Exact theory for localized envelope modulated electrostatic wavepackets in space and dusty plasmas

Abundant evidence for the occurrence of modulated envelope plasma wave packets is provided by recent satellite missions. These excitations are characterized by a slowly varying localized envelope structure, embedding the fast carrier wave, which appears to be the result of strong modulation of the wave amplitude. This modulation may be due to parametric interactions between different modes or, simply, to the nonlinear (self-)interaction of the carrier wave. A generic exact theory is presented in this study, for the nonlinear self-modulation of known electrostatic plasma modes, by employing a collisionless fluid model. Both cold (zero-temperature) and warm fluid descriptions are discussed and the results are compared. The (moderately) nonlinear oscillation regime is investigated by applying a multiple scale technique. The calculation leads to a Nonlinear Schrodinger-type Equation (NLSE), which describes the evolution of the slowly varying wave amplitude in time and space. The NLSE admits localized envelope (solitary wave) solutions of bright(pulses) or dark- (holes, voids) type, whose characteristics (maximum amplitude, width) depend on intrinsic plasma parameters. Effects like amplitude perturbation obliqueness (with respect to the propagation direction), finite temperature and defect (dust) concentration are explicitly considered. Relevance with similar highly localized modulated wave structures observed during recent satellite missions is discussed.

Modulational instability of dust acoustic waves in dusty plasmas: Modulation obliqueness, background ion nonthermality, and dust charging effects

The oblique modulational instability of dust acoustic (DA) waves in an unmagnetized warm dusty plasma with nonthermal ions, taking into account dust grain charge variation (charging), is investigated. A nonlinear Schrodinger-type equation governing the slow modulation of the wave amplitude is derived. The effects of dust temperature, dust charge variation, ion deviation from Maxwellian equilibrium (nonthermality) and constituent species' concentration on the modulational instability of DA waves are examined. It is found that these parameters modify significantly the oblique modulational instability domain in the k-theta plane. Explicit expressions for the instability rate and threshold have been obtained in terms of the dispersion laws of the system. The possibility and conditions for the existence of different types of localized excitations are also discussed. The findings of this investigation may be useful in understanding the stable electrostatic wave packet acceleration mechanisms close to the Moon, and also enhances our knowledge on the occurrence of instability associated to pickup ions around unmagnetized bodies, such as comets, Mars, and Venus.

Electrostatic mode envelope excitations in e-p-i plasmas - application in warm pair ion plasmas with a small fraction of stationary ions

The nonlinear propagation of amplitude-modulated electrostatic wavepackets in an electron-positron-ion (e-p-i) plasma is considered, by employing a two-fluid plasma model. Considering propagation parallel to the external magnetic field, two distinct electrostatic modes are obtained, namely a quasi-thermal acoustic-like lower mode and a Langmuir-like optic-type upper one. These results equally apply in warm pair ion ( e. g. fullerene) plasmas contaminated by a small fraction of stationary ions ( or dust), in agreement with experimental observations and theoretical predictions in pair plasmas. Considering small yet weakly nonlinear deviations from equilibrium, and adopting a multiple-scales perturbation technique, the basic set of model equations is reduced to a nonlinear Schrodinger (NLS) equation for the slowly varying electric field perturbation amplitude. The analysis reveals that the lower ( acoustic) mode is mostly stable for large wavelengths, and may propagate in the form of a dark-type envelope soliton ( a void) modulating a carrier wavepacket, while the upper linear mode is intrinsically unstable, and thus favours the formation of bright-type envelope soliton ( pulse) modulated wavepackets. The stability ( instability) range for the acoustic ( Langmuir-like optic) mode shifts to larger wavenumbers as the positive-to-negative ion temperature ( density) ratio increases. These results may be of relevance in astrophysical contexts, where e-p-i plasmas are encountered, and may also serve as prediction of the behaviour of doped ( or dust-contaminated) fullerene plasmas, in the laboratory.

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.

Low frequency localized wavepackets in dusty plasmas with opposite charge polarity dust components

The reductive perturbation technique is employed to investigate the modulational instability of dust-acoustic (DA) waves propagating in a four-component dusty plasma. The dusty plasma consists of both positive- and negative-charge dust grains, characterized by a different mass, temperature and density, in addition to a background of Maxwellian electrons and ions. Relying on a multi-fluid plasma model and employing a multiple scales technique, a nonlinear Schrodinger type equation (NLSE) is obtained for the electric potential amplitude perturbation. The occurrence of localized electrostatic wavepackets is shown, in the form of oscillating structures whose modulated envelope is modelled as a soliton (or multi-soliton) solution of the NLSE. The DA wave characteristics, as well as the associated stability thresholds, are studied analytically and numerically. The relevance of these theoretical results with dusty plasmas observed in cosmic and laboratory environments is analysed in detail, by considering realistic multi-component plasma configurations observed in the polar mesosphere, as well as in laboratory experiments.

Evolution of linearly polarized electromagnetic pulses in laser plasmas

An analytical and numerical investigation is presented of the behavior of a linearly polarized electromagnetic pulse as it propagates through a plasma. Considering a weakly relativistic regime, the system of one-dimensional fluid-Maxwell equations is reduced to a generalized nonlinear Schrodinger type equation, which is solved numerically using a split step Fourier method. The spatio-temporal evolution of an electromagnetic pulse is investigated. The evolution of the envelope amplitude of density harmonics is also studied. An electromagnetic pulse propagating through the plasma tends to broaden due to dispersion, while the nonlinear frequency shift is observed to slow down the pulse at a speed lower than the group velocity. Such nonlinear effects are more important for higher density plasmas. The pulse broadening factor is calculated numerically, and is shown to be related to the background plasma density. In particular, the broadening effect appears to be stronger for dense plasmas. The relation to existing results on electromagnetic pulses in laser plasmas is discussed. (c) 2008 American Institute of Physics.

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).

Electromagnetic envelope solitons in magnetized plasma

A multiple scales technique is employed to solve the fluid-Maxwell equations describing a weakly nonlinear circularly polarized electromagnetic pulse in magnetized plasma. A nonlinear Schrodinger-type (NLS) equation is shown to govern the amplitude of the vector potential. The conditions for modulational instability and for the existence of various types of localized envelope modes are investigated in terms of relevant parameters. Right-hand circularly polarized (RCP) waves are shown to be modulationally unstable regardless of the value of the ambient magnetic field and propagate as bright-type solitons. The same is true for left-hand circularly polarized (LCP) waves in a weakly to moderately magnetized plasma. In other parameter regions, LCP waves are stable in strongly magnetized plasmas and may propagate as dark-type solitons (electric field holes). The evolution of envelope solitons is analyzed numerically, and it is shown that solitons propagate in magnetized plasma without any essential change in amplitude and shape. (C) 2009 Elsevier B.V. All rights reserved.

Fokker-Planck equation for a test-particle weakly coupled to a magnetized plasma

We consider the derivation of a kinetic equation for a charged test particle weakly interacting with an electrostatic plasma in thermal equilibrium, subject to a uniform external magnetic field. The Liouville equation leads to a generalized master equation to second order in the `weak' interaction; a Fokker-Planck-type equation then follows as a `Markovian' approximation. It is shown that such an equation does not preserve the positivity of the distribution function f(x,v;t). By applying techniques developed in the theory of open systems, a correct Fokker-Planck equation is derived. Explicit expressions for the diffusion and drift coefficients, depending on the magnetic field, are obtained.

A comparison of nonstaggered compact FDTD schemes for the 3D wave equation

This paper aims at providing a better insight into the 3D approximations of the wave equation using compact finite-difference time-domain (FDTD) schemes in the context of room acoustic simulations. A general family of 3D compact explicit and implicit schemes based on a nonstaggered rectilinear grid is analyzed in terms of stability, numerical error, and accuracy. Various special cases are compared and the most accurate explicit and implicit schemes are identified. Further considerations presented in the paper include the direct relationship with other numerical approaches found in the literature on room acoustic modeling such as the 3D digital waveguide mesh and Yee's staggered grid technique.

Berry phase in open quantum systems: a quantum Langevin equation approach

The evolution of a two level system with a slowly varying Hamiltonian, modeled as a spin 1/2 in a slowly varying magnetic field, and interacting with a quantum environment, modeled as a bath of harmonic oscillators is analyzed using a quantum Langevin approach. This allows to easily obtain the dissipation time and the correction to the Berry phase in the case of an adiabatic cyclic evolution.

CRITICAL PROCESSES, LANGEVIN EQUATION AND UNIVERSALITY

In nature there are ubiquitous systems that can naturally approach critical states, The Langevin equation in the discrete version can be used to describe a class of critical processes, which are characterized by power-law behaviors and scaling relations. As an example, we present a simple model for a clinical thermometer, whose reading cannot fall even when its temperature decreases. The fibers bundle model and the spring-block model are also shown to belong to such a class.

Note on the single-shock solutions of the Korteweg-de Vries-Burgers equation

The well-known shock solutions of the Korteweg-de Vries-Burgers equation are revisited, together with their limitations in the context of plasma (astro)physical applications. Although available in the literature for a long time, it seems to have been forgotten in recent papers that such shocks are monotonic and unique, for a given plasma configuration, and cannot show oscillatory or bell-shaped features. This uniqueness is contrasted to solitary wave solutions of the two parent equations (Korteweg-de Vries and Burgers), which form a family of curves parameterized by the excess velocity over the linear phase speed.

Nonlinear wavepackets in pair-ion and electron-positron-ion plasmas

The occurrence of amplitude-modulated electrostatic and electromagnetic
wavepackets in pair plasmas is investigated. A static additional charged background species is considered, accounting for dust defects or for heavy ion
presence in the background. Relying on a two-fluid description, a nonlinear
Schrodinger type evolution equation is obtained and analyzed, in terms of the
slow dynamics of the wave amplitude. Exact envelope excitations are obtained,
modelling envelope pulses or holes, and their characteristics are discussed.