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.

Nonlinear Lagrangian theory of envelope electrostatic plasma waves in a two-electron-temperature plasma

An analytical model based on Lagrangian variables is presented for the description of ion-acoustic waves propagating in an unmagnetized, collisionless, three-component plasma composed of inertial positive ions and two thermalized electron populations, characterized by different temperatures. The wave's amplitude is shown to be modulationally unstable. Different types of localized envelope electrostatic excitations are shown to exist, and their forms are analytically and numerically investigated in terms of the plasma dispersion and nonlinearity laws. These results are in qualitative agreement with satellite observations in the magnetosphere. (C) 2004 American Institute of Physics.

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.

Weakly nonlinear effects associated with transverse oscillations in dusty plasma crystals

We study the amplitude modulation of transverse dust lattice waves (TDLW) propagating in a single- and double-layer dusty plasma (DP) crystal. It is shown that a modulational instability mechanism, which is related to an intrinsic nonlinearity of the sheath electric field, may occur under certain conditions. Possibility of the formation of localized excitations (envelope solitons) in the dusty plasma crystal is discussed.

Nonlinear propagation of electromagnetic waves in negative-refraction-index composite materials

We investigate the nonlinear propagation of electromagnetic waves in left-handed materials. For this purpose, we consider a set of coupled nonlinear Schrodinger (CNLS) equations, which govern the dynamics of coupled electric and magnetic field envelopes. The CNLS equations are used to obtain a nonlinear dispersion, which depicts the modulational stability profile of the coupled plane-wave solutions in left-handed materials. An exact (in)stability criterion for modulational interactions is derived, and analytical expressions for the instability growth rate are obtained.

Nonlinear compressional electromagnetic ion-cyclotron wavepackets in space plasmas

The parametric coupling between large amplitude magnetic field-aligned circularly polarized electromagnetic ion-cyclotron (EMIC) waves and ponderomotively driven ion-acoustic perturbations in magnetized space plasmas is considered. A cubic nonlinear Schrodinger equation for the modulated EMIC wave envelope is derived, and then solved analytically. The modulated EMIC waves are found to be stable (unstable) against ion-acoustic density perturbations, in the subsonic (supersonic, respectively) case, and they may propagate as "supersonic bright" ("subsonic dark", i.e. "black" or "grey") type envelope solitons, i.e. electric field pulses (holes, voids), associated with (co-propagating) density humps. Explicit bright and dark (black/grey) envelope excitation profiles are presented, and the relevance of our investigation to space plasmas is discussed.

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.

Nonlinear propagation of modulated ion-acoustic plasma waves in the presence of an electron beam

Theoretical and numerical studies are presented of the amplitude modulation of ion-acoustic waves (IAWs) in a plasma consisting of warm ions, Maxwellian electrons, and a cold electron beam. Perturbations parallel to the carrier IAW propagation direction have been investigated. The existence of four distinct linear ion acoustic modes is shown, each of which possesses a different behavior from the modulational stability point of view. The stability analysis, based on a nonlinear Schrodinger equation (NLSE) reveals that the IAW may become unstable. The stability criteria depend on the IAW carrier wave number, and also on the ion temperature, the beam velocity and the beam electron density. Furthermore, the occurrence of localized envelope structures (solitons) is investigated, from first principles. The numerical analysis shows that the two first modes (essentially IAWs, modified due to the beam) present a complex behavior, essentially characterized by modulational stability for large wavelengths and instability for shorter ones. Dark-type envelope excitations (voids, holes) occur in the former case, while bright-type ones (pulses) appear in the latter. The latter two modes are characterized by an intrinsic instability, as the frequency develops a finite imaginary part for small ionic temperature values. At intermediate temperatures, both bright- and dark-type excitations may exist, although the numerical landscape is intertwined between stability and instability regions.(c) 2006 American Institute of Physics.

Nonlinear perpendicular propagation of ordinary mode electromagnetic wave packets in pair plasmas and electron-positron-ion plasmas

The nonlinear amplitude modulation of electromagnetic waves propagating in pair plasmas, e.g., electron-positron or fullerene pair-ion plasmas, as well as three-component pair plasmas, e.g., electron-positron-ion plasmas or doped (dusty) fullerene pair-ion plasmas, assuming wave propagation in a direction perpendicular to the ambient magnetic field, obeying the ordinary (O-) mode dispersion characteristics. Adopting a multiple scales (reductive perturbation) technique, a nonlinear Schrodinger-type equation is shown to govern the modulated amplitude of the magnetic field (perturbation). The conditions for modulation instability are investigated, in terms of relevant parameters. It is shown that localized envelope modes (envelope solitons) occur, of the bright- (dark-) type envelope solitons, i.e., envelope pulses (holes, respectively), for frequencies below (above) an explicit threshold. Long wavelength waves with frequency near the effective pair plasma frequency are therefore unstable, and may evolve into bright solitons, while higher frequency (shorter wavelength) waves are stable, and may propagate as envelope holes.(c) 2007 American Institute of Physics.

Nonlinear modulation of ion-acoustic waves in two-electron-temperature plasmas

The amplitude modulation of ion-acoustic waves IS investigated in a plasma consisting of adiabatic warm ions, and two different populations of thermal electrons at different temperatures. The fluid equations are reduced to nonlinear Schrodinger equation by employing a multi-scale perturbation technique. A linear stability analysis for the wave packet amplitude reveals that long wavelengths are always stable, while modulational instability sets in for shorter wavelengths. It is shown that increasing the value of the hot-to-cold electron temperature ratio (mu), for a given value of the hot-to-cold electron density ratio (nu): favors instability. The role of the ion temperature is also discussed. In the limiting case nu = 0 (or nu -> infinity). which correspond(s) to an ordinary (single) electron-ion plasma, the results of previous works are recovered.

Nonlinear Dynamics of Rotating Multi-Component Pair Plasmas and e-p-i Plasmas

The propagation of small amplitude stationary profile nonlinear electrostatic excitations in a pair plasma is investigated, mainly drawing inspiration from experiments on fullerene pair-ion plasmas. Two distinct pair ion species are considered of opposite polarity and same mass, in addition to a massive charged background species, which is assumed to be stationary, given the frequency scale of interest. In the pair-ion context, the third species is thought of as a background defect (e.g. charged dust) component. On the other hand, the model also applies formally to electron-positron-ion (e-p-i) plasmas, if one neglects electron-positron annihilation. A two-fluid plasma model is employed, incorporating both Lorentz and Coriolis forces, thus taking into account the interplay between the gyroscopic (Larmor) frequency ?c and the (intrinsic) plasma rotation frequency O0. By employing a multi-dimensional reductive perturbation technique, a Zakharov-Kuznetsov (ZK) type equation is derived for the evolution of the electric potential perturbation. Assuming an arbitrary direction of propagation, with respect to the magnetic field, we derive the exact form of nonlinear solutions, and study their characteristics. A parametric analysis is carried out, as regards the effect of the dusty plasma composition (background number density), species temperature(s) and the relative strength of rotation to Larmor frequencies. It is shown that the Larmor and mechanical rotation affect the pulse dynamics via a parallel-to-transverse mode coupling diffusion term, which in fact diverges at ?c ? ±2O0. Pulses collapse at this limit, as nonlinearity fails to balance dispersion. The analysis is complemented by investigating critical plasma compositions, in fact near-symmetric (T- ˜ T+) “pure” (n- ˜ n+) pair plasmas, i.e. when the concentration of the 3rd background species is negligible, case in which the (quadratic) nonlinearity vanishes, so one needs to resort to higher order nonlinear theory. A modified ZK equation is derived and analyzed. Our results are of relevance in pair-ion (fullerene) experiments and also potentially in astrophysical environments, e.g. in pulsars.