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Title: Nonlinear modulated dust lattice wave packets in two-dimensional hexagonal dust crystals

Abstract

The amplitude modulation of dust lattice waves (DLWs) propagating in a two-dimensional hexagonal dust crystal is investigated in a continuum approximation, accounting for the effect of dust charge polarization (dressed interactions). A dusty plasma crystalline configuration with constant dust grain charge and mass is considered. The dispersion relation and the group velocity for DLWs are determined for wave propagation in both longitudinal and transverse directions. The reductive perturbation method is used to derive a (2+1)-dimensional nonlinear Schroedinger equation (NLSE). New expressions for the coefficients of the NLSE are derived and compared, for a Yukawa-type potential energy and for a 'dressed' potential energy, taking into account interaction and geometric nonlinearities.

Authors:
; ;  [1];  [2];  [3]
  1. Department of Physics, Arak-University, Arak, 38156-879 (Iran, Islamic Republic of)
  2. (Belgium) and Institut fuer Theoretische Physik IV, Fakultaet fur Physik und Astronomie, Ruhr-Universitaet Bochum, D-44780 Bochum (Germany)
  3. (Germany)
Publication Date:
OSTI Identifier:
20860428
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 13; Journal Issue: 12; Other Information: DOI: 10.1063/1.2400594; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; AMPLITUDES; APPROXIMATIONS; CRYSTALS; DISPERSION RELATIONS; DUSTS; MODULATION; NONLINEAR PROBLEMS; ONE-DIMENSIONAL CALCULATIONS; PERTURBATION THEORY; PLASMA; PLASMA WAVES; POLARIZATION; POTENTIAL ENERGY; SCHROEDINGER EQUATION; TWO-DIMENSIONAL CALCULATIONS; WAVE PACKETS; WAVE PROPAGATION; YUKAWA POTENTIAL

Citation Formats

Farokhi, B., Kourakis, I., Shukla, P. K., Universiteit Gent, Sterrenkundig Observatorium, Krijgslaan 281, B-9000 Gent, and Institut fuer Theoretische Physik IV, Fakultaet fur Physik und Astronomie, Ruhr-Universitaet Bochum, D-44780 Bochum. Nonlinear modulated dust lattice wave packets in two-dimensional hexagonal dust crystals. United States: N. p., 2006. Web. doi:10.1063/1.2400594.
Farokhi, B., Kourakis, I., Shukla, P. K., Universiteit Gent, Sterrenkundig Observatorium, Krijgslaan 281, B-9000 Gent, & Institut fuer Theoretische Physik IV, Fakultaet fur Physik und Astronomie, Ruhr-Universitaet Bochum, D-44780 Bochum. Nonlinear modulated dust lattice wave packets in two-dimensional hexagonal dust crystals. United States. doi:10.1063/1.2400594.
Farokhi, B., Kourakis, I., Shukla, P. K., Universiteit Gent, Sterrenkundig Observatorium, Krijgslaan 281, B-9000 Gent, and Institut fuer Theoretische Physik IV, Fakultaet fur Physik und Astronomie, Ruhr-Universitaet Bochum, D-44780 Bochum. Fri . "Nonlinear modulated dust lattice wave packets in two-dimensional hexagonal dust crystals". United States. doi:10.1063/1.2400594.
@article{osti_20860428,
title = {Nonlinear modulated dust lattice wave packets in two-dimensional hexagonal dust crystals},
author = {Farokhi, B. and Kourakis, I. and Shukla, P. K. and Universiteit Gent, Sterrenkundig Observatorium, Krijgslaan 281, B-9000 Gent and Institut fuer Theoretische Physik IV, Fakultaet fur Physik und Astronomie, Ruhr-Universitaet Bochum, D-44780 Bochum},
abstractNote = {The amplitude modulation of dust lattice waves (DLWs) propagating in a two-dimensional hexagonal dust crystal is investigated in a continuum approximation, accounting for the effect of dust charge polarization (dressed interactions). A dusty plasma crystalline configuration with constant dust grain charge and mass is considered. The dispersion relation and the group velocity for DLWs are determined for wave propagation in both longitudinal and transverse directions. The reductive perturbation method is used to derive a (2+1)-dimensional nonlinear Schroedinger equation (NLSE). New expressions for the coefficients of the NLSE are derived and compared, for a Yukawa-type potential energy and for a 'dressed' potential energy, taking into account interaction and geometric nonlinearities.},
doi = {10.1063/1.2400594},
journal = {Physics of Plasmas},
number = 12,
volume = 13,
place = {United States},
year = {Fri Dec 15 00:00:00 EST 2006},
month = {Fri Dec 15 00:00:00 EST 2006}
}
  • The propagation of nonlinear dust-lattice waves in a two-dimensional hexagonal crystal is investigated. Transverse (off-plane) dust grain oscillatory motion is considered in the form of a backward propagating wave packet whose linear and nonlinear characteristics are investigated. An evolution equation is obtained for the slowly varying amplitude of the first (fundamental) harmonic by making use of a two-dimensional lattice multiple scales technique. An analysis based on the continuum approximation (spatially extended excitations compared to the lattice spacing) shows that wave packets will be modulationally stable and that dark-type envelope solitons (density holes) may occur in the long wavelength region. Evidencemore » is provided of modulational instability and of the occurrence of bright-type envelopes (pulses) at shorter wavelengths. The role of second neighbor interactions is also investigated and is shown to be rather weak in determining the modulational stability region. The effect of dissipation, assumed negligible in the algebra throughout the article, is briefly discussed.« less
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  • Taking into account the random charge fluctuation on embedded micro spheres in low pressure gas discharge two differential equation for two-dimensional dust lattice wave is derived. 2D hexagonal crystal is investigated in this paper. The dispersion relation for both longitudinal and transverse waves in different direction is studied as well. It is in agreement between analytical results and the experimental ones reported previously.
  • We consider the nonlinear propagation of electrostatic wave packets in an ultra-relativistic (UR) degenerate dense electron-ion plasma, whose dynamics is governed by the nonlocal two-dimensional nonlinear Schroedinger-like equations. The coupled set of equations is then used to study the modulational instability (MI) of a uniform wave train to an infinitesimal perturbation of multidimensional form. The condition for the MI is obtained, and it is shown that the nondimensional parameter, {beta}{proportional_to}{lambda}{sub C}n{sub 0}{sup 1/3} (where {lambda}{sub C} is the reduced Compton wavelength and n{sub 0} is the particle number density) associated with the UR pressure of degenerate electrons, shifts the stablemore » (unstable) regions at n{sub 0{approx}}10{sup 30}cm{sup -3} to unstable (stable) ones at higher densities, i.e., n{sub 0} > or approx. 7x10{sup 33}. It is also found that the higher the values of n{sub 0}, the lower is the growth rate of MI with cut-offs at lower wave numbers of modulation. Furthermore, the dynamical evolution of the wave packets is studied numerically. We show that either they disperse away or they blowup in a finite time, when the wave action is below or above the threshold. The results could be useful for understanding the properties of modulated wave packets and their multidimensional evolution in UR degenerate dense plasmas, such as those in the interior of white dwarfs and/or pre-Supernova stars.« less
  • The influence of a constant magnetic field on the propagation of dust-lattice waves in a two-dimensional hexagonal strongly coupled dusty plasma crystal is considered. The expression for the wave dispersion relation clearly shows that high- and low-frequency dust lattice vibrations exist as a result of the coupling between the longitudinal and transverse dust lattice modes due to the Lorentz force acting on the charged dust particles. It is found that in an external magnetic field the damping rate of the high-frequency (low-frequency) dust lattice wave is increased (decreased). For special values of the wave number and the direction of themore » wave propagation, the imaginary part of low-frequency is zero and the imaginary part of high-frequency attains a maximum value. The present investigation indicates that the damping rates depend on direction of the external magnetic field. The polarization of dust lattice wave modes is found for different magnetic field strengths and for different directions.« less