Propagation Of Dust-acoustic Waves Research Articles

Novel nonlinear quantum dust acoustic waves for modified variable coefficients Zakharove–Kusnetsov equation in dusty plasma

In this paper, the direct similarity reduction method is used to reduce the modified variable coefficient Zakharove–Kusnetsov equation (vcmZK), which represents the propagation of quantum dust acoustic waves (QDAWs) in an inhomogeneous magnetized dusty plasma field, into a nonlinear ordinary differential equation (NODE). Moreover, the Jacobi elliptic method is used to solve the NODE, where many novel double periodic, kink, and solitary wave solutions are obtained. Additionally, we have chosen to plot periodic, kink, and soliton QDAWs solutions according to some choices for the variable coefficients. According to the a chieved results, we can conclude that the choices of the functional forms of the variable coefficients can control the QDAWs propagation. Finally, the new discovered results may have many important applications in astrophysics, atmospheric science, nanotechnology, and industrial plasma physics.

Low frequency dust acoustic drift instability in the equatorial electrojet

The dust acoustic drift instability has been investigated at the lower electrojet region of the dusty ionosphere by considering a linearized fluid model. The effect of dust-neutral collisions, electron–ion recombination at the surface of the dust particles, and electron and ion inertia on the onset and growth of the instability have been explored in minutiae. The perturbed densities are gleaned from the electron, ion, and dust dynamics, which engendered generalized dispersion relations. The generalized dispersion relation delineates the propagation of low-frequency dust acoustic drift waves. The dispersion relation is solved numerically for various cases of interest at the two different altitudes(∼90km and ∼100km) of the lower electrojet region. It has been found that the instability is unlikely to develop due to recombination alone, similar as observed in the case of laboratory dusty plasma. A significant reduction of the growth rate has been observed in the low-frequency mode due to the dust-neutral collision both in the presence and absence of an equilibrium electron density gradient. However, the effect of dust-neutral collision is not discernible in the relatively higher frequency mode, which exists at an altitude of 100km. Moreover, the presence of electron and ion inertia has a stabilizing effect on the instability. The analysis presented here is germane to the lower ionospheric dusty electrojet region in which electrons are magnetized, but ions and dust particles are unmagnetized.

Overtaking interactions in a strongly coupled inhomogeneous dusty plasma: the role of polarization force

The nonlinear propagation of dust-acoustic waves (DAWs) is considered in a collisionless, inhomogeneous, weakly and strongly coupled dusty plasma composed of negatively charged dust, electrons, and ions. The reductive perturbation method is used to derive a Korteweg–de Vries equation (KdV). It is found that the KdV solitons are affected by the plasma parameters, whereas only rarefactive DAWs are obtained. Hirota’s bilinear approach is used to investigate the overtaking collision of two and three-soliton solutions. Physical parameters such as polarization, and the ions and electrons density gradient scale lengths have a significant impact and cause alterations in the behaviour of the solitons. Notably, as the polarization and ion density gradient scale length increase, the amplitude and width of the solitons decrease. Furthermore, the system parameters also affect the phase shifts of the solitons. The findings presented here have potential applications in the study of acoustic waves in compact astrophysical systems, where quantum polarization and inhomogeneity effects cannot be ignored, as well as in laboratory plasmas.

Nonlinear propagation of dust-acoustic waves and its modulation instability

Investigation the nonlinear dust-acoustic waves in a complex plasma in Titan’s ionosphere sets to become a vital factor in understanding different wave profiles in such space plasma. As for dust on Titan, there is evidence that suggests the Moon has a dusty surface. The Cassini spacecraft, which explored Saturn and its moons, detected bright spots on Titan’s surface that could be the result of dust or ice particles reflecting sunlight. Based on the above finding, a convenient mathematical model is considered and an appropriate evolution equation (Korteweg–de Vries-Burgers KdVB equation) is derived. At low wavenumber, the KdVB equation is transformed to a complex Ginzburg-Landau (CGL) equation that describes the propagation of the wave packet in the system, which is an efficient tool for studying rogue waves in space plasmas. Different plasma parameters are examined on the propagating waves in Titan’s ionosphere.

Propagation of Arbitrary Amplitude Dust Acoustic (DA) Waves in a Magnetized Plasma with Non-thermal Electrons and Ions

Propagation of Arbitrary Amplitude Dust Acoustic (DA) Waves in a Magnetized Plasma with Non-thermal Electrons and Ions

Small amplitude dust acoustic solitary waves in a magnetized dusty plasma with nonthermal distribution for both electrons and ions

The propagation of dust acoustic solitary waves (DASWs) has been investigated in a magnetized dusty plasma consisting of negatively charged dust particles, nonthermal ions and nonthermal electrons. Using reductive perturbation method, the Korteweg-de-Vries (K-dV) equation is derived. It is found that the basic structures (such as polarity, amplitude, width) of DASWs are influenced by nonthermal ions and nonthermal electrons. The results show that both compressive and rarefactive DASWs exist in such dusty plasma. It is observed that by increasing the nonthermality parameter of ions and electrons, the nonlinear wave phase velocity increases. Furthermore, nonthermal distributed ions have more effect on the nonlinear wave phase velocity of the DASWs than nonthermal distributed electrons. The dependence of the angle that the external magnetic field makes with the propagation direction of wave on the amplitude and width of DASWs has been also investigated. It was concluded that this angle strongly affects the DASWs. Finally, the effect of the magnetic field appears only in the width and not in the amplitude of the DASWs. The findings of this study can be helpful in understanding the structures of DASWs in the dusty plasma in which both nonthermal ions and nonthermal electrons exist. Such structures can be found in different regions of space and astrophysics mediums such as the upper ionosphere and Saturn’s E-ring.

Solitary wave solution of (3+1)-dimensional cylindrical Kadomstev–Petviashvili equation in warm opposite polarity dusty plasma

A theoretical investigation is done to study the propagation of dust-acoustic (DA) solitary waves in a dusty plasma system containing dynamic positively as well as negatively charged warm dust species and nonthermally distributed ion and electron species. The standard reductive perturbation method is employed to derive the (3+1)-dimensional cylindrical Kadomstev–Petviashvili (KP) equation (also known as cylindrical Korteweg–de Vries equation), which admits solitary wave solution for small but finite amplitudes. The parametric regimes for the existence of DA solitary waves are obtained. Two modes, namely, slow and fast are observed corresponding to different phase velocities. The slow mode has negative solitary pulses, whereas the fast mode contains both positive and negative DA solitary waves. It is shown that the ratio of positively charged dust to negatively charged dust number density significantly modifies the basic features of the DA solitary waves. The noteworthy effects of other parameters (viz. the nonthermal parameter and ion-to-electron temperature ratio) on the basic properties (namely, phase speed, polarity, amplitude, and width) of the DA solitary waves are also mentioned. The fundamental features and the underlying physics of the electrostatic solitary structures that are relevant to cometary tails, upper mesosphere, Jupiter’s magnetosphere, etc., are briefly discussed.

Propagation and Head-On Collision of Dust Acoustic Waves in Collisional Dusty Plasma: the Saturn Main Rings

Propagation and Head-On Collision of Dust Acoustic Waves in Collisional Dusty Plasma: the Saturn Main Rings

Dust-acoustic solitary and periodic waves in a plasma with ion distribution with trapped particles

The nonlinear propagation of electrostatic dust-acoustic waves is studied in an unmagnetized three-component dusty plasma consisting of negatively charged dust, free as well as a small percentage of trapped ions and Maxwellian electrons. By using the reductive perturbation technique, a Korteweg de Vries type equation, which governs the dynamics of the small-amplitude solitary and periodic waves of the dusty plasma under consideration, is derived. The traveling soliton (shown to be only of the rarefactive type) and periodic solutions of the KdV type equation are obtained. Bifurcation analysis for the obtained nonlinear KdV type equation is used to describe the qualitative phase portrait for the corresponding dynamical system, which is found to be controlled by the plasma system parameters. The effects of trapped ions and free electrons on the dust-acoustic solitons and periodic waves are discussed. The present investigation may be useful in understanding some nonlinear features of the dust-acoustic waves, which have been observed in astrophysical plasmas such as Saturn's moon Enceladus.

Propagation of dust-acoustic nonlinear waves in a homogeneous collisional dusty plasma

Nonlinear propagation of dust-acoustic waves DAWs in a weakly collisional dusty plasma comprising warm adiabatic fluid dust particles, isothermal electrons, and ions is investigated. We used the reductive perturbation theory to reduce the basic set of fluid equations to one evolution equation, namely damped Kadomtsev–Petviashivili (DKP). The analytical stationary solutions of the DKP equation are numerically analyzed, and the effect of various dusty plasma parameters on DAWs wave propagation is taken into account. We obtained, blast, anti-kink, periodic cnoidal and cnoidal waves. It is well known that explosive waves are a double edged sword. They can be seen, for example, in the atmosphere, or in engineering applications in metal coating.

Dissipative dust acoustic solitons in magnetized nonextensive warm dusty plasma

A systematic theoretical investigation has been carried out in order to explore the propagation of both linear and nonlinear dust acoustic waves (DAWs) in a collisional magnetized warm dusty plasma in the presence of nonextensive electrons and ions. A linear dispersion relation is analyzed to show that the wave frequencies of both parallel and perpendicular modes are modified by the relevant plasma parameters. The standard reductive perturbative technique leads to a Korteweg–de Vries equation with a linear damping term for the propagation dynamics of the finite amplitude waves in warm dusty plasma. It is found that the dust-neutral collision induced dissipation is responsible for the linear damping. The analysis reveals that DAW propagates in the form of a weakly dissipative compressive/rarefactive solitons and the nonlinear excitations are significantly influenced by different plasma parameters, such as dust concentration, nonextensivity, external magnetic field strength, and dust-neutral collisionality. The present results can be relevant to the DAWs in some astrophysical plasma environments, such as Saturn’s rings, interstellar dusty clouds, etc.

The existence and propagation of dust acoustic waves in quantum four-component plasma

The existence and propagation of dust acoustic waves in quantum four-component plasma are investigated by employing Sagdeev pseudo-potential. The plasma under consideration consists of both quantum electrons and ions beside negative and positive dust particulates. The general determining equation of the Sagdeev pseudo-potential is obtained, and it is found that the equation is very difficult to integrate. Due to the complexity involved in the structure of Sagdeev potential, this equation can only be solved in some limiting cases, such as semi-classical limit and small amplitude approximation. Our findings support the existence of compressive, rarefactive solitary waves and double layers in our plasma system. The influence of the relevant plasma parameters on the existence and profile of the obtained quantum nonlinear waves has been studied. The implications of the obtained results have wide relevance in the study of space and laboratory quantum dusty plasmas situations such as Jupiter’s magnetosphere, upper and lower mesosphere, and comet tails, as well as in condensed matter systems.

Effect of non adiabatic dust charge fluctuation on nonplanar dust acoustic waves in superthermal polarized plasma

Some properties of cylindrical/spherical dust acoustic solitary waves have been studied in collisionless dusty plasma with variable charges under the influence of polarization force by reductive perturbation method. It is shown that the collisionless damping due to dust charge fluctuation causes the dust acoustic wave propagation to be described by the nonplanar damped Korteweg de Vries equation. By use of weighted residual method, a progressive wave solution to nonplanar damped KdV equation is presented for the first time. It is shown that dust charge fluctuation produce damping which is responsible for wave attenuation. The solution shows that as one goes towards the axis of the cylinder or centre of the sphere, the wave attenuates faster and the effects are shown in some 2D figures. Within a small amplitude limit, the influence of dust charge fluctuation, polarisation power, superthermality and ion temperature on the time evolution of dust acoustic solitons is also demonstrated. In laboratory experiments and space regions, findings obtained here may shed light on the salient characteristics of DA waves.

Collisionless damping of nonplanar dust acoustic waves due to dust charge fluctuation in nonextensive polarized plasma

A rigorous theoretical investigation has been made of the cylindrical/spherical dust acoustic waves in collisionless dusty plasma with variable charges under the influence of polarization force by reductive perturbation method. It is shown that the collisionless damping due to dust charge fluctuation causes the dust acoustic wave propagation to be described by the nonplanar damped Korteweg–de Vries equation. By use of weighted residual method, a progressive wave solution to nonplanar damped KdV equation is presented for the first time. It is shown that dust charge fluctuation produce damping which is responsible for wave attenuation. The solution shows that as one goes towards the axis of the cylinder or centre of the sphere, the wave attenuates faster and the effects are shown in some 2D figures. Within a small amplitude limit, the influence of dust charge fluctuation, polarisation power, nonextensivity and ion temperature on the time evolution of dust acoustic solitons is also demonstrated. In laboratory experiments and space regions, findings obtained here may shed light on the salient characteristics of DA waves.

Electrostatic Dust-Acoustic Rogue Waves in an Electron Depleted Dusty Plasma

The formation of gigantic dust-acoustic (DA) rouge waves (DARWs) in an electron depleted unmagnetized opposite polarity dusty plasma system is theoretically predicted. The nonlinear Schrödinger equation (NLSE) is derived by employing the reductive perturbation method. It is found that the NLSE leads to the modulational instability (MI) of DA waves (DAWs), and to the formation of DARWs, which are caused by to the effects of nonlinearity and dispersion in the propagation of DAWs. The conditions for the MI of DAWs and the basic properties of the generated DARWs are numerically identified. It is also seen that the striking features (viz., instability criteria, amplitude and width of DARWs, etc.) of the DAWs are significantly modified by the effects of super-thermality of ions, number density, mass and charge state of the plasma species, etc. The results obtained from the present investigation will be useful in understanding the MI criteria of DAWs and associated DARWs in electron depleted unmagnetized opposite polarity dusty plasma systems like Earth’s mesosphere (where the D-region plasma could suffer from electron density depletion), cometary tails, Jupiter’s magnetosphere, and F-ring of Saturn, etc.

On the approximate solutions of a damped nonplanar modified Korteweg–de Vries equation for studying dissipative cylindrical and spherical solitons in plasmas

In this work, the effect of both nonplanar (cylindrical and spherical) geometry and the dust-neutral collision on the propagation of dissipative nonplanar electrostatic dust-acoustic solitary waves (DASWs) in a strongly coupled complex plasma (SCCP) is examined. The electrons and ions are assumed to follow a Maxwellian and non-Maxwellian trapped velocity distributions, respectively. The fluid governing equations of the plasma species are reduced to an evolution equation using the reductive perturbation technique (RPT). For describing the dynamical mechanism of the dissipative nonplanar DASWs, the evolution equation (the damped nonplanar Shamel Korteweg–de Vries (SKdV)) is solved numerically using both homotopy perturbation method (HPM) and the improved multistage homotopy perturbation method (MsHPM). The numerical solutions of the integrable planar Shamel-KdV (SKdV) equation using both HPM and MsHPM is compared with the exact solution of the SKdV. Also, the comparison between the numerical solutions of the damped nonplanar SKdV using both HPM and MsHPM is discussed. Moreover, the maximum global residual error for both HPM and MsHPM is estimated for measuring the accuracy of the obtained numerical solutions. Furthermore, the dependence of dissipative nonplanar solitons characteristics on various plasma parameters are investigated.

Generalized non-ideal treatment and growth rates analysis of drift waves instabilities in a collisions-free magnetized dusty plasma

Dust acoustic wave propagation in weak magnetized homogeneous dusty plasmas has been extensively and successfully studied by different authors. Here, it is analyzed the behavior of electrostatic drift waves of very low frequency, appearing as due to the motion of plasma particles across the static magnetic field and the inhomogeneity introduced by the distribution of the particles in the dusty plasma generating the well-known diamagnetic effect. To study this situation, the kinetic Vlasov model in plasmas will be used. However, these models tend to behave unstably driven by the quasi-equilibrium of the diamagnetic current arising by the heavier species of dusty plasma particles. While other authors have used a standard state equation, such as the Van der Waals one, here, a more accurate model has been chosen as the equation of Ree and Hoover, a state equation that can be considered as a new form of the state equation. Together with the multipole approximation of the dispersion function, Z53 [P. Martin et al., J. Math. Phys. 21, 280–283 (1980)] allows a new derivation to obtain the simplest form of the dispersion relation in the form of a polynomial with complex coefficients. This mathematical approach was realized successfully and allowed straightforward calculus of the growth rate due to the drift unstable mode. This problem has been extensively analyzed in this work, including the non-ideal effect of dusty plasmas. These unstable modes are well discriminated and plotted as a function of the density of the grains in dusty plasma and their radius. Temperature gradients and charge fluctuation have been ignored.

Damping of dark envelope soliton in a viscous bounded dusty plasma

The propagation of dust-acoustic waves in a dusty plasma bounded in finite symmetrical cylindrical geometry has been theoretically investigated. By using the reductive perturbation method, we obtain a quasi-nonlinear Schrodinger equation. It is shown that there is a dark envelope soliton under certain conditions, while its amplitude will decrease with the time. The dependence of both the dispersion relation and group velocity of envelope solitary waves on the radius of cylinder has been given. Moreover, we define the duration time of dark envelope solitons and give the theoretical ones. It is found that the duration time increases as the radius of cylinder increases, while it decreases as the viscosity coefficient of dusty plasmas increases.

Propagation of dust-acoustic nonlinear waves in a superthermal collisional magnetized dusty plasma

The nonlinear features of dust-acoustic waves (DAWs) propagating in a multicomponent, collisional, magnetized dusty plasma whose constituents are negative dust grains, superthermal ions, and electrons are investigated. The hydrodynamic fluid equations are reduced to a damped Zakharov–Kuznetsov (DZK) equation, using the reductive perturbation technique. The DZK equation is solved using both the generalized $$(G^{{\prime }}/G)$$ –expansion method and the Painleve analysis method. Each method gives a class of solutions. This indicates that these methods are sufficient to give all possible solutions of the DZK equation. These solutions successfully describe different kinds of nonlinear waves such as explosive, soliton, shocklike, periodical, and cnoidal waves. Additionally, the effects of different plasma parameters such as relative densities and temperatures as well as superthermality parameters of ions and electrons on the behavior of the obtained diverse waves are investigated. The relevance of the present investigation can be used to understand the cosmic dust-laden plasmas.

New cutoff and resonance for dust acoustic waves in dusty mesosphere

The WKB approximation has been employed to study the impacts of dust density inhomogeneity and dust size variation on dust acoustic (DA) wave propagation in the mesosphere. A local dispersion relation is obtained, which introduces one cutoff and one resonance frequency. It is shown that the growth rate of a gradient instability and the range of the amplifying wave propagation are substantially affected by the dust size distribution and density inhomogeneity. Moreover, in the low dust density region, the amplitude and the steepness of DA increase.