Dust acoustic waves in a collisional strongly coupled dusty plasmas

Progress in understanding the nonlinear features of dust-acoustic waves (DAWs) which accompany a collisional strongly and weakly coupled unmagnetized dusty plasma with Boltzmann distributed electrons, ions and negatively charged dust grains is presented. By using a hydrodynamic model, the Korteweg–de Vries-Burgers (KdV-Burgers) equation is derived. The existence regions of the solitary pulses are defined precisely. Furthermore, numerical calculations reveal that, due to collisions, the DAWs damp waves and the damping rate of the waves depends mainly on the collision frequency. The collisions are found to significantly change the basic properties of the DAWs. The effects of electron-to-ion concentration ratio, and ion-to-electron temperature ratio have important roles in the behavior of the DAWs. The results may have relevance in space and laboratory dusty plasmas.     

Cylindrical and spherical positron-acoustic Gardner solitons in electron-positron-ion plasmas with nonthermal electrons and positrons

A theoretical investigation has been performed on the nonlinear propagation of nonplanar (cylindrical and spherical) Gardner solitons (GSs) associated with the positron-acoustic (PA) waves in a four component plasma system consisting of nonthermal distributed electrons and hot positrons, mobile cold positrons, and immobile positive ions. The well-known reductive perturbation method has been employed to derive the modified Gardner (MG) equation. The basic features (viz. amplitude, polarity, speed, etc.) of nonplanar PA Gardner solitons (GSs) have been examined by the numerical analysis of the MG equation. It has been observed that the properties of the PA GSs in a nonplanar geometry differ from those in a planar geometry. It has been also investigated that the presence of nonthermal (Cairns distributed) electrons and hot positrons significantly modify the amplitude, polarity, speed, and thickness of such PA GSs. The results of our investigation should play an important role in understanding various interstellar space plasma environments as well as laboratory plasmas.     

Solitary solution and energy for the Kadomstev–Petviashvili equation in two temperatures charged dusty grains

The nonlinear properties of small amplitude dust-acoustic solitary waves (DAWs) in a homogeneous unmagnetized plasma having electrons, singly charged ions, hot and cold dust species with Boltzmann distributions for electrons and ions have been investigated. A reductive perturbation method was employed to obtain the Kadomstev-Petviashvili (KP) equation. The effects of the presence of charged hot and cold dust grains on the nature of DAWs were discussed. Moreover, the energy of two temperatures charged dusty grains were computed. The present investigation can be of relevance to the electrostatic solitary structures observed in various space plasma environments.     

Dust-acoustic solitary waves and double layers with two temperature ions in a nonextensive dusty plasma

Small amplitude dust-acoustic solitary waves in an unmagnetized dusty plasma consisting of electrons and two temperature ions obeying the q-nonextensive distribution are investigated. Employing reductive perturbation method, the Korteweg-de Vries (KdV) equation is derived. From the solitonic solutions of KdV equation, the influence of nonextensivity of electrons as well as ions and dust concentration on the amplitude and width of dust-acoustic solitary waves has been studied. It is observed that both positive and negative potential dust acoustic solitary waves occur in this case. The modified KdV (mKdV) equation is derived in order to examine the solitonic solutions for the critical plasma parameters for which KdV theory fails. The parametric regimes for the existence of mKdV solitons and double layers (DLs) have also been determined. Positive potential double layers are found to occur in the present study.     

Arbitrary amplitude ion-acoustic solitons in two-electron temperature warm ion plasma

The large amplitude Ion-acoustic solitons in collisionless plasma consisting of warm adiabatic ions, isothermal positrons and two-temperature distribution of electrons are investigated. Using pseudo-potential approach, an energy integral equation for the system has been derived which encompasses complete nonlinearity for the plasma system. The existence region of the solitons is analyzed numerically. It is found that for selected set of plasma parameters, both rarefactive and compressive solitons exist in the electron-positron-ion (EPI) plasma. It is also found that due to finite positron concentration both subsonic and supersonic rarefactive soliton exist in EPI plasma. An increase in finite ion temperature ratio decreases the amplitude of the rarefactive solitons. In the case of small amplitude, it is found that there exist supersonic compressive as well as rarefactive solitons simultaneously. The amplitude of the solitons decreases with increase in ion temperature ratio (σ), however an increase in positron concentration (α) and temperature ratio of positron to electrons (γ) increases the amplitude of the solitons. Effect of various plasma parameters on the characteristics of the solitons are discussed in detail. The results of the investigation may be helpful to understand the nonlinear structures in auroral plasma, pulsars and magnetospheric astrophysical environment as well as laboratory plasmas.     

Ion acoustic solitons of KdV and modified KdV equations in weakly relativistic plasma containing nonthermal electron,positron and warm ion

In this paper, the ion-acoustic solitons in a weakly relativistic electron-positron-ion plasma have been investigated. Relativistic ions, Maxwell-Boltzmann distributed positrons and nonthermal electrons are considered in collisionless warm plasma. Using a reductive perturbation theory, a Korteweg-de Vries (KdV) equation is derived, and the relativistic effect on the solitons is studied. It is found that the amplitude of solitary waves of the KdV equation diverges at the critical values of plasma parameters. Finally, in this situation, the solitons of a modified KdV (mKdV) equation with finite amplitude is derived.     

Properties of dispersive Alfven waves: 4. Hydrodynamics (finite and high-pressure plasmas)

The behavior of dispersive Alfven waves (DAWs) in astrophysical plasmas of finite and high pressure, which have not been considered thus far, is studied in the hydrodynamic approximation. The results are analyzed and compared with those obtained in the kinetic approach. It is shown that one general solution for DAWs in plasmas of finite and high pressure can be obtained using the hydrodynamic approach in contrast to the kinetic one. Kinetic and hydrodynamic solutions correspond to each other very well in a domain with weakly damped DAWs; however, solutions may differ appreciably in some parameter domains, especially in high-pressure plasma. The effect of parameters of the astrophysical medium on the DAW behavior and properties is analyzed. All the main wave characteristics were determined: dispersion, damping, polarization, density perturbations, and charge density perturbations. Since finite-pressure plasma is one of the most frequently encountered states of astrophysical plasma, it is very important to take into account specific features in behavior of these waves for their detecting and a more correct understanding of their behavior and the role they play in different astrophysical processes that occur in space environment.     

Fully nonlinear heavy ion-acoustic solitary waves in astrophysical degenerate relativistic quantum plasmas

Fully nonlinear features of heavy ion-acoustic solitary waves (HIASWs) have been investigated in an astrophysical degenerate relativistic quantum plasma (ADRQP) containing relativistically degenerate electrons and non-relativistically degenerate light ion species, and non-degenerate heavy ion species. The pseudo-energy balance equation is derived from the fluid dynamical equations by adopting the well-known Sagdeev-potential approach, and the properties of arbitrary amplitude HIASWs are examined. The small amplitude limit for the propagation of HIASWs is also recovered. The basic features (width, amplitude, polarity, critical Mach number, speed, etc.) of HIASWs are found to be significantly modified by the relativistic effect of the electron species, and also by the variation of the number density of electron, light ion, and heavy ion species. The basic properties of HIASWs, that may propagated in some realistic astrophysical plasma systems (e.g., in white dwarfs), are briefly discussed.     

Kepler’s celestial two-body equation: a second attempt to establish a continuous and integrable solution via the <Emphasis Type="Italic">BPES</Emphasis>: Boubaker Polynomials Expansion Scheme

The propagation of nonlinear waves in warm dusty plasmas with variable dust charge, two-temperature ions, and nonthermal electrons is studied. By using the reductive perturbation theory, the Kadomtsev–Petviashivili (KP) equation is derived. The energy of the soliton has been calculated. By using standard normal modes analysis a linear dispersion relation has been obtained. The effects of variable dust charge on the energy of the soliton and the angular frequency of the linear wave are also discussed. It is shown that the amplitude of solitary waves of the KP equation diverges at the critical values of plasma parameters. We derive solitons of a modified KP equation with finite amplitude in this situation.     

Universal characteristics of ion-acoustic wave dynamics in magnetized plasmas with emphasis on Tsallis distribution

Using the extended Poincaré-Lighthill-Kuo (PLK) reductive perturbation method, which incorporates the phase-shift variations, it is shown that common features on propagation and head-on collisions of ion-acoustic waves exist for a magnetized plasmas of different inertial-less particle distributions. For instance it is remarked that, the soliton amplitude is always independent of magnetic field strength while strictly depends on its angle regarding the propagation direction. Both types of solitons (compressive or rarefactive) are shown to exist which are defined through the critical angle γ=π/2 or other critical values depending on plasma fractional parameters. These critical plasma parameter values also define the sign of head-on collision phase shift. Furthermore, it is proved that for a given set of plasma parameters there is always a relative angle of propagation regarding to that of the magnetic-field for which the soliton width is maximum. Current findings apply to a wide range of magnetized plasmas including those containing background dust ingredients or two-temperature inertial-less particles and may be used to study laboratory or astrophysical magnetoplasmas.     

Dust-acoustic wave modulation in the presence of q-nonextensive electrons and/or ions in dusty plasma

A study is presented of the nonlinear self-modulation of low-frequency electrostatic dust acoustic waves (DAWs) propagating in a dusty plasma, within the theoretical framework of the nonextensive statistics proposed by Tsallis. Using the reductive perturbation method (RPM), the nonlinear Schrödinger equation (NLSE) which governs the modulational instability (MI) of the DAWs is obtained. The presence of the nonextensive electron/ion distribution is shown to influence the MI of the waves. Furthermore it is observed that nonextensive distributed ions has more effect on the MI of the DAW than electrons.     

Solitary waves in a dusty plasma with negatively (positively) charged dust grains and non-thermal electrons

For an unmagnetized multicomponent dusty plasma, the effects of non-thermal electron distribution, ion temperature and two oppositely charged dust grains are incorporated in the study of arbitrary amplitude solitary waves. An energy-like integral equation involving Sagdeev potential is derived, and the existence, formation and basic properties of solitons are studied. It is also found a definite interval for the Mach number for which solitary waves exist and depends sensitively upon the population of fast or non-thermal electrons present. Our results should be useful to understand the properties of localized electrostatic disturbances that may occur in space dusty plasma.     

On the speed and shape of electron acoustic solitary waves

Electron acoustic solitary waves in a collisionless plasma consisting of a cold electron fluid and non-thermal hot electrons are investigated by a direct analysis of the field equations. The Sagdeev potential is obtained in terms of electron acoustic speed by simply solving an algebraic equation. It is found that the amplitude and width of the electron acoustic solitary waves as well as the parametric regime where the solitons can exist are very sensitive to the population of energetic non-thermal hot electrons. The soliton and double layer solutions are obtained as a small-amplitude approximation. The effect of non-thermal hot electrons is found to significantly change the properties of the electron acoustic solitary waves (EAWs). A comparison with the Viking Satellite observations in the day side auroral zone is also discussed.     

Higher-order Zakharov–Kuznetsov equation for dust-acoustic solitary waves with dust size distribution

Nonlinear propagating dust-acoustic solitary waves (DASWs) in a warm magnetized dusty plasma containing different size and mass negatively charged dust particles, isothermal electrons, high- and low-temperature ions are investigated. For this purpose, a reasonable normalization of the hydrodynamic and Poisson equations is used to derive the Zakharov–Kuznetsov (ZK) equation for the first-order perturbed potential. As the wave amplitude increases, the width and the velocity of the solitons deviate from the prediction of the ZK equation, i.e., the breakdown of the ZK approximation. To describe the soliton of larger amplitude, a linear inhomogeneous Zakharov-Kuznetsov-type (ZK-type) equation for the second-order perturbed potential is derived. Stationary solutions of both equations are obtained using the renormalization method. Numerically, the effect of power law distribution on the higher-order corrections is examined. It is found that the soliton amplitude in case of power law distribution is smaller than that of monosized dust grains. The higher-order corrections play a role to reduce the strength of the nonlinearity for power law distribution case. The relevance of the present investigation to Saturn's F-ring and laboratory experiment is discussed.     

Ion acoustic solitons in a nonextensive plasma with multi-temperature electrons

The properties of propagation of small amplitude ion acoustic solitary waves (IASWs) are studied in a plasma containing cold fluid ions and multi-temperature electrons (cool and hot electrons) with nonextensive distribution. Korteweg-de Vries (KdV) equation with finite amplitude is derived using a reductive perturbation method. From the solitary solutions of KdV equation, the combined effects of nonextensivity and density ratio are studied on characteristics of ion acoustic (IA) solitary waves. Positive as well as negative polarity solitons exist. Since singularity exists for A=0 so we have also derived modified Korteweg de Vries (mKdV) equation to study the solitonic solution for critical values of physical parameters (q,f,σ). The nonextensivity of electrons (via q) and density ratio of electrons and ions (via f) and temperature ratio (σ) significantly influence the characteristics of ion acoustic solitary structures.     

Large amplitude dust ion-acoustic solitary waves in a plasma in the presence of positrons

Properties of propagation of large amplitude dust ion-acoustic solitary waves and double layers are investigated in electron-positron-ion plasma with highly charged negative dust. Sagdeev pseudopotential method has been used to derive the energy balance equation. The expression for the critical Mach number (lower/upper limit) for the existence of solitary structures has also been derived. The Sagdeev pseudopotential is a function of numbers of physical parameters such as ion temperature (σ), positron density (δ _p ), dust density (δ _d ) and electron to positron temperature ratio (β). These parameters significantly influence the properties of the solitary structures and double layers. Further it is found that both polarity (compressive and rarefactive) solitons and negative potential double layers are observed.     

Propagation of ion-acoustic waves in a warm dusty plasma with electron inertia

The KdV equation is derived for weakly nonlinear ion-acoustic waves in an unmagnetized warm dusty plasma with electron inertia. It has been shown that the inclusion of electron inertia and pressure variation of the species not only significantly modifies the basic features (width and amplitude) of dust ion-acoustic solitions, but also introduces a new parametric regime for the existence of positive and negative solitons.     

Ion acoustic drift solitons and shocks with κ-distributed electrons

The impact of superthermal particles on nonlinear drift solitary and shock like structures are presented in an inhomogeneous electron-ion plasma with κ-distributed electrons. It is shown that the amplitude of the drift solitons and shocks is modified significantly in the presence of superthermal particles. The condition for the existence of drift solitons is found modified in the presence of higher energy particles. Furthermore, Kadomtsev–Petviashvili (KP) equation is also derived for the present plasma model.