Sheared Flow Driven Drift Instability and Vortices in Dusty Plasmas with Opposite Polarity

Low-frequency electrostatic drift waves are studied in an inhomogeneous dust magnetoplasma containing dust with components of opposite polarity. The drift waves are driven by the magnetic-field-aligned (parallel) sheared flows in the presence of electrons and ions. Due to sheared flow in the linear regime, the electrostatic dust drift waves become unstable. The conditions of mode instability, with the effects of dust streaming and opposite polarity, are studied. These are excited modes which gain large amplitudes and exhibit interactions among themselves. The interaction is governed by the Hasegawa-Mima (HM) nonlinear equation with vector nonlinearity. The stationary solutions of the HM equation in the form of a vortex chain and a dipolar vortex, including effects of dust polarity and electron (ion) temperatures, are studied. The relevance of the present work to space and laboratory four component dusty plasmas is noted.     

磁化等离子体中静电漂移波和剪切阿耳芬波的非线性耦合

本文采用Hasegawa-Wakatani方程组研究磁化等离子体中静电漂移波和剪切阿耳芬波的非线性耦合。求得非线性方程组的偶极涡旋解。这些解属于本性电磁涡旋,对应的扰动磁场和纵向电流在涡旋边界上是连续的。 关键词：     

On some properties of linear and nonlinear waves in pair-ion plasmas

It is pointed out that the observation of the electrostatic ion acoustic wave frequency can be a suitable check to determine whether the produced plasma is a pure pair-ion plasma or whether it comprises some concentration of electrons. A theoretical model for the pair-ion plasma dynamics is presented along with a new electrostatic mode which can exist only in such systems. It can become unstable in the presence of shear flow and it can give rise to vortex structures in the nonlinear regime. The possibility of shocks and solitons, due to nonlinear drift waves in a pair-ion plasma comprising electrons, is also discussed. The relevance of this investigation to both laboratory and astrophysical plasmas is pointed out.     

A new spiky soliton and an explosive mode of the nonlinear driftwave equation

A new type of nonlinear wave modes which occurs in the electrostatic drift waves in an inhomogeneous magnetized plasma is presented. The author predicts the existence of a new type of spiky solitary wave and an explosive mode with a negative potential as stationary solutions of this equation. These solutions are a consequence of a density gradient and not connected with a temperature gradient. These new nonlinear wave solutions appear to make a step forward in the general scheme of nonlinear normal modes for plasma waves. Using these nonlinear wave modes, the author can explain the solitary structure and the explosive event concerning nonlinear drift waves propagating in space     

Formation of solitons and shocks in toroidal ion temperature gradient mode in the presence of non-Maxwellian electrons

Linear and nonlinear phenomena are investigated in toroidal ion temperature gradient (TITG)-driven pure drift mode. The model includes inhomogeneity in background magnetic field, ion temperature, and density. Finite Larmor radius effect is incorporated to understand the effect of low-frequency wave on ion dynamics. Electrons are assumed to follow nonthermal distribution, that is, kappa and Cairns distributions. Dispersion relation is obtained to analyse the linear behaviour of the TITG mode in the presence of non-Maxwellian electron distribution. In the nonlinear regime, exact solutions (soliton and shocks) are obtained (in dispersive and dissipative medium respectively) by using functional variable method to solve the nonlinear partial differential equation obtained for the system under consideration. Graphical illustrations are used to exhibit the characteristics of linear and nonlinear structures and their dependence on different physical parameters. It is observed that for TITG-driven pure drift mode, rarefactive solitons are formed for both thermal and nonthermal electron distributions. It is also observed that variation of electrons from standard thermal distribution affects the propagation characteristics of linear and nonlinear structures in TITG-driven modes. Results of our investigations will be helpful to understand the low-frequency waves in inhomogeneous plasmas in the presence of nonthermal electron distributions which are frequently observed by satellite missions and are also observed in laboratory plasmas.     

Steady vortices in plasmas and geophysical flows

A number of two-dimensional fluid models in geophysical fluid dynamics and plasma physics are examined to find out whether they have steady and localized monopole vortex solutions. A simple and general method that consists of two steps is used. First the dispersion relation is calculated, to find all possible values of the phase velocity of the linear waves. Then an integral relation that determines the center-of-mass velocity of localized structures must be found. The existence condition is that this velocity should be outside the region of linear phase velocities. After a presentation of the method, previous work on the plasma drift wave model and the shallow-water equations is reviewed. In both cases it is found that the center-of-mass velocity is larger than the maximum phase velocity of the linear waves if the amplitude is large enough, and steady localized vortices can therefore exist. New results are then obtained for a number of two-field models. For the coupled ion acoustic-drift modes in plasmas, it is found that the center-of-mass velocity depends on the ratio between the parallel ion velocity component and the electrostatic potential in the vortex. If this ratio is large enough, the vortex can be steady. For the drift-Alfven mode the "center-of-charge" velocity is proportional to the ratio between the parallel current and the total charge in the vortex. It can therefore be steady if this ratio satisfies the appropriate conditions. For the quasigeostrophic two-layer equations, describing stratified flow on a rotating planet, it is found that the center-of-mass velocity is determined by the ratio between the baroclinic and the barotropic components in the vortex. If a baroclinic component with an appropriate sign is added to a barotropic vortex, it propagates faster than the barotropic Rossby waves, and can be steady. Finally, the existence conditions for a vortex in an external zonal flow are examined. It is found that the center-of-mass velocity acquires an additional westward contribution in an anticyclonic shear zone in the framework of the shallow-water equations, and also that an easterly jet south of this shear zone partly shields a vortex situated in the shear zone from the dispersive influence of the fast Rossby waves on the equatorward side.     

Nonlinear propagation of weakly relativistic ion-acoustic waves in electron–positron–ion plasma

This work presents theoretical and numerical discussion on the dynamics of ion-acoustic solitary wave for weakly relativistic regime in unmagnetized plasma comprising non-extensive electrons, Boltzmann positrons and relativistic ions. In order to analyse the nonlinear propagation phenomena, the Korteweg–de Vries (KdV) equation is derived using the well-known reductive perturbation method. The integration of the derived equation is carried out using the ansatz method and the generalized Riccati equation mapping method. The influence of plasma parameters on the amplitude and width of the soliton and the electrostatic nonlinear propagation of weakly relativistic ion-acoustic solitary waves are described. The obtained results of the nonlinear low-frequency waves in such plasmas may be helpful to understand various phenomena in astrophysical compact object and space physics.     

Nonlinear propagation of fast and slow magnetosonic waves in collisional plasmas

Low-frequency fast and slow magnetosonic waves propagating in electron ion plasmas with damping effects through ions and neutral atoms collisions are investigated. Linear wave analysis is performed to obtain dispersion relation. The reductive perturbation method is applied and it is shown that fast and slow modes of nonlinear magnetosonic wave are governed by damped Korteweg-de Vries (DKdV) equation in the presence of ion neutral collisions in plasmas. The analytical solution of DKdV soliton is presented under the assumption of weak collisional effects and numerical solutions of DKdV equation are also obtained using two-level finite difference scheme with the help of Runge–Kutta method at different plasma parameters. The damping of nonlinear fast and slow magnetosonic wave structures at different times are discussed in the context of space plasma situations where ions and neutral atoms collisions exist.     

On Modulational Interaction of the Lower-Hybrid Drift Oscillations

The general nonlinear equation of the third order in field strength for the lower-hybrid drift waves in inhomogeneous plasma is obtained on the basis of kinetic theory. This equation enables us to describe strong turbulence effects (modulational instability, soliton-like solutions, etc.) as well as weak turbulence effects (decays, scattering). The investigation of the modulational instability of the lower-hybrid drift waves is carried out. It is demonstrated that the development of the lower-hybrid drift wave modulational instability is possible only when the wavevector of the modulational perturbations is less or of the order of the wavevector of the pump wave. The condition on the wave vectors, when the nonlinear response defining the character of the modulational instability is determined by the inhomogeneity effects, is obtained.     

Freak waves in laboratory and space plasmas

Generation of large-amplitude short-lived wave groups from small-amplitude initial perturbations in plasmas is discussed. Two particular wave modes existing in plasmas are considered. The first one is the ion-sound wave. In a plasmas with negative ions it is described by the Gardner equation when the negative ion concentration is close to critical. The results of numerical solution of the Gardner equation with the modulationally unstable initial condition are presented. These results clearly show the possibility of generation of freak ion-acoustic waves due to the modulational instability. The second wave mode is the Alfvén wave. When this wave propagates at a small angle with respect to the equilibrium magnetic field, and its wave length is comparable with the ion inertia length, it is described by the DNLS equation. Studying the evolution of an initial perturbation using the linearized DNLS equation shows that the generation of freak Alfvén waves is possible due to linear dispersive focusing. The numerical solution of the DNLS equation reveals that the nonlinear dispersive focusing can also produce freak Alfvén waves.     

Novel solitary and shock wave solutions for the generalized variable-coefficients (2+1)-dimensional KP-Burger equation arising in dusty plasma

The 2-D generalized variable-coefficient Kadomtsev-Petviashvili-Burgers equation representing many types of acoustic waves in cosmic and/or laboratory dusty plasmas is reduced by the modified classical direct similarity reduction method to nonlinear ordinary differential equation of fourth-order. Using the extended Riccati equation mapping method for solving the reduced equation, many new shock wave, solitary wave and periodic wave solutions are obtained with some constraints between the variable coefficients. Finally, some physical interpretations for the obtained solutions as, bright and dark solitons, periodic solitary wave, and shock wave in dust plasma and quantum plasma are achieved.     

Resonant excitation and nonlinear evolution of waves in the equatorial waveguide in the presence of the mean current

We study interactions of planetary waves propagating across the equator with trapped Rossby or Yanai modes, and the mean flow. The equatorial waveguide with a mean current acts as a resonator and responds to planetary waves with certain wave numbers by making the trapped modes grow. Thus excited waves reach amplitudes greatly exceeding the amplitude of the incoming wave. Nonlinear saturation of the excited waves is described by an amplitude equation with one or two attracting equilibrium solutions. In the latter case spatial modulation leads to formation of characteristic defects in the wave field. The evolution of the envelopes of long trapped Rossby waves is governed by the driven complex Ginzburg-Landau equation, and by the damped-driven nonlinear Schr?dinger equation for short waves. The envelopes of the Yanai waves obey a simple wave equation with cubic nonlinearity.     

Electron-acoustic supernonlinear waves and their multistability in the framework of the nonlinear Schrödinger equation

Finite-amplitude supernonlinear electron-acoustic waves (EAWs) are investigated under the nonlinear Schrödinger (NLS) equation in a plasma system that is composed of cold electron fluid, immobile ions and q-nonextensive hot electrons. Using the wave transfiguration, the NLS equation is deduced in a dynamical system. The presence of finite-amplitude nonlinear and supernonlinear EAWs is shown by phase plane analysis. The effects of the nonextensive parameter (q) and the speed of waves (v) on different traveling wave solutions of EAWs are presented. Furthermore, by introducing a small external periodic force in the dynamical system, multistability behaviors of EAWs under the NLS equation are shown for the first time in classical plasmas.     

Formation and dynamics of relativistic electromagnetic solitons in plasmas containing high-and low-energy electron components

We present theoretical and numerical studies of the nonlinear interactions between intense electromagnetic waves in plasmas containing high-and low-energy electron components. Such plasmas are frequently observed in laser-plasma experiments, where the hot electron component is created by the acceleration of electrons by strong electrostatic waves that are created by the laser-induced Raman forward and backward instabilities. The two-component electron plasma is described by the Vlasov equation for the hot electrons and the hydrodynamic equations for the cold electrons, which are coupled nonlinearly to the electromagnetic wave equation and the Poisson equation for the potential. The present nonlinear system is shown to admit electromagnetic solitary waves correlated with a positive potential and trapped electron islands from the hot electron population. The text was submitted by the authors in English.     

Vortices in an anisotropic plasma

Localized electrostatic nonlinear drift wave structures in a plasma with hot electrons and anisotropic ions are considered. The anisotropic energy distribution leads to a new nonlinearity in the evolution equation of finite amplitude drift waves. One- and two-dimensional solutions of physical interest are presented.     

Nonlinear Evolution of Driven Electron Plasma Oscillations in Inhomogeneous Plasmas

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Linear and Nonlinear Magnetic Electron Drift Waves in a Nonuniform Strong Magnetic Field

Linear and nonlinear propagation of magnetic electron drift vortex waves in a nonuniform magnetic field is investigated by means of a generalized adiabatic law which takes into account the effect of strong fields and reduces in the appropriate limits to several well known energy conservation equations in a collisionless plasma. In the linear limit, an instability is shown to exist, whereas in the nonlinear regime, steady-state dipole vortices associated with the electron drift vortex waves may appear. The anomalous electron energy transport associated with the unstable magnetic electron drift vortex waves is investigated by means of a quasilinear theory.     

[Russian Text Ignored]

The plasmon turbulence parametrically excited by two strong external waves with a frequency difference close to twice the electron plasma frequency is investigated in underdense plasmas. The nonlinear stabilization of the growing plasmons due to scattering by ions is described by a nonlinear integro-differential equation for the spectral plasmon energy density. The dependence of the turbulent relaxation of the plasmon energy and its stationary level on the parameters of the plasma and the pump waves is given by analytical and numerical solutions of this equation.     

Drift vortices in inhomogeneous collisional dusty magnetoplasma

For the sake of investigating the drift coherent vortex structure in an inhomogeneous dense dusty magnetoplasma,using the quantum hydrodynamic model a nonlinear controlling equation is deduced when the collision effect is considered.New vortex solutions of the electrostatic potential are obtained by a special transformation method, and three evolutive cases of monopolar vortex chains with spatial and temporal distribution are analyzed by representative parameters. It is found that the collision frequency, particle density, drift velocity, dust charge number, electron Fermi wavelength, quantum correction,and quantum parameter are all influencing factors of the vortex evolution. Compared to the uniform dusty system, the vortex solutions of the inhomogeneous system present richer spatial evolution and physical meaning. These results may explain corresponding vortex phenomena and support beneficial references for the dense dusty plasma atmosphere.