Finite ion temperature effects on oblique modulational stability and envelope excitations of dust-ion acoustic waves

Theoretical and numerical investigations are carried out for the amplitude modulation of dust-ion acoustic waves (DIAW) propagating in an unmagnetized weakly coupled collisionless fully ionized plasma consisting of isothermal electrons, warm ions and charged dust grains. Modulation oblique (by an angle theta) to the carrier wave propagation direction is considered. The stability analysis, based on a nonlinear Schrodinger-type equation (NLSE), exhibits a sensitivity of the instability region to the modulation angle theta, the dust concentration and the ion temperature. It is found that the ion temperature may strongly modify the wave's stability profile, in qualitative agreement with previous results, obtained for an electron-ion plasma. The effect of the ion temperature on the formation of DIAW envelope excitations (envelope solitons) is also discussed.

Linear and nonlinear properties of Rao-dust-Alfven 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, Ampere'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 amplitude modulated R-D-MHD waves is governed by the cubic nonlinear Schrodinger 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. (C) 2004 American Institute of Physics.

Nonlinear modulation of transverse dust lattice waves in complex plasma crystals

The occurrence of the modulational instability 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. (C) 2004 American Institute of Physics.

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. (C) 2004 American Institute of Physics.

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 phi(r) 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 v(0). 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.

Weakly nonlinear vertical dust grain oscillations in dusty plasma crystals in the presence of a magnetic field

The weakly nonlinear regime of transverse paramagnetic dust grain oscillations in dusty (complex) plasma crystals is discussed. The nonlinearity, which is related to the sheath electric/magnetic field(s) and to the intergrain (electrostatic/magnetic dipole) interactions, is shown to lead to the generation of phase harmonics and, in the case of propagating transverse dust-lattice modes, to the modulational instability of the carrier wave due to self-interaction. The stability profile depends explicitly on the form of the electric and magnetic fields in the plasma sheath. The long term evolution of the modulated wave packet, which is described by a nonlinear Schrodinger-type equation, may lead to propagating localized envelope structures whose exact forms are presented and discussed. Explicit suggestions for experimental investigations are put forward. (C) 2004 American Institute of Physics.

Lagrangian description of nonlinear dust-ion acoustic waves in dusty plasmas

An analytical model is presented for the description of nonlinear dust-ion-acoustic waves propagating in an unmagnetized, collisionless, three component plasma composed of electrons, ions and inertial dust grains. The formulation relies on a Lagrangian approach of the plasma fluid model. The modulational stability of the wave amplitude is investigated. Different types of localized envelope electrostatic excitations are shown to exist.

Complete nonlinear theory of longitudinal-to-transverse dust lattice mode coupling in a single-layer dusty plasma crystal

A comprehensive nonlinear model is put forward for coupled longitudinal to transverse displacements in a horizontal dust mono-layer, levitated under the combined influence of gravity and an electric and/or magnetic sheath field. A set of coupled nonlinear evolution equations are obtained in a discrete description, and a pair of coupled (Boussinesq-like) PDEs are obtained in the continuum approximation. Finally, the amplitude modulation of the coupled modes is discussed, pointing out the importance of the coupling. All these results are generic, i.e. valid for any assumed form of the inter-grain interaction potential U and the sheath potential Phi.

Discrete breather modes associated with vertical dust grain oscillations in dusty plasma crystals

Accounting for the lattice discreteness and the sheath electric field nonlinearity in dusty plasma crystals, it is demonstrated that highly localized structures (discrete breathers) involving vertical (transverse, off-plane) oscillations of charged dust grains may exist in a dust lattice. These structures correspond to either extremely localized bright breather excitations (pulses) or dark excitations composed of dips/voids. Explicit criteria for selecting different breather modes are presented. (C) 2005 American Institute of Physics.

Modulated dust-acoustic wave packets in a plasma with non-isothermal electrons and ions

The Nonlinear self-modulation of dust acoustic waves is studied in the presence of non-thermal (non-Maxwellian) ion and electron populations. By employing a multiple scale technique, a nonlinear Schrodinger-type equation (NLSE) is derived for the wave amplitude. The influence of non-thermality, in addition to obliqueness (between the propagation and modulation directions), on the conditions for modulational instability to occur is discussed. Different types of localized solutions (envelope excitations) which may possibly occur are discussed, and the dependence of their characteristics oil physical parameters is traced. The ion deviation from a Maxwellian distribution comes out to be more important than the electron analogous deviation alone. Both yield a de-stabilizing effect oil (the amplitude of) DAWs propagating in a dusty plasma with negative dust grains, and thus favour the formation of bright- (rather than dark-) type envelope structures, (solitons) in the plasma. A similar tendency towards amplitude de-stabilization is found for the ease of the presence of positively charged dust in the plasma.

Linear and nonlinear dynamics of a dust bicrystal consisting of positive and negative dust particles

A dusty plasma crystalline configuration consisting of charged dust grains of alternating charge sign (.../+/-/+/-/+/...) and mass is considered. Both charge and mass of each dust species are taken to be constant. Considering the equations of longitudinal motion, a dispersion relation for linear longitudinal vibrations is derived from first principles and then analyzed. Two harmonic modes are obtained, namely, an acoustic mode and an inverse-dispersive optic-like one. The nonlinear aspects of acoustic longitudinal dust grain motion are addressed via a generalized Boussinesq (and, alternatively, a generalized Korteweg-de Vries) description. (C) 2005 American Institute of Physics.

Localized excitations of charged dust grains in dusty plasma lattices

The nonlinear aspects of charged dust grain motion in a one-dimensional dusty plasma (DP) monolayer are discussed. Both horizontal (longitudinal, acoustic mode) and vertical (transverse, optic mode) displacements are considered, and various types of localized excitations are reviewed, in a continuum approximation. Dust crystals are shown to support nonlinear kink-shaped supersonic longitudinal solitary excitations, as well as modulated envelope (either longitudinal or transverse) localized modes. The possibility for Discrete Breather (DB-) type excitations (Intrinsic Localized Modes, ILMs) to occur is investigated, from first principles. These highly localized excitations owe their existence to lattice discreteness, in combination with the interaction and/or
substrate (sheath) potential nonlinearity. This possibility may open new directions in DP- related research. 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.

Nonlinearly coupled whistlers and dust-acoustic perturbations in dusty plasmas

The nonlinear interaction between magnetic-field-aligned coherent whistlers and dust-acoustic perturbations (DAPs) in a magnetized dusty plasma is considered. The interaction is governed by a pair of equations consisting of a nonlinear Schrodinger equation for the modulated whistler wave packet and an equation for the nonresonant DAPs in the presence of the ponderomotive force generated by the whistlers. The coupled equations are employed to investigate the occurrence of modulational instability, in addition to the formation of whistler envelope solitons. This investigation is relevant to amplitude modulated electron whistlers in magnetized space dusty plasmas. (c) 2005 American Institute of Physics.

Stability of dust lattice modes in the presence of charged dust grain polarization in plasmas

We discuss the effect of the attractive force associated with overlapping Debye spheres on the dispersion properties of the longitudinal and transverse dust lattice waves in strongly coupled dust crystals. The dust grain attraction is shown to contribute to a destabilization of the longitudinal dust lattice oscillations. The (optic-like) transverse mode dispersion law is shown to change. due to the Debye sphere dressing effect, from the known inverse-dispersive ("backward wave") form into a normal dispersive law (i.e. the group velocity changes sign). The stability of one-dimensionless bi-layers, consisting of (alternating) negatively and positively charged dust particles, is also discussed. The range of parameter values (mainly in terms of the lattice parameter kappa) where the above predictions are valid, are presented. (c) 2005 Elsevier B.V. All rights reserved.