Coupled dispersive drift acoustic modes in inhomogeneous dusty plasmas with different nonthermal distributions for electrons and ions

Linear dispersion characteristics of the coupled drift acoustic modes are investigated in inhomogeneous dusty magnetoplasmas both when the dust is considered immobile and when the dust dynamics is taken into account in the presence of nonthermal population of electrons and ions. In this regard, Cairns and Kappa distributed electrons and ions are considered. It is found that the nonthermal distributions affect the phase velocities and the fundamental scalelengths of the plasma. It is found that for both the ion and dust dynamics driven waves, the phase velocities are highest for Cairns, intermediate for Kappa, whereas they are minimum for the Maxwellian distributed electrons. The work presented here may be useful to understand the low frequency electrostatic modes in inhomogeneous dusty plasmas such as those found in planetary environments.     

Formation of solitary structures in uniform and nonuniform magnetoplasmas with superthermal electrons: a non-reductive perturbative approach

Electrostatic solitary structures are studied in uniform and nonuniform magnetoplasmas with superthermal electrons. In the linear analysis, the differences in the acoustic frequencies for Maxwellian, Cairns, and Kappa distributed electrons for both homogeneous and inhomogeneous plasmas are highlighted and discussed. It is shown that using the linear dispersion relation, nonlinear Zakharov-Kuznetsov (ZK) equation can be derived both for the homogeneous and inhomogeneous magnetoplasmas. The solution of the ZK equation is presented using the tangent hyperbolic method. It is found that the increasing magnetic field and the angle of propagation enhances the amplitude whereas the increasing number density mitigates the amplitude of the acoustic drift solitary wave. Furthermore, it is observed that the amplitude of the solitary structure is maximum for Cairns, intermediate for Maxwellian, and minimum for the Kappa distributed electrons. The results presented in this paper may be beneficial to understand the formation of electrostatic drift solitary waves in planetary environments where the nonthermal population of electrons are observed by various satellite missions.     

Dust drift solitary waves with superthermal electrons and ions

Linear and nonlinear dust drift waves are investigated in the presence of kappa distributed electrons and ions. The dispersion characteristics of linear waves show that the phase velocity decreases with the inclusion of highly energetic particles in the tail of the distribution. In the nonlinear regime, a nonlinear partial differential equation is obtained in the long wave length limit. A stationary solution of this equation in the form of solitary waves is discussed and noticed that the amplitude of the solitary pulse decreases with the increase of superthermal particle’s effect, and its width expands. Further, it is found that speed limit of the nonlinear structures is also modified in the non-Maxwellian plasma. Theoretically obtained results are applied to Saturn’s’ dusty plasma environment. It is also pointed out that the present results can be helpful for further understanding of space plasmas.     

Current-driven solitons and shocks in plasmas having non-Maxwellian electrons

The current-driven electrostatic solitons and shocks are investigated in flowing plasmas having stationary dust and non-Maxwellian electrons. The propagation of solar wind parallel to the external magnetic field in the boundary regions of dusty magnetospheres of planets can give rise to drift type unstable electrostatic waves and nonlinear structures even if density is homogeneous. These waves can be produced in laboratory plasma experiments as well. Here the theoretical model is applied to Saturn’s magnetosphere.     

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.     

Modulational instability of dust ion acoustic waves in dusty plasmas with superthermal electrons

The propagation of dust ion acoustic waves is studied in plasmas composed of superthermal distributed electrons and stationary dust particles. The nonlinear Schrödinger equation is derived using the reductive perturbation technique and the modulational instability of dust ion acoustic waves is analyzed. Parametric investigations indicate that the presence of superthermal distributed electrons significantly modify the modulational instability and its growth rate. The effect of particle relative density on the wave characters is also investigated.     

Nonlinear electrostatic coherent structures: solitary and shock waves in a dissipative, nonplanar multi-component quantum plasma

The nonlinear propagation of ion-acoustic solitary and shock waves in a dissipative, nonplanar quantum plasma comprised of electrons, positrons, and ions are studied. A modified Korteweg-de Vries Burgers equation is derived in the limit of low frequency and long wavelength by taking into account the kinematic viscosity among the plasma constituents. It is shown that this plasma system supports the propagation of both compressive and rarefactive nonlinear waves. The effects of variation of various plasma parameters on the time evolution of nonplanar solitary waves, the profile of shock waves, and the nonlinear structure induced by the collision of solitary waves are discussed. It is found that these parameters have significant effects on the properties of nonlinear waves in cylindrical and spherical geometries, and these effects for compressive and rarefactive nonlinear waves are obviously different.     

Shear flow driven tripolar vortices in a nonuniform electron-ion magnetoplasma with non-Maxwellian electrons

A set of nonlinear equations governing the dynamics of finite amplitude drift-ion acoustic-waves is derived for sheared ion flows parallel and perpendicular to the ambient magnetic field in the presence of Cairns and Kappa distributed electrons. It is shown that stationary solution of the nonlinear equations can be represented in the form of a tripolar vortex for specific profiles of the equilibrium sheared flows. The tripolar vortices are, however, observed to form on a scale of the order of ion Larmor radius ρ _i which is calculated to be around a Kilometer for the plasma parameters found in the Saturn’s E-ring. The relevance of the present investigation in planetary environments is also pointed out.     

Nonlinear propagation of dust ion-acoustic waves in dusty multi-ion dense plasma

We have studied the nonlinear propagation of dust ion-acoustic (DIA) waves in a dusty multi-ion dense plasma (with the constituents being degenerate, either non-relativistic or ultra-relativistic) and the propagation of such waves have been investigated by the reductive perturbation method. From the stationary solution of the Korteweg de-Vries (K-dV) equation and Burgers’ equation the nonlinear waves (specially, solitary and shock waves) have been found to be formed in the dusty plasma system under consideration. It has shown that the basic features of these waves are significantly modified by both the positive and negative ions and dust number densities, the degenerate of the constituents. The implications of our results have been briefly discussed.     

Effects of double temperature superthermal electrons on dust-ion-acoustic shock waves in electron-positron-ion dusty plasmas

A rigorous theoretical investigation on the characteristics of dust-ion-acoustic (DIA) shock waves in an unmagnetized multi component electron-positron-ion dusty plasma (consisting of inertial ions, electrons of two distinct temperatures referred to as low and high temperature superthermal electrons where superthermality is introduced via the κ-type of nonthermal distribution, Boltzmann distributed positrons, and negatively charged immobile dust grains) has been made both theoretically and analytically. The hydrodynamic equation for inertial ions has been used to derive the Burgers equation. The influence of superthermal electrons, Maxwellian positrons and ion kinematic viscosity, which are found in this investigation, significantly modify the basic features of DIA shock waves, are briefly discussed. The present investigation can be very effective for studying and understanding the basic characteristics of shock wave propagation through different astrophysical situations where distinct temperature superthermal electrons dominate the wave dynamics.     

Dust ion-acoustic solitary and shock waves in a dusty plasma with non-thermal electrons

A theoretical investigation of the one dimensional dynamics of nonlinear electrostatic dust ion-acoustic (DIA) waves in an unmagnetized dusty plasma consisting of ion fluid, non-thermal electrons and fluctuating immobile dust particles has been made by the reductive perturbation technique. The basic features of DIA solitary and shock waves are studied by deriving the Korteweg-de Vries (KdV) and KdV Burger equations, respectively. It is shown that the special patterns of nonlinear electrostatic waves are significantly modified by the presence of the non-thermal electron component. In particular, the rarefactive solitary and shock structures are found with smaller amplitude in comparison to the isothermal case. The transition from DIA solitary to shock waves is also studied which is related to the contributions of the dispersive and dissipative terms. It is found that the dust charge fluctuation is a source of dissipation, and is responsible for the formation of the dust ion-acoustic shock waves. Furthermore, the dissipative effect becomes important and may prevail over that of dispersion as the population of non-thermal electrons present decreases. The present investigation may be of relevance to electrostatic solitary structures observed in many space dusty plasma, such as Saturn’s E-ring.     

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.     

Stability of colour-flavour locked quark matter with three massive quark flavours

The Kadomtsev-Petviashvili-Burgers (KPB) equation is derived for coupled drift acoustic shock waves in a partially ionized non-uniform pair-ion-electron (PIE) plasma in the presence of both density and temperature gradients respectively. Both linear and nonlinear studies are presented. The nonlinear KPB equation is derived in the small amplitude approximation method and its solution is found using the tanh method. The numerical calculations also presented for PIE plasmas of fullerene plasma for illustration keeping in view the recent experiments. The effect of density and temperature inhomogeneities on the nature of the shock is also highlighted. The role of the velocity of the nonlinear structure with regard to the density and temperature gradients driven drift velocities is also pointed out and the effect of ion-neutral collision frequency is also investigated. This work may be useful for future laboratory experimental investigations on pair-ion-electron plasmas.     

Shock structures in dusty plasma in the presence of strong electrostatic interaction

The fluid approach is employed to investigate theoretically the effect of strong electrostatic interaction on the dust acoustic (DA) shock waves near to the liquid-crystal phase transition in strongly coupled dusty plasma. The strong electrostatic interaction is modeled by effective electrostatic temperature which is considered as a dynamical variable. It is shown that the nonlinear evolution of dust acoustic shock waves in the present model is governed by a Burger equation, the coefficients in which are modified by strong coupling effect. Then, it is shown that how the perturbation of the effective electrostatic temperature modifies the basic properties of the DA shock waves.     

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.     

Two dimensional electromagnetic shock structures in dense electron-positron-ion magnetoplasmas

Linear and nonlinear analysis of low frequency magnetoacoustic waves propagating at an angle θ with the ambient magnetic field are investigated in dense electron-positron-ion (e-p-i) plasmas using the quantum magnetohydrodynamic (QMHD) model. In this regard, a quantum Kadomtsev-Petviashvili-Burgers (KPB) equation is derived in the small amplitude limit. The stability of KPB equation is also presented. The variation of the nonlinear fast and slow magnetoacoustic shock waves with the positron concentration, kinematic viscosity, obliqueness parameter θ, and the magnetic field, are also investigated. It is observed that the aforementioned plasma parameters significantly modify the propagation characteristics of two dimensional nonlinear magnetoacoustic shock waves in dissipative quantum magnetoplasmas. The relevance of the present investigation with regard to dense astrophysical environments is also pointed out.     

Nonlinear electrostatic drift Kelvin-Helmholtz instability

Nonlinear analysis of electrostatic drift Kelvin-Helmholtz instability is performed. It is shown that the analysis leads to the propagation of the weakly nonlinear dispersive waves and the nonlinear behaviour is governed by the nonlinear Burger's equation.     

Small Amplitude Nonlinear Dust Acoustic Wave Propagation in Saturn's F, G and E Rings

Nonlinear properties of small amplitude dust acoustic waves, incorporatingboth the ion inertial effect and dust drift effect have been studied.The effect of dust charge variation is also incorporated. It is seen thatdue to the dust charge variation, a Korteweg-de Vries (KdV) equationwith positive or negative damping term depending on the wave velocityand the ring parameters governes the nonlinear dust acoustic wave. It isseen that the damping or growth arises due to the assumption that dusthydrodynamical time scale is much smaller than that of the dust chargingscale. This assumption is valid only for planetary rings such as Saturn'sF, G and E rings. Numerical investigations reveal thatall the three rings in F, G and E, dust acoustic solitary wave admits both negative and positive potentials. Instability arises from the available freeenergy of drift motion of dust grains only for the wave with wave velocity 0, the drift velocity of the dust.     

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.     

Formation of obliquely propagating dust-ion-acoustic shock waves due to dust charge fluctuation in magnetized nonthermal dusty plasma

A theoretical investigation is made on the formation as well as basic properties of dust-ion-acoustic (DIA) shock waves in a magnetized nonthermal dusty plasma consisting of immobile charge fluctuating dust, inertial ion fluid and nonthermal electrons. The reductive perturbation method is employed to derive the Korteweg-de Vries-Burgers equation governing the DIA shock waves. The combined effects of external static magnetic field, obliqueness, nonthermal electron distribution and dust charge fluctuation on the DIA shock waves are also investigated. It is shown that the dust charge fluctuation is a source of dissipation, and is responsible for the formation of the DIA shock waves. It is also observed that the combined effects of obliqueness, nonthermal electron distribution and dust charge fluctuation significantly modify the basic properties of the DIA shock waves. The implications of our results in space and laboratory dusty plasma situations are briefly discussed.