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.     

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-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 Solitary Structures in a Magnetized Two-ion-temperature Dusty Plasma

A rigorous theoretical investigation has been made of obliquely propagating dust-acoustic solitary structures in a cold magnetized two-ion-temperature dusty plasma consisting of a negatively charged, extremely massive, cold dust fluid and ions of two different temperatures. The reductive perturbation method has been employed to derive the Korteweg-de Vries (K-dV) equation which admits a solitary wave solution for small but finite amplitude limit. It has been shown that the presence of second component of ions modifies the nature of dust-acoustic solitary structures and may allow rarefactive dust-acoustic solitary waves (solitary waves with density dip) to exist in such a dusty plasma system. The effects of obliqueness and external magnetic field on the properties of these dust-acoustic solitary structures are also briefly discussed.     

Critical density solitary waves structures in a hot dusty plasma with vortex-like ion distribution in phase space

The nonlinear properties of solitary waves structure in a hot dusty plasma consisting of isothermal hot electrons, non isothermal ions and high negatively charged massive dust grains, are reported. A modified Korteweg-de Vries equation (modified KdV), which admits a solitary waves solution for small but finite amplitude, is derived using a reductive perturbation theory. A nonisothermal ions distribution provides the possibility of coexistence of amplitude rarefactive as well as compressive solitary waves. On the other hand, consideration of a critical ions density gives a stationary solution of solitary waves and the dynamics of small but finite amplitude of solitary waves is governed by Korteweg-de Vries equation (KdV). The properties of solitary waves in the two cases are discussed.     

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.     

Detection of ionospheric perturbation due to a soft gamma ray repeater SGR J1550-5418 by very low frequency radio waves

The properties of cylindrical and spherical dust acoustic (DA) solitary and shock waves in an unmagnetized electron depleted dusty plasma consisting of inertial dust fluid and ions featuring Tsallis statistics are investigated by employing the reductive perturbation technique. A Korteweg-de Vries Burgers (KdVB) equation is derived and its numerical solution is obtained. The effects of ion nonextensivity and dust kinematic viscosity on the basic features of DA solitary and shock waves are discussed in nonplanar geometry. It is found that nonextensive nonplanar DA waves behave quite differently from their one-dimensional planar counterpart.     

Non-linear localized ion-acoustic waves in electron–positron–ion plasmas with trapped and non-thermal electrons

For an unmagnetized collisionless electron–positron–ion plasma, the effects of trapped and non-thermal electron distributions are incorporated in the study of arbitrary amplitude ion-acoustic solitary structures. Both highly and weakly analyses are examined by deriving an energy integral equation involving the Sagdeev potential for the large amplitude limit, and obtaining the non-linear partial-differential equations for the small but finite amplitude limit. It is shown that there exist ion-acoustic solitary waves with qualitatively different structures in a way that depend on the population of trapped and non-thermal electrons. In the presence of trapped electrons, fully non-linear analyses show that plasma can support only arbitrary amplitude compressive solitary waves. On the other hand, a consideration of the fast or non-thermal electron distribution provides the possibility of the coexistence of large amplitude compressive and rarefactive solitary waves, whereas both of them are decoupled in the small amplitude limit. It is found that the effects of such electron distributions and positron concentration change the maximum values of the Mach number and the amplitude for which solitary waves can exist. Furthermore, the non-thermally distributed electrons provide a KdV equation in the small amplitude limit, whereas the trapped electrons give rise to a modified KdV equation which exhibits a stronger non-linearity.     

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.     

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 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.     

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.     

Influence of arbitrarily charged dust and trapped electrons on propagation of localized dust ion-acoustic waves

A theoretical investigation is developed to study the existence, formation and basic properties of arbitrary amplitude dust ion-acoustic solitary potentials in a dusty plasma consisting of warm ions, trapped electrons and immobile negative (positive) dust particles. It is found a definite interval for the Mach number for which solitary waves exist and depend sensitively on the ion temperature and negative (positive) dust concentration. In addition, the effects of ion temperature, two oppositely charged dust species and resonant electrons on the shape of the solitary waves are also investigated extensively. For both cases of negative and positive dust grains, the effect of ion temperature is found to be destructive for the formation of localized structures. Further, the amplitude of the solitary structures decreases (increases) with the increase in the negative (positive) dust concentration.     

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.     

Propagation of two dimensional cylindrical fast magnetoacoustic solitary waves in a warm dust plasma

A set of multi-fluid equations and Maxwell’s equations are carried out to investigate the properties of nonlinear fast magnetoacoustic solitary waves with the combined effects of dusty plasma pressure and transverse perturbation in the bounded cylindrical geometry. The reductive perturbation method has been applied to the dynamical system causeway and the derived two dimensional cylindrical Kadomtsev–Petviashvili equation (CKP) predicts different natures of solitons in complex plasma. Under a suitable coordinate transformation the CKP equation can be solved analytically. The change in the soliton structure due to mass of dust, ion temperature, ion density, and dust temperature is studied by numerical calculation of the CKP equation. It is noted that the dust cylindrical fast magnetoacoustic solitary waves in warm plasmas may disappear slowly because of an increase in dust mass. The present analysis could be helpful for understanding the nonlinear ion-acoustic solitary waves propagating in interstellar medium and pulsar wind,which contain an excess of superthermal particles.     

Arbitrary amplitude dust acoustic solitary waves in an electron-depleted dusty plasma with two high energy-tail ion distributions

Arbitrary amplitude dust acoustic waves (DAW’s) in two high energy-tail ion distributions are investigated. The electron number density has been assumed sufficiently depleted during the charging of the dust grains, on account of the attachment of the background plasma electrons on the surface of the dust grains. Our results reveal that under certain conditions, DA solitary waves with either negative or positive potential may be admitted. The high degree of suprathermalization of the relatively low temperature ion component favors the development of compressive localized structures. This behavior is preserved to a large extent in the small but finite amplitude regime. This means that the presence of additional relatively low temperature suprathermal ions does not only significantly modify the basic properties of DA structures, but also causes the existence of positive solitary potentials. This feature is completely new in a dusty plasma with two suprathermal ion components with widely disparate temperatures. Our results may be relevant to a number of space dusty plasma systems, particularly, the Saturn’s F-ring where electron depletion and suprathermality are thought to come into play.     

The effect of q-distributed ions during the head-on collision of dust acoustic solitary waves

The head-on collision of dust acoustic solitary waves are studied in a dusty plasma composed of dust and nonextensive distributed ions by using the extended version of Poincaré-Lighthill-Kuo (PLK) method. The effect of the nonextensivity on the phase shift is studied. It is found that the presence of nonextensive distributed ions plays a significant role on the collision of dust acoustic solitary waves.     

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.     

Effects of two-temperature electrons, external oblique magnetic field, and higher-order nonlinearity on dust acoustic solitary waves in a dusty plasma with vortex-like ion distribution

Nonlinear properties of the dust acoustic (DA) solitary waves in a dusty plasma consisting of negatively variable-charged dust particles, vortex-like distributed ions and two-temperature isothermal electrons are reported. A reductive perturbation theory has been used to derive a modified Korteweg-de Vries (mKdV) equation for the first-order perturbed potential and a linear inhomogeneous mKdV-type equation for the second-order perturbed potential. The renormalization method is used to obtain stationary solutions of these coupled equations. The modifications in the amplitude and width of the solitary wave structure due to the inclusion of two different types of isothermal electrons, external oblique magnetic field, higher-order nonlinearity, and vortex-like distributed ions are investigated. Also a method based on energy consideration was used to obtain the stability condition. Moreover, the numerical results are applied to investigate some nonlinear characteristics of the DA solitary waves.