K-dV and Burgers’ equations on DA waves with strongly coupled dusty plasma

A rigorous theoretical investigation has been made on the nonlinear structures, mainly, dust-acoustic (DA) solitary and shock waves propagating in a strongly coupled dusty plasma consisting of strongly coupled correlated positively and negatively charged inertial cold dust fluid, weakly correlated inertialess Maxwellian electron and ion fluids. The presence of arbitrary (negative and positive) charged dust grains in such a plasma system causes the presence opposite potentials (positive and negative) DA solitary and shock structures and significantly modify it’s basic features. The results obtained from this analysis can be employed in understanding the nature of plasma waves both in laboratory and space plasma system.     

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.     

Observing the effects of the polarization force in strongly coupled dusty plasmas with suprathermal electrons

Our objective here is to investigate a strongly coupled dusty plasma system with the presence of polarization force (PF). This plasma consists of superthermal electrons, Maxwellian ions, and negatively charged dust grains. The nonlinear propagation of dust-acoustic (DA) waves in such dusty plasma system has been theoretically investigated by employing the reductive perturbation method. The Burgers’ and K-dV equations have been derived to and numerically analyzed. It has been found that the dust-acoustic shock and solitary waves exist associated with a negative potential only, and that the effect of the dust fluid temperature significantly modifies the basic properties (amplitude and width) of such nonlinear waves’ potential structures. We hope that the results of our present investigation should help us in understanding the localized electrostatic disturbances in space and laboratory strongly coupled dusty plasmas with superthermal electrons and polarization force.     

Effect of nonthermality of ions on the nature of dust acoustic waves in two temperatures charged dusty grains

Effect of nonthermality of ions on the propagation of dust-acoustic waves (DAWs) in unmagnetized plasma having electrons, singly charged ions, hot and cold dust grains have been investigated. The reductive perturbation method is employed to reduce the basic set of fluid equations to the Korteweg-de Vries (KdV) equation. 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.     

Interaction of ion beam with dust grains produces dust-acoustic solitary waves in Herbig-Haro objects

Properties of dust-acoustic solitary waves in a warm dusty plasma are analyzed by using the hydrodynamic model for massive dust grains, electrons, ions, and streaming ion beam. For this purpose, Korteweg-de Vries (KdV) equation for the first-order perturbed potential and linear inhomogeneous KdV-type equation for the second-order perturbed potential have been derived and their analytical solutions are presented. In order to show the characteristics of the dust-acoustic solitary waves are influenced by the plasma parameters, the relevant numerical analysis of the KdV and linear inhomogeneous KdV-type equations are obtained. The dust-acoustic solitary waves, as predicted here, may be associated with the nonlinear structures caused by the interaction of polar jets with the interstellar medium, which is known as Herbig-Haro objects.     

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.     

Arbitrary Amplitude Dust-acoustic Solitary Structures in aThree-component Dusty Plasma

A rigorous theoretical investigation has been made of arbitrary amplitude dust-acoustic solitary structures in an unmagnetized three-component dusty plasma whose constituents are an inertial charged dust fluid and Boltzmann distributed ions and electrons. The pseudo-potential approach and the reductive perturbation technique are employed for this study. It is found from both weakly and highly nonlinear analyses that the dusty plasma model can support solitary waves only with negative potential but not with positive potential. The effects of equilibrium free electron density and its temperature on these solitary structures are discussed. The implications of these results to some astrophysical and space plasma systems, especially to planetary ring-systems and cometary tails, are briefly mentioned. This revised version was published online in July 2006 with corrections to the Cover Date.     

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.     

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).     

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.     

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.     

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.     

Electrostatic solitary structures in a four-component adiabatic dusty plasma

A theoretical investigation has been made of propagating electrostatic waves in a four-component adiabatic dusty plasma, whose constituents are adiabatic electrons, adiabatic ions, adiabatic positively and as well as negatively charged warm dust. The basic features of the solitary structures in such a four-component adiabatic dusty plasma are studied by the reductive perturbation method. It is found that the presence of the positive dust component does not only significantly modify the basic properties of the solitary waves, but also causes the existence of the positive solitary potential structures, which is an interesting feature shown in an adiabatic dusty plasma with the dust of opposite polarity. It is also observed that the basic properties (polarity, speed, amplitude and width) of the DA SWs are significantly modified by the effects of adiabaticity (γ>1) of electrons, ions, negatively as well as positively charged warm dust. The present investigation can be of relevance to the electrostatic solitary structures observed in various dusty space plasma environments (viz. cometary tails, upper mesosphere, Jupiter’s magnetosphere, etc.).     

Dust-acoustic solitary waves in a magnetized dusty plasmas with nonthermal ions and two-temperature nonextensive electrons

A rigorous theoretical investigation has been made on the obliquely propagating dust-acoustic (DA) waves in a magnetized dusty plasmas consisting of distinct temperature q-distributed electrons with distinct strength of nonextensivities, nonthermal ions and negatively charged mobile dust grains, and analyzed by deriving the Zakharov-Kuznetsov equation. It is found that the characteristics and the properties of the DA solitary waves (DASWs) are significantly modified by the external magnetic field, relative temperature ratio of ions, relative number densities of electrons as well as ions, the nonextensivity of electrons, nonthermality of ions and the obliqueness of the system. The possible implications of the results obtained from this analysis in space and laboratory dusty plasmas are briefly addressed.     

Arbitrary amplitude dust acoustic waves in a nonextensive dusty plasma

Making use of the Sagdeev pseudo-potential approach, we derive the energy like equation for dust-acoustic (DA) solitary waves in a complex plasma having negatively charged cold dust, and electrons/ions featuring the Tsallis distribution. The effects of electron and ion nonextensivity on the DA soliton profile are examined. It is shown that depending on the strength of particle nonextensivity, our plasma model may admit compressive as well as rarefactive DA solitary waves. Our results complement previously published results on this problem.     

Head-on collision of dust-acoustic solitary waves in an adiabatic hot dusty plasma with external oblique magnetic field and two-temperature ions

In the present paper, the characteristics of the head-on collision between two dust-acoustic solitary waves (DASWs) in an adiabatic dusty plasma consisting of variable negatively charged dust grains, isothermal electrons and two-temperature isothermal ions in the presence of an external oblique magnetic field are investigated. Using the extended Poincaré–Lighthill–Kuo (PLK) method, the Korteweg–de Vries (KdV) equations and the analytical phase shifts after the head-on collision of two solitary waves are derived. The effects of the magnetic field and its obliqueness, two different type of isothermal ions and the dust particles adiabaticity are discussed. It is found that these factors significantly affect the phase shifts.     

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.     

The impacts of dust size distribution on the head-on collision of quantum dust-acoustic solitary waves in ultradense astrophysical objects

The head-on collision between two quantum dust-acoustic solitary waves (QDASWs) in ultradense astrophysical objects has been investigated theoretically using the extended Poincaré-Lighthill-Kuo (PLK) method. The Korteweg-de Vries equations and the analytical phase shifts after the head-on collision of the two QDASWs in quantum dusty plasmas are obtained. Numerically, the obtained results demonstrate that the dust size distribution, the quantum corrections of diffraction and the temperatures of electrons and ions have strong effects on the nature of the phase shifts and the trajectories of the two QDASWs after collision.     

Cosmic ray spectrum from diffusive shock acceleration

Nonlinear propagation of cylindrical and spherical dust-acoustic solitons in an unmagnetized dusty plasma consisting of cold dust grains, superthermal ions and electrons are investigated. For this purpose, the standard reductive perturbation method is employed to derive the cylindrical/spherical Korteweg-de-Vries equation which governs the dynamics of dust-acoustic solitons. The effects of nonplanar geometry and superthermal distributions on the cylindrical and spherical dust acoustic solitons structures are also studied by numerical calculation of the cylindrical/spherical Korteweg-de-Vries equation.     

Current-driven electrostatic dust-cyclotron instability in a collisional plasma

Electrostatic dust-cyclotron (EDC) waves can be excited in a collisional, magnetized, dusty plasma by passing a current along the magnetic field, B, permeating the plasma. The minimum B field-aligned electric field required for excitation of the EDC waves is typically several times smaller than the one required for excitation of dust-acoustic (DA) waves.Two dusty plasmas are considered in more detail, namely (a) a comet tail plasma, and (b) one which may be produced in a laboratory device of the type described by Xu et al. (1992).