Electrostatic shock structures in a multi-species nonthermal dusty plasma

Propagation of the dust-acoustic shock waves (DASWs) in a dusty plasma containing arbitrarily charged dust, positive and negative ions following nonthermal (Cairn’s) distribution, and electrons following q-(nonextensive) distribution, has been investigated. The reductive perturbation technique is used to derive the Burgers equation for dust’s fluid dynamics. The basic features (viz. polarity, amplitude, speed, etc.) of DASWs are found to be significantly modified due to the effects of arbitrarily charged dust, number density and temperatures of heavier/lighter ions, nonextensive electrons, and dust kinematic viscosity. The present investigation can be very effective for understanding the nonlinear characteristics of the DASWs in space and laboratory dusty plasmas.     

Shock waves in a dusty plasma having q-nonextensive electron velocity distribution

The dust-acoustic shock waves have been theoretically investigated using reductive perturbation technique. An unmagnetized four-component dusty plasma system consisting of nonextensive q-distributed electrons, Boltzmann distributed ions, and negatively as well as positively charged dust particles has been considered. The solution of Burgers equation in planar geometry is numerically analyzed. It has been observed that the nonextensive q-distribution of electrons has a significant role in the formation of shock waves. The relevance of our results to astrophysics as well as laboratory plasmas are briefly discussed.     

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.     

Dust ion-acoustic shock waves in nonextensive dusty plasma

A parametric survey on the propagation characteristics of the dust ion-acoustic (DIA) shock waves showing the effect of nonextesivity with nonextensive electrons in a dissipative dusty plasma system has been carried out using the reductive perturbation technique. We have considered continuity and momentum equations for inertial ions, q-distributed nonextensive electrons, and stationary charged dust grains, to derive the Burgers equation. It has been found that the basic features of DIA shock waves are significantly modified by the effects of electron nonextensivity and ion kinematic viscosity. Depending on the degree of nonextensivity of electrons, the dust ion-acoustic shock structures exhibit compression and rarefaction. The implications of our results would be useful to understand some astrophysical and cosmological scenarios like stellar polytropes, hadronic matter and quark-gluon plasma, protoneutron stars, dark-matter halos, etc., where effects of nonextensivity can play the significant roles.     

K-dV solitons in a magnetized dusty plasma with two distinct temperature nonextensive electrons and Maxwellian ions

Nonlinear propagation of dust-acoustic (DA) waves in a magnetized dusty plasma, consisting of negatively charged mobile dust, Maxwellian ions and two distinct temperature nonextensive electrons (following nonextensive q-distribution each), has been studied and analyzed by deriving and solving the Korteweg-de-Vries (K-dV) equation. According to the outcomes of the investigation, the basic characteristics of the DA solitary profiles are found to be strongly modified by the external magnetic field, nonextensivity of the electrons and the respective number densities of the two species of electrons. The results of this investigation can be applied in both laboratory and astrophysical plasma scenarios for understanding the basic features of the localized electrostatic dust-acoustic solitary waves (DASWs).     

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 and rogue waves in a Thomas-Fermi degenerate dusty plasma

The formation and propagation of dust-acoustic (DA) solitary and rogue waves are studied in a non-relativistic degenerate Thomas-Fermi thermal dusty plasma incorporating transverse velocity perturbation effects. The electrons and ions are described by the Thomas-Fermi density distributions, whereas the dust grains are taken as dynamic and classical. By using the reductive perturbation technique, the cylindrical Kadomtsev-Petviashvili (CKP) equation is derived, which is then transformed into a Korteweg-deVries (KdV) equation by using appropriate variable transformations. The latter admits a solitary wave solution. However, when the carrier waves frequency is much smaller than the dust plasma frequency, the DA waves evolve into the nonlinear modulation instability, generating modulated wave packets in the form of Rogue waves. For the study of DA-rogue waves, the KdV equation is transformed into a self-focusing nonlinear Schrödinger equation. The variation of dust temperature and the electron density affects the nonlinearity and dispersion coefficients which suppress the amplitudes of the DA solitary and rogue waves. The present results aim to describe the nonlinear electrostatic excitations in astrophysical degenerate dense plasma.     

Time-fractional Burgers equation for dust acoustic waves in a two different temperatures dusty plasma

The reductive perturbation method has been used to derive the Burgers equation for dust acoustic shock waves in unmagnetized plasma having electrons, singly charged ions, hot and cold dust species with Boltzmann distributions for electrons and ions in the presence of the cold (hot) dust viscosity coefficients. The time-fractional Burgers equation is formulated using Euler-Lagrange variational technique and is solved using the variational-iteration method. The effect of time fractional parameter on the behavior of the shock waves in the dusty plasma has been investigated.     

Effects of two-temperature electrons, external oblique magnetic field, concentration of charged dust grains and higher-order nonlinearity on dust ion-acoustic solitary waves in Saturn's E-ring

The purpose of the present work is to investigate some nonlinear properties of the dust ion-acoustic (DIA) solitary waves in a four-component hot-magnetized dusty plasma consisting of charged dust grains, positively charged ions and two-temperature isothermal electrons. Applying a reductive perturbation theory, a nonlinear Korteweg-de Vries (KdV) equation for the first-order perturbed potential and a linear inhomogeneous KdV-type equation for the second-order perturbed potentials are derived. Stationary solutions of these coupled equations are obtained using a renormalization method. A method based on energy consideration is used to obtain a condition for stable solitons. The effects of two different types of isothermal electrons, external oblique magnetic field, concentration of negatively (positively) charged dust grains and higher-order nonlinearity on the nature of the DIA solitary waves are discussed. The numerical results are applied to Saturn's E-ring.     

Effects of nonthermal ions of distinct temperatures on dust acoustic shock waves in a dusty plasma

The nonlinear propagation of dust acoustic (DA) waves in an unmagnetized dusty plasma system consisting of negatively charged mobile dust fluid, Boltzmann distributed electrons, and two-temperature nonthermally distributed ions, is rigorously investigated. The reductive perturbation method has been employed to derive the Burgers equation. The hydrodynamic equation for inertial dust grains has been used to derive the Burgers equation. The effects of two temperature nonthermally distributed ions and dust kinematic viscosity, which are found to significantly modify the basic features of DA shock waves, are briefly discussed. Our present investigation can be effectively utilized in many astrophysical situations (e.g. satellite or spacecraft observations, Saturn’s E ring, etc.), which are discussed briefly in this analysis.     

Solitary and rogue waves in Fermi-Dirac plasmas: relativistic degeneracy effects

Ion acoustic (IA) solitary and rogue waves are studied in an unmagnetized plasma consisting of non-degenerate warm ions, relativistically degenerate electrons and positrons. By using the reductive perturbation technique, the evolution of IA solitary waves is described by the Korteweg-de Vries (KdV) equation. However, when the frequency of the carrier wave is much smaller than the ion plasma frequency then the KdV equation is also used to study the nonlinear evolution of modulationally unstable modified IA wavepackets through the derivation of nonlinear Schrödinger equation. It is found that the characteristics of the IA solitary and rogue waves are substantially influenced by the intrinsic plasma parameters. The relevance of the present investigation involving IA solitary and rogue waves in astrophysical plasma environments is also highlighted.     

Astrophysical naturally moderated classical positron beam interaction with nonlinear waves in nonextensive astrophysical plasmas

The positron acoustic shock and solitary wave are explored in nonextensive electron-positron-ion plasma. The plasma system under-consideration, consists of a classical positron beam, q distributed electrons and positively charged bulky ions constitute a neutralizing background. The nonlinear Korteweg-de Vries and Burger equations are derived by employing the standard reductive perturbation method. The positron acoustic wave in linear limit is also discussed for dissipative as well as nondissipative cases of nonextensive plasmas. The plasma parameters such as, the concentration of neutralizing ions background, beam velocity, temperature and q parameter of the nonextensive electrons are noticed to significantly affect the positron acoustic shock and solitary waves. Our findings may be helpful in the understanding of laboratory beam plasma interaction experiments as well as the astrophysical nonextensive plasmas interacting with positron beam.     

Nonextensive dust acoustic shock structures in complex plasmas

Nonlinear dust acoustic (DA) shock waves are studied in a nonextensive charge varying complex plasma. A burger-like equation the coefficients of which is significantly modified by nonextensivity and dust charge fluctuation is derived. It is found that the influence of particle (electrons and ions) nonextensivity and dust charge fluctuation affect the basic properties of the collisionless DA shock wave drastically.     

Rogue waves for Kadomstev-Petviashvili equation in electron-positron-ion plasma

The nonlinear ion-acoustic waves in plasma having excess super-thermal electrons and positrons have been investigated. Reductive perturbation method is used to obtain a Kadomstev-Petviashvili equation describing the system. The dynamics of the modulationally unstable wave packets described by the Kadomstev-Petviashvili equation gives rise to the formation of rogue excitation that is described by a nonlinear Schrödinger equation. The dependence of rogue waves profiles on the system parameters investigated numerically. The result of the present investigation may be applicable to some plasma environments, such as galactic clusters, interstellar medium.     

Obliquely propagating electrostatistic solitary structures in a hot magnetized dusty plasma with vortex-like electron distribution

The nonlinear properties of solitary waves structure in a hot magnetized dusty plasma consisting of a negatively charged, extremely massive hot dust fluid, positively charged hot ion fluid and vortex-like distributed electrons, are reported. A modified Korteweg de Vries equation (mKdV) which admits a solitary wave solution for small but finite amplitude is derived using a reductive perturbation theory. The modifications in the amplitude and width of the solitary wave structures due to the inclusion of an external magnetic field and dust and ions temperature are investigated. This revised version was published online in July 2006 with corrections to the Cover Date.     

Nonlinear propagation of dust-acoustic waves in a magnetized nonextensive dusty plasma

A theoretical investigation has been made of obliquely propagating dust-acoustic solitary waves in a magnetized three-component dusty plasma, which consists of a negatively charged dust fluid, ions, and nonextensive electrons. The reductive perturbation method has been employed to derive the Korteweg-de Vries equation which admits a solitary wave solution. It has been shown that the combined effects of external magnetic field (obliqueness), ions, and electron nonextensivity change the behavior of these electrostatic solitary structures that have been found to exist with positive and negative potential in this dusty plasma model. The implications of our results in astrophysical and cosmological scenarios like vicinity of the Moon, magnetospheres of Jupiter and Saturn, dark-matter halos, hadronic matter, quark-gluon plasma, protoneutron stars, stellar polytropes etc. have been mentioned.     

Dust-ion acoustic waves modulation in dusty plasmas with nonextensive electrons

The nonlinear amplitude modulation of dust-ion acoustic wave (DIAW) is studied in the presence of nonextensive distributed electrons in dusty plasmas with stationary dust particles. Using the reductive perturbation method (RPM), the nonlinear Schrödinger equation (NLSE) which governs the modulational instability (MI) of the DIAWs is obtained. Modulational instability regions and the growth rate of nonlinear waves are discussed. It is shown that the wave characters are affected by the value of nonextensive parameter and also relative density of plasma constituents.     

Effect of <Emphasis Type="Italic">q</Emphasis>-nonextensive distribution of electrons on ion acoustic shock waves in dissipative plasma

Ion acoustic shock waves (IASWs) are studied in a plasma consisting of nonextensive electrons and ions. The dissipation is taken into account the kinematic viscosity among the plasma constituents. The Korteweg-de Vries-Burgers (KdV-Burgers) equation is derived by reductive perturbation method. Shock waves are solutions of KdV-Burgers equation. It is shown that acceptable values of q-parameter (where q stands for the electron nonextensive parameter) are more than 3 in a weakly nonlinear analysis. We have found that the amplitude of shock waves decreases by an increasing q-parameter.     

On dust ion acoustic solitary waves in collisional dusty plasmas with ionization effect

The propagation of solitary waves in an unmagnetized collisional dusty plasma consisting of a negatively charged dust fluid, positively charged ions, isothermal electrons, and background neutral particles is studied. The ionization, ion loss, ion–neutral, ion–dust, and dust–neutral collisions are considered. Applying a reductive perturbation theory, a damped Korteweg–de Vries (DKdV) equation is derived. On the other hand, at a critical phase velocity, the dynamics of solitary waves is governed by a damped modified Korteweg–de Vries (DMKdV) equation. The nonlinear properties of solitary waves in the two cases are discussed.     

Arbitrary amplitude electron acoustic waves in a magnetized nonextensive plasma

Arbitrary amplitude electron acoustic (EA) solitary waves in a magnetized nonextensive plasma comprising of cool fluid electrons, hot nonextensive electrons, and immobile ions are investigated. The linear dispersion properties of EA waves are discussed. We find that the electron nonextensivity reduces the phase velocities of both modes in the linear regime: similarly the nonextensive electron population leads to decrease of the EA wave frequency. The Sagdeev pseudopotential analysis shows that an energy-like equation describes the nonlinear evolution of EA solitary waves in the present model. The effects of the obliqueness, electron nonextensivity, hot electron temperature, and electron population are incorporated in the study of the existence domain of solitary waves and the soliton characteristics. It is shown that the boundary values of the permitted Mach number decreases with the nonextensive electron population, as well as with the electron nonextensivity index, q. It is also found that an increase in the electron nonextensivity index results in an increase of the soliton amplitude. A comparison with the Vikong Satellite observations in the dayside auroral zone is also taken into account.