188 research outputs found
Modulational instability in asymmetric coupled wave functions
The evolution of the amplitude of two nonlinearly interacting waves is
considered, via a set of coupled nonlinear Schroedinger-type equations. The
dynamical profile is determined by the wave dispersion laws (i.e. the group
velocities and the GVD terms) and the nonlinearity and coupling coefficients,
on which no assumption is made. A generalized dispersion relation is obtained,
relating the frequency and wave-number of a small perturbation around a coupled
monochromatic (Stokes') wave solution. Explicitly stability criteria are
obtained. The analysis reveals a number of possibilities. Two (individually)
stable systems may be destabilized due to coupling. Unstable systems may, when
coupled, present an enhanced instability growth rate, for an extended wave
number range of values. Distinct unstable wavenumber windows may arise
simultaneously.Comment: NEXT Sigma-Phi Statistical Physics Conference (2005, Kolymbari,
Greece) Proceedings, submitted; v.2 is a shorter version of the text in v.1
(more detailed and somehow more explanatory, yet abbreviated due to
submission regulations); some typos corrected as wel
Nonlinear modulation of transverse dust lattice waves in complex plasma crystals
The occurrence of the modulational instability (MI) in transverse dust
lattice waves propagating in a one-dimensional dusty plasma crystal is
investigated. The amplitude modulation mechanism, which is related to the
intrinsic nonlinearity of the sheath electric field, is shown to destabilize
the carrier wave under certain conditions, possibly leading to the formation of
localized envelope excitations. Explicit expressions for the instability growth
rate and threshold are presented and discussed.Comment: 5 pages, no figures; submitted to Physics of Plasma
Nonlinear theory of solitary waves associated with longitudinal particle motion in lattices - Application to longitudinal grain oscillations in a dust crystal
The nonlinear aspects of longitudinal motion of interacting point masses in a
lattice are revisited, with emphasis on the paradigm of charged dust grains in
a dusty plasma (DP) crystal. Different types of localized excitations,
predicted by nonlinear wave theories, are reviewed and conditions for their
occurrence (and characteristics) in DP crystals are discussed. Making use of a
general formulation, allowing for an arbitrary (e.g. the Debye electrostatic or
else) analytic potential form and arbitrarily long site-to-site range
of interactions, it is shown that dust-crystals support nonlinear kink-shaped
localized excitations propagating at velocities above the characteristic DP
lattice sound speed . Both compressive and rarefactive kink-type
excitations are predicted, depending on the physical parameter values, which
represent pulse- (shock-)like coherent structures for the dust grain relative
displacement. Furthermore, the existence of breather-type localized
oscillations, envelope-modulated wavepackets and shocks is established. The
relation to previous results on atomic chains as well as to experimental
results on strongly-coupled dust layers in gas discharge plasmas is discussed.Comment: 21 pages, 12 figures, to appear in Eur. Phys. J.
Linear and nonlinear properties of Rao-dust-Alfv\'en waves in magnetized plasmas
The linear and nonlinear properties of the Rao-dust-magnetohydrodynamic
(R-D-MHD) waves in a dusty magnetoplasma are studied. By employing the
inertialess electron equation of motion, inertial ion equation of motion,
Amp\`ere's law, Faraday's law, and the continuity equation in a plasma with
immobile charged dust grains, the linear and nonlinear propagation of
two-dimensional R-D-MHD waves are investigated. In the linear regime, the
existence of immobile dust grains produces the Rao cutoff frequency, which is
proportional to the dust charge density and the ion gyrofrequency. On the other
hand, the dynamics of an amplitude modulated R-D-MHD waves is governed by the
cubic nonlinear Schroedinger equation. The latter has been derived by using the
reductive perturbation technique and the two-timescale analysis which accounts
for the harmonic generation nonlinearity in plasmas. The stability of the
modulated wave envelope against non-resonant perturbations is studied. Finally,
the possibility of localized envelope excitations is discussed.Comment: 30 pages, 8 figures, to appear in Physics of Plasma
Shock creation and particle acceleration driven by plasma expansion into a rarefied medium
The expansion of a dense plasma through a more rarefied ionised medium is a
phenomenon of interest in various physics environments ranging from
astrophysics to high energy density laser- matter laboratory experiments. Here
this situation is modeled via a 1D Particle-In-Cell simulation; a jump in the
plasma density of a factor of 100 is introduced in the middle of an otherwise
equally dense electron-proton plasma with an uniform proton and electron
temperature of 10eV and 1keV respectively. The diffusion of the dense plasma,
through the rarified one, triggers the onset of different nonlinear phenomena
such as a strong ion-acoustic shock wave and a rarefaction wave. Secondary
structures are detected, some of which are driven by a drift instability of the
rarefaction wave. Efficient proton acceleration occurs ahead of the shock,
bringing the maximum proton velocity up to 60 times the initial ion thermal
speed
Modulated wavepackets associated with longitudinal dust grain oscillations in a dusty plasma crystal
The nonlinear amplitude modulation of longitudinal dust lattice waves (LDLWs)
propagating in a dusty plasma crystal is investigated in a continuum
approximation. It is shown that long wavelength LDLWs are modulationally
stable, while shorter wavelengths may be unstable. The possibility for the
formation and propagation of different envelope localized excitations is
discussed. It is shown that the total grain displacement bears a (weak)
constant displacement (zeroth harmonic mode), due to the asymmetric form of the
nonlinear interaction potential. The existence of asymmetric envelope localized
modes is predicted. The types and characteristics of these coherent nonlinear
structures are discussed.Comment: 18 pages, 7 figures, to appear in Physics of Plasma
Comment on Weakly dissipative dust-ion acoustic wave modulation
In a recent article (J. Plasma Phys., vol. 82, 2009, 905820104), weakly dissipative dust-ion acoustic wave modulation in dusty plasmas was considered. It is shown in this Comment that the analysis therein involved severe fallacies, and is in fact based on an erroneous plasma fluid model, which fails to satisfy an equilibrium condition, among other shortcomings. The subsequent analysis therefore is dubious and of limited scientific value.</jats:p
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