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.

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.

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.

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.

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.

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.

Dust-acoustic wave modulation in the presence of superthermal ions

A study is presented of the nonlinear self-modulation of low-frequency electrostatic (dust acoustic) waves propagating in a dusty plasma, in the presence of a superthermal ion (and Maxwellian electron) background. A kappa-type superthermal distribution is assumed for the ion component, accounting for an arbitrary deviation from Maxwellian equilibrium, parametrized via a real parameter kappa. The ordinary Maxwellian-background case is recovered for kappa ->infinity. By employing a multiple scales technique, a nonlinear Schrodinger-type equation (NLSE) is derived for the electric potential wave amplitude. Both dispersion and nonlinearity coefficients of the NLSE are explicit functions of the carrier wavenumber and of relevant physical parameters (background species density and temperature, as well as nonthermality, via kappa). The influence of plasma background superthermality on the growth rate of the modulational instability is discussed. The superthermal feature appears to control the occurrence of modulational instability, since the instability window is strongly modified. Localized wavepackets in the form of either bright-or dark-type envelope solitons, modeling envelope pulses or electric potential holes (voids), respectively, may occur. A parametric investigation indicates that the structural characteristics of these envelope excitations (width, amplitude) are affected by superthermality, as well as by relevant plasma parameters (dust concentration, ion temperature).

Spatial evolution of a q-Gaussian laser beam in relativistic plasma

In a recent experimental study, the beam intensity profile of the Vulcan petawatt laser beam was measured; it was found that only 20% of the energy was contained within the full width at half maximum of 6.9 mu m and 50% within 16 mu m, suggesting a long-tailed non-Gaussian transverse beam profile. A q-Gaussian distribution function was suggested therein to reproduce this behavior. The spatial beam profile dynamics of a q-Gaussian laser beam propagating in relativistic plasma is investigated in this article. A non-paraxial theory is employed, taking into account nonlinearity via the relativistic decrease of the plasma frequency. We have studied analytically and numerically the dynamics of a relativistically guided beam and its dependence on the q-parameter. Numerical simulation results are shown to trace the dependence of the focusing length on the q-Gaussian profile.

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.