heights predicted by linear theory. Numerical solutions of the Schrödinger equation are compared with the results of fully nonlinear simulations to establish the validity of the weakly nonlinear theory. Actual wave overturning heights are determined quantitatively from a range of fully nonlinear simulations.

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 Dispersion properties of electrostatic oscillations in quantum plasmas

2009 ◽  
Vol 76 (1) ◽  
pp. 7-17 ◽  
Author(s):  
BENGT ELIASSON ◽  
PADMA KANT SHUKLA
Keyword(s):  
Low Frequency ◽  
Electron Plasma ◽  
Quantum Plasma ◽  
Plasma Oscillations ◽  
Heisenberg Uncertainty Principle ◽  
Electrostatic Wave ◽  
Dense Plasmas ◽  
Astrophysical Objects ◽  
Heisenberg Uncertainty ◽  
Semiconductor Plasmas

AbstractWe present a derivation of the dispersion relation for electrostatic oscillations in a zero-temperature quantum plasma, in which degenerate electrons are governed by the Wigner equation, while non-degenerate ions follow the classical fluid equations. The Poisson equation determines the electrostatic wave potential. We consider parameters ranging from semiconductor plasmas to metallic plasmas and electron densities of compressed matter such as in laser compression schemes and dense astrophysical objects. Owing to the wave diffraction caused by overlapping electron wave function because of the Heisenberg uncertainty principle in dense plasmas, we have the possibility of Landau damping of the high-frequency electron plasma oscillations at large enough wavenumbers. The exact dispersion relations for the electron plasma oscillations are solved numerically and compared with the ones obtained by using approximate formulas for the electron susceptibility in the high- and low-frequency cases.

Two-Dimensional Numerical Model for Studies of Collective Beam-Plasma Interaction

2010 ◽  
Vol 5 (2) ◽  
pp. 85-97
Author(s):  
Andrey V. Terekhov ◽  
Igor V. Timofeev ◽  
Konstantin V. Lotov
Keyword(s):  
Numerical Model ◽  
Electron Beams ◽  
Modulational Instability ◽  
Two Dimensional ◽  
Particle In Cell ◽  
Plasma Energy ◽  
Proposed Model ◽  
The Laplace Operator ◽  
Physical Phenomena ◽  
Powerful Electron

A two-dimensional particle-in-cell numerical model is developed to simulate collective relaxation of powerful electron beams in plasmas. To increase the efficiency of parallel particle-in-cell simulations on supercomputers, the Dichotomy Algorithm is used for inversion of the Laplace operator. The proposed model is tested with several well-known physical phenomena and is shown to adequately simulate basic effects of the beam driven turbulence. Also, the modulational instability is studied in the regime when the energy of pumping wave significantly exceeds the thermal plasma energy

scholarly journals Two-dimensional modulational instability in photorefractive media

2004 ◽  
Vol 6 (5) ◽  
pp. S397-S403 ◽  
Author(s):  
M Saffman ◽  
Glen McCarthy ◽  
Wieslaw Królikowski
Keyword(s):  
Modulational Instability ◽  
Two Dimensional
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