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.     

Influence of suprathermality on the obliquely propagating dust-acoustic solitary waves in a magnetized dusty plasma

Dust-acoustic (DA) solitary waves are investigated in a magnetized dusty plasma comprising cold dust fluid and kappa-distributed ions and/or electrons. The influence of suprathermal particles, obliqueness, and ion temperature on the DA solitary waves is investigated. We find that only negative DA solitary waves will be excited in this model. Also it is shown that the amplitude of the DA solitary wave decreases with deviation of electrons or ions from Maxwellian distribution via decrease of κ _e or κ _i . The effect of the temperature of the ion decreases with the amplitude and steepness of the solitary wave front.     

Oblique collision effects on nonlinear quantum dust-acoustic solitary waves in magnetized dense dusty plasmas

The oblique collision of nonlinear quantum dust-acoustic (NQDA) solitary waves in a three-dimensional (3D) magnetized dense dusty plasma is investigated. Furthermore, two coupled Kortwege–de Vries equations for describing our model and the analytical phase shifts after the oblique collision of two NQDA solitary waves are derived using the extended Poincaré–Lighthill–Kuo (PLK) method. The modification in the phase shift and the trajectory of the NQDA solitary waves structures due to the inclusion of oblique collision and external magnetic field are discussed numerically. The numerical results are applied to high density astrophysical situations such as in superdense white dwarfs.     

Bifurcations of dust ion acoustic travelling waves in a magnetized quantum dusty plasma

Bifurcation behavior of nonlinear dust ion acoustic travelling waves in a magnetized quantum dusty plasma has been studied. Applying the reductive perturbation technique (RPT), we have derived a Kadomtsev-Petviashili (KP) equation for dust ion acoustic waves (DIAWs) in a magnetized quantum dusty plasma. By using the bifurcation theory of planar dynamical systems to the KP equation, we have proved that our model has solitary wave solutions and periodic travelling wave solutions. We have derived two exact explicit solutions of the above travelling waves depending on different parameters.     

Nonextensive collisioneless dust-acoustic shock waves in a charge varying dusty plasma

Nonlinear dust-acoustic (DA) shock waves are addressed in a nonextensive dusty plasma exhibiting self-consistent nonadiabatic charge variation. Our results reveal that the amplitude, strength and nature of the DA shock waves are extremely sensitive to the degree of ion nonextensivity. Significant differences in the potential function occur for very small changes in the value of the nonextensive parameter. Stronger is the ions correlation, more important is the charge variation induced nonlinear wave damping.     

Finite larmor-radius effects on Rayleigh-Taylor instability of a dusty magnetized plasma

This paper discusses the Rayleigh-Taylor (RT) instability of an infinitely conducting medium having an exponential density distribution which includes the effects of finite ion Larmor-radius (FLR) corrections and suspended particles in the presence of a uniform horizontal magnetic field. The relevant equations of the problem are linearized and from the linearized perturbation equations a dispersion relation is obtained, using appropriate boundary conditions. It has been found that the criterion for the stable density stratification remains uninfluenced by the simultaneous inclusion of the FLR corrections and suspended particles. The stability of the medium has been proved for the case of stable stratification when the FLR corrections are not considered in the analysis. The growth rate of unstable RT modes with increasing relaxation frequency of the suspended particles is evaluated analytically. It has been shown that the presence of suspended particles in the medium suppresses the growth rate of the unstable RT modes, thereby implying a stabilizing influence of the particles on the considered configuration.     

Dust-ion-acoustic solitary waves and their multi-dimensional instability in a magnetized nonthermal dusty electronegative plasma

A rigorous theoretical investigation has been made on multi-dimensional instability of obliquely propagating electrostatic dust-ion-acoustic (DIA) solitary structures in a magnetized dusty electronegative plasma which consists of Boltzmann electrons, nonthermal negative ions, cold mobile positive ions, and arbitrarily charged stationary dust. The Zakharov-Kuznetsov (ZK) equation is derived by the reductive perturbation method, and its solitary wave solution is analyzed for the study of the DIA solitary structures, which are found to exist in such a dusty plasma. The multi-dimensional instability of these solitary structures is also studied by the small-k (long wave-length plane wave) perturbation expansion technique. The combined effects of the external magnetic field, obliqueness, and nonthermal distribution of negative ions, which are found to significantly modify the basic properties of small but finite-amplitude DIA solitary waves, are examined. The external magnetic field and the propagation directions of both the nonlinear waves and their perturbation modes are found to play a very important role in changing the instability criterion and the growth rate of the unstable DIA solitary waves. The basic features (viz. speed, amplitude, width, instability, etc.) and the underlying physics of the DIA solitary waves, which are relevant to many astrophysical situations (especially, auroral plasma, Saturn’s E-ring and F-ring, Halley’s comet, etc.) and laboratory dusty plasma situations, are briefly discussed.     

Compressive and rarefactive dust-acoustic Gardner solitons beyond the K-dV limit with two-temperature ions dusty plasma

The Gardner equation is derived and numerically solved. This equation shows the existence of compressive and rarefactive dust-acoustic (DA) solitons with two-temperature ions beyond the K-dV (Korteweg–de Vries) limit. These may be referred to as DA Gardner solitons (DA-GSs). Here we deal with a dusty plasma, composed of negatively charged cold mobile dust fluids, inertialess Boltzmann electrons and ions with two distinctive temperatures. The basic features of the compressive and rarefactive DA solitons are identified. These solitons are found to exist beyond the K-dV limit, i.e. they exist for μ _i1～μ _c. Here μ _i1=n _i10/Z _d n _d0, Z _d is the number of electrons residing upon the dust grain surface, and n _i0 (n _d0) is the lower temperature ion (dust) number density at equilibrium. These DA-GSs are completely different from the K-dV solitons, because μ _c (the critical value) corresponds to vanishing of the nonlinear coefficient of the K-dV equation, and μ _i1～μ _c corresponds to K-dV solitons, with extremely large amplitude, for which the validity of the reductive perturbation method breaks down. It has been found that, depending on whether the parameter μ _i1 is less than or greater than the critical value, the DA-GSs exhibit compression for μ _i1>μ _c and rarefaction for μ _i1<μ _c. The basic features of double layers with arbitrary amplitude are also briefly discussed, employing the pseudo-potential approach. The present investigation might be relevant to the electrostatic solitary structures observed in various cosmic dust-laden plasmas, such as supernova shells, Saturn’s F-ring, the ionopause of Halley’s comet, etc.     

Vortex formation in nonlinearly coupled modes in a magnetized quantum plasma

Linear and nonlinear properties of coupled modes in a magnetized quantum plasma in the presence of electron Fermi pressure are studied in a nonuniform magnetoplasma composed of electrons, ions, and extremely massive and negatively charged immobile dust grains. Stationary solutions of the nonlinear equations that govern the dynamics of coupled modes are presented. It is found that electrostatic dipolar vortex structure can form in such a plasma. The dipolar structures in dense plasmas are observed to be formed on a much shorter scalelength by comparison with their classical counterparts. It is found that the increasing Fermi temperature shortens the scalelength over which the nonlinear coherent structures are formed. The relevance of the present investigation with regard to the dense astrophysical plasmas is also pointed out.     

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.     

Head on collision of dust ion acoustic solitary waves in magnetized quantum dusty plasmas

The Head on collision of dust ion acoustic solitary waves (DIASWs) in a magnetized quantum dusty plasma is investigated. Two sides Korteweg-de Vries (KdV) equations are obtained, the analytical phase shifts and the trajectories after the head-on collision of two DIASWs in a three species quantum dusty plasma are derive by using the extended version of Poincaré-Lighthill-Kuo (PLK) method. It is observed that the phase shifts are significantly affected by the quantum parameters like quantum diffraction, the ion cyclotron frequency and the ratio of the densities of electrons to ions.     

Current-driven dust-acoustic instability in a collisional plasma

The excitation of the dust-acoustic instability in a collisional dusty plasma is investigated. For conditions similar to those of recent laboratory experiments with neutral gas pressures of 100mTorr, it is found that zero-order electric fields E₀ 10 Vm⁻¹ are sufficient for the growth of perturbations with centimeter wavelengths. Much larger wavelengths generally require larger values of E₀. Free electrons in the dusty plasma have a stabilizing effect, which can be very pronounced at the longest wavelengths.     

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).     

Effect of quantum corrections on the Jeans instability of self-gravitating viscoelastic dusty fluid

In this paper we investigate the effects of quantum correction on the Jeans instability of self-gravitating viscoelastic dusty electron-ion quantum fluids. The massive self-gravitating dust grains are assumed to be strongly coupled and non-degenerate having both viscous and elastic behavior while the inertialess electrons and ions are considered as weakly coupled and Fermi degenerate. The hydrodynamic model is modified and a linear dispersion relation is derived employing the plane wave solutions on the linearized perturbation equations for the considered system. It is observed that the dispersion properties are affected due to the presence of viscoelastic effects and quantum statistical corrections. The modified condition of Jeans instability and expression of critical Jeans wavenumber are obtained. Numerically it is shown that viscoelastic effects, dust plasma frequency and quantum statistical effects all have stabilizing influence on the growth rate of gravitationally Jeans mode. The growth rates are also compared in kinetic and hydrodynamic limits and it is found that decay in the growth of unstable Jeans mode is larger under the kinetic limits than the hydrodynamic limits. The results are discussed for the understanding of formation of dense degenerate dwarf star through gravitational collapsing which is assumed to be strongly coupled dusty quantum fluid where the strongly coupled dust provides inertia and Fermi degenerate electron and ions provide quantum statistical effects.     

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.     

Arbitrary amplitude dust-acoustic double-layers in a warm dusty plasma with suprathermal electrons, two-temperature thermal ions, and drifting dust grains

Arbitrary amplitude dust-acoustic double-layers (DA-DLs) in a plasma with suprathermal electrons, two-temperature thermal ions, and warm drifting dust grains are investigated. Our results reveal that the spatial patterns of the DA-DLs are affected by the degree of the electron suprathermality. The electron thermalization involves a decrease of the cold ion component density, for the existence of localized DA-DLs. An increase of the dust drift velocity requires a decrease of κ (the electron spectral index), for the onset of dust-acoustic double-layers. An increase of the Mach number M leads to an increase of the DL amplitude as well as the corresponding electron spectral index for which the DL occurs.     

Dust-ion-acoustic solitary waves and their multi-dimensional instability in a magnetized dusty electronegative plasma with trapped negative ions

A theoretical investigation has been made on obliquely propagating dust-ion-acoustic solitary waves (DIASWs) in magnetized dusty electronegative plasma containing Boltzmann electrons, trapped negative ions, cold mobile positive ions, and arbitrarily charged stationary dust. The reductive perturbation method has been employed to derive the modified Zakharov-Kuznetsov (MZK) equation which admits solitary wave solution under certain conditions. The multi-dimensional instability of these solitary waves is also studied by the small-k (long wavelength plane wave) perturbation-expansion technique. The basic properties (speed, amplitude, width, instability, etc.) of small but finite amplitude DIASWs are significantly modified by the effects of external magnetic field, obliqueness, polarity of dust, and trapped negative ions. The implications of our results in space and laboratory plasmas are briefly discussed.