Dust-acoustic Research Articles

Generation of rogue waves in space dusty plasmas

The basic features of dust-acoustic (DA) waves (DAWs) in a four component dusty plasma system (containing inertial cold and hot dust grains and inertialess non-extensive ions and electrons) have been theoretically investigated by deriving the nonlinear Schrödinger equation. The analytic analysis under consideration demonstrates two types of modes, namely, fast and slow DA modes. The unstable domain, which can be recognized by the critical wave number (kc), gives rise to the DA rogue waves (DARWs). It is observed that the amplitude and width of the DARWs are significantly modified by various plasma parameters. The present results should be useful in understanding the conditions for modulational instability of DAWs and generation of DARWs in Saturn F-rings.

Modulational instability, rogue waves, and envelope solitons in opposite polarity dusty plasmas

Dust-acoustic (DA) waves (DAWs) and their modulational instability (MI) have been investigated theoretically in a plasma system consisting of inertial opposite polarity (positively and negatively) warm adiabatic charged dust grains as well as inertialess non-extensive q−distributed electrons and non-thermal ions. A nonlinear Schrödinger equation (NLSE) is derived by using the reductive perturbation method. It has been observed from the analysis of NLSE that the modulationally stable solitary DAWs give rise to the existence of dark envelope solitons, and that the modulationally unstable solitary DAWs give rise to the existence of bright envelope solitons or rogue structures. It is also observed for the fast mode of DAWs that the basic features (viz. stability of the DAWs, MI, growth rate, amplitude, and width of the DA rogue waves, etc.) are significantly modified by the related plasma parameters (viz. dust masses, dust charge state, non-extensive parameter q, and non-thermal parameter α). The results of our present investigation might be useful for understanding different nonlinear electrostatic phenomena in both space (viz. ionosphere and mesosphere) and laboratory plasmas (viz. high intensity laser irradiation and hot cathode discharge).

Effect of polarization force on dust-acoustic cnoidal waves in dusty plasma

A theoretical investigation has been presented to study the effect of polarization force on nonlinear dust acoustic (DA) cnoidal waves in dusty plasma composed of negatively charged dust fluid, Maxwellian electrons and superthermally distributed ions. The effect of polarization force is significantly modified due to the presence of the superthermal ions. In particular, an increase in superthermality index of ions leads to a decrease in polarization parameter. By employing reductive perturbation method, the nonlinear Korteweg–de Vries (KdV) equation is derived for the study of DA cnoidal waves. Further, the Sagdeev potential approach is employed to find the solution of KdV equation to analyze the characteristics of DA cnoidal waves. Only negative potential DA cnoidal waves are observed. Furthermore, the combined effects of polarization force and superthermality of ions on the characteristics of negative potential DA cnoidal waves have been studied in detail. It is emphasized that the real implementation of our present results is in laboratory experiments as well as in different regions of space and astrophysical environments especially in Saturn’s magnetosphere, comet tails, etc.

Nonplanar dust-acoustic waves and chaotic motions in Thomas Fermi dusty plasmas

The properties of linear and nonlinear nonplanar dust acoustic (DA) solitary waves and chaotic behavior are investigated in an unmagnetized Thomas Fermi dusty plasma, whose components are degenerate electrons, ions, and negatively charged inertial cold dust grains. A linear dispersion relation is obtained and solved numerically. It has been observed that linear excitation characteristics are influenced by radial distance r, geometric term ν, and ion-to-electron Fermi temperature ratio σi. We have also noted that the addition of a geometrical term in dispersion relation gives damping along the radial axis. A modified Korteweg-de Vries (KdV) equation is derived by employing the reductive perturbation technique, and its numerical solutions are obtained. The modified KdV equation is discussed for cold dust grains in planar and nonplanar frameworks. Upon the introduction of external periodic perturbation, the perturbed modified KdV equation is studied in planar geometry via some qualitative and quantitative approaches. The perturbed KdV equation can give rise to the periodic, quasiperiodic, and chaotic motions for DA waves. The strength of the external perturbation and dust concentration h play the major role of the switching parameter in the transition of dynamic motion. The developed chaos can be weakened with the variation of dust concentration h. It has been observed that the dust concentration affects the dynamics of DA waves in planar geometry which is an important observation in this study.

Dust acoustic shock waves in magnetized dusty plasma

We have presented a theoretical study of the dust acoustic (DA) shock structures in a magnetized, electron depleted dusty plasma in the presence of two temperature superthermal ions. By deriving a Korteweg–de Vries–Burgers equation and studying its shock solution, we aim to highlight the effects of magnetic field and obliqueness on various properties of the DA shock structures in the presence of kappa-distributed two temperature ion population. The present model is motivated by the observations of Geotail spacecraft in the Earth's magnetotail and it is seen that the different physical parameters such as superthermality of the cold and hot ions, the cold to hot ion temperature ratio, the magnetic field strength, obliqueness and the dust kinematic viscosity greatly influence the dynamics of the shock structures so formed. The results suggest that the variation of superthermalities of the cold and hot ions have contrasting effects on both positive and negative polarity shock structures. Moreover, it is noted that the presence of the ambient magnetic field affects the dispersive properties of the medium and tends to make the shock structures less wide and more abrupt. The findings of present investigation may be useful in understanding the dynamics of shock waves in dusty plasma environments containing two temperature ions where the electrons are significantly depleted.

Effect of Ion Beam on Low-Frequency Cnoidal Waves in a Non-Maxwellian Dusty Plasma

The propagation properties of dust acoustic (DA) cnoidal waves in unmagnetized dusty plasma consisting of dust fluid, nonextensive electrons, and ions penetrated by a positive ion beam have been studied in this investigation. Korteweg de Vries equation is derived using the reductive perturbation method, and appropriate boundary conditions are applied to investigate the characteristics of nonlinear cnoidal waves. Only negative potential (rarefactive) DA cnoidal structures are observed in the given plasma system. The combined effect of various plasma parameters, such as nonextensivity of electrons and ions, temperature, and concentration of ion beam, are observed on the characteristics of DA cnoidal waves. The findings of the present investigations may be helpful in understanding the characteristics of nonlinear excitations in the polar cap region and other space/astrophsical environments.

Bifurcation Analysis for Dust-Acoustic Waves in a Four-Component Plasma Including Warm Ions

Investigation of linear dust-acoustic (DA) waves was analyzed in a system of collisionless, dissipative, and unmagnetized four-component dusty plasma consisting of cold positively and negatively charged particles of dust, with ions and electrons are of the Boltzmann distribution. The compatibility condition is obtained by using the normal mode analysis. The Korteweg de Vries–Burgers (KdV–Burgers) equation is obtained when the plasma system is nonlinearly analyzed by the reductive perturbation method. To study the nonlinear waves, we obtain some interesting physical solutions. These solutions are in the form of soliton, a combination between a shock and a soliton, and finally monotonic and oscillatory shock waves. Graphical illustration for these solutions was presented. The characteristics of the DA solitary and shock waves are significantly modified by the presence of positive and negative dust ions, the ratio of the ion to electron temperatures, and it is also found that the basic features are affected by the dust kinematic viscosity. The planar dynamical systems bifurcation theory, which was used to establish the existence of solitary wave solutions and periodic traveling wave solutions, has been established. Accordingly, the phase portrait topology and the potential diagram are illustrated for the KdV–Burgers equation. As a result of different phase orbits, there is an advantage to predict different classes of traveling wave solutions. The electric field is determined. Generalization of the obtained results in this paper can be used to investigate the nature of plasma waves in both laboratory and space.

Effects of Polarized Debye Sheath and Trapped Ions on Solitary Structures in a Strongly Coupled Inhomogeneous Dusty Plasma

The effects of polarized Debye sheath (i.e., polarization force) and trapped ions on the nonlinear propagation of dust-acoustic (DA) waves are investigated, including the dust inhomogeneity in the strongly coupled dusty plasma. Dispersion relation and propagation of possible modes are calculated from the underlying usual hydrodynamic model. Then, a variable coefficient’s modified Korteweg-de Vries equation describing the dynamics of DA solitary waves is derived from a weakly nonlinear analysis, and is solved to get the stationary solutions using a sine–cosine method. It is found that for experimental conditions under which the interaction of resonant ions and highly negatively charged dust grains is important, only soliton with negative potential can propagate in such a strongly coupled inhomogeneous dusty plasma. In the presence of trapped ions, the amplitude of solitary waves is found to be smaller compared with that for the Boltzmann distribution. Moreover, it is argued that the soliton profile is highly sensitive to the effects of modified strength of the polarization force, dust temperature, and dust density inhomogeneity.

Effect of polarization force on head-on collision between multi-solitons in dusty plasma

Head-on collision among dust acoustic (DA) multi-solitons in a dusty plasma with ions featuring non-Maxwellian hybrid distribution under the effect of the polarization force is investigated. The presence of the non-Maxwellian ions leads to eloquent modifications in the polarization force. Specifically, an increase in the superthermality index of ions (via κi) and nonthermal parameter (via α) diminishes the polarization parameter. By employing the extended Poincaré-Lighthill-Kuo method, two sided KdV equations are derived. The Hirota direct method is used to obtain multi-soliton solutions for each KdV equation, and all of them move along the same direction where the fastest moving soliton eventually overtakes the others. The expressions for collisional phase shifts after head-on collision of two, four, and six-(DA) solitons are derived under the influence of polarization force. It is found that the effect of polarization force and the presence of non-Maxwellian ions have an emphatic influence on the phase shifts after the head-on collision of DA rarefactive multi-solitons. In a small amplitude limit, the impact of polarization force on time evolution of multi-solitons is also illustrated. It is intensified that the present theoretical pronouncements actually effectuate in laboratory experiments and in space/astrophysical environments, in particular in Saturn's magnetosphere and comet tails.

Dust Acoustic (DA) Waves in a Magnetised Plasma with Boltzmann Distributed Electrons and Ions

Dust Acoustic (DA) Waves in a Magnetised Plasma with Boltzmann Distributed Electrons and Ions

Dust acoustic cnoidal waves in a polytropic complex plasma

The nonlinear characteristics of dust acoustic (DA) waves in an unmagnetized collisionless complex plasma containing adiabatic electrons and ions and negatively charged dust grains (including the effects of modified polarization force) are investigated. Employing the reductive perturbation technique, a Korteweg–de Vries–Burgers (KdVB) equation is derived. The analytical solution for the KdVB equation is discussed. Also, the bifurcation and phase portrait analyses are presented to recognize different types of possible solutions. The dependence of the properties of nonlinear DA waves on the system parameters is investigated. It has been shown that an increase in the value of the modified polarization parameter leads to a fast decay and diminishes the oscillation amplitude of the DA damped cnoidal wave. The relevance of our findings and their possible applications to laboratory and space plasma situations is discussed.

Landau damping of dust acoustic solitary waves in nonthermal plasmas

Dust acoustic (DA) solitary and shock structures have been investigated under the influence of Landau damping in a dusty plasma containing two temperature nonthermal ions. Motivated by the observations of Geotail spacecraft that reported two-temperature ion population in the Earth's magnetosphere, we have investigated the effect of resonant wave-particle interactions on DA nonlinear structures. The Korteweg-de Vries (KdV) equation with an additional Landau damping term is derived and its analytical solution is presented. The solution has the form of a soliton whose amplitude decreases with time. Further, we have illustrated the influence of Landau damping and nonthermality of the ions on DA shock structures by a numerical solution of the Landau damping modified KdV equation. The study of the time evolution of shock waves suggests that an initial shock-like pulse forms an oscillatory shock at later times due to the balance of nonlinearity, dispersion, and dissipation due to Landau damping. The findings of the present investigation may be useful in understanding the properties of nonlinear structures in the presence of Landau damping in dusty plasmas containing two temperature ions obeying nonthermal distribution such as in the Earth's magnetotail.

Study of the Characteristics of Dust Acoustic Solitary Waves and Dust Acoustic Shock Waves in Electron Free Dusty Space Plasma

A theoretical investigation has been done for the study of dust acoustic solitary waves and dust acoustic shock waves propagating in an unmagnetized, collisionless Lorentzian dusty plasma considering adiabatic and non-adiabatic dust charge variation. Plasma under consideration is composed of inertialess Lorentzian positive and negative ions along with inertial positively charged dust grains. Such dust grains are charged by the flow of positive ion and negative ion current over the grain surface. Adiabatic grain charge variation shows the existence of compressive soliton whose amplitude decreases and width increases with increasing number of suprathermal particles. Non-adiabatic dust charge variation is concerned with the propagation of monotonic dust acoustic shock waves which do not loose monotonicity even when a number of suprathermal particles are very large.

Quasi-electrostatic twisted waves in Lorentzian dusty plasmas

The quasi electrostatic modes are investigated in non thermal dusty plasma using non-gyrotropic Kappa distribution in the presence of helical electric field. The Laguerre Gaussian (LG) mode function is employed to decompose the perturbed distribution function and helical electric field. The modified dielectric function is obtained for the dust ion acoustic (DIA) and dust acoustic (DA) twisted modes from the solution of Vlasov-Poisson equation. The threshold conditions for the growing modes is also illustrated.

Higher order corrections to dust-acoustic shock waves in a strongly coupled cryogenic dusty plasma

To investigate the contribution of higher-order nonlinearity and dissipation to nonlinear ultra-low-frequency dust-acoustic shock waves (DASWs), a reductive perturbation technique is employed in a strongly coupled cryogenic dusty plasma. The model consists of Boltzmann distributed electrons and ions, as well as equations for strongly coupled charged dust grains. A nonlinear Burger equation and a linear inhomogeneous Burger-type equation are derived. The present model admits both compressive and rarefactive dust-acoustic (DA) shocks. Including these higher-order corrections results in creating new shock wave structures called “humped DASWs.” It is shown that the effects of kinematic viscosity, the number of electrons residing on the dust grain surface, Zd, and the dust number density via β have important roles in the basic features of the produced DA shocks and the associated electric fields. It has been shown that it is more important to be included. These findings are devoted to explaining the observed waves propagating in the laboratory plasma experiments at cryogenic temperature. This kind of plasma is used for etching nano-patterns without defects, used in nonideal systems, and physics of nucleation to deposit nanosize Si compounds.

Rogue waves in space dusty plasmas

The modulational instability of dust-acoustic (DA) waves (DAWs) and corresponding DA rogue waves (DARWs) in a realistic space dusty plasma system (containing inertial warm positively and negatively charged dust, isothermal ions, and super-thermal kappa distributed electrons) has been theoretically investigated. The nonlinear Schrödinger equation is derived by using a reductive perturbation method for this investigation. It is observed that the dusty plasma system under consideration supports two branches of modes, namely, fast and slow DA modes, and that both of these two modes can be stable or unstable depending on the sign of ratio of the dispersive and nonlinear coefficients. The numerical analysis has shown that the basic features (viz., stability/instability, growth rate, amplitude, and width of the rogue structures, etc.) of the DAWs associated with the fast DA modes are significantly modified by super-thermal parameter (κ) and other various plasma parameters. The results of our present investigation should be useful for understanding DARWs in space plasma systems, viz., mesosphere and ionosphere.

Large-amplitude dust acoustic shocklets in non-Maxwellian dusty plasmas

The formation and propagation of fully nonlinear dust-acoustic (DA) waves and shocks are studied in a non-Maxwellian thermal dusty plasma which is composed of Maxwellian electrons and nonthermal energetic ions with a neutralizing background of negatively charged dust grains. For this purpose, we have solved dust dynamical equations along with quasineutrality equation by using a diagonalization matrix technique. A set of two characteristic wave equations is obtained, which admits both analytical and numerical solutions. Taylor expansion in the small-amplitude limit (Φ≪1) leads to nonlinear effective phase and shock speeds accounting for nonthermal energetic ions. It is numerically shown that DA pulses can be developed into DA shocklets involving the negative electrostatic potential, dust fluid velocity, and dust number density. These structures are significantly influenced by the ion-nonthermality, dust thermal correction, and temporal variations. However, the amplitudes of solitary and shock waves are found smaller in case of Cairns-distributed ions as compared to Kappa-distributed ions due to smaller linear and nonlinear effective phase speeds that cause smaller nonlinearity effects. The present results should be useful for understanding the nonlinear characteristics of large-amplitude DA excitations and nonstationary shocklets in a laboratory non-Maxwellian dusty plasma, where nonthermal energetic ions are present in addition to Maxwellian electrons.

Twisted electrostatic waves in a self‐gravitating dusty plasma

A generalized response (dielectric) function for twisted electrostatic waves is derived for an un‐magnetized self‐gravitating thermal dusty plasma, whose constituents are the Boltzmann‐distributed electrons and positive ions in the presence of negatively charged micrometre‐sized massive dust particulates. For this purpose, a set of Vlasov–Poisson coupled equations is solved along with the perturbed Laguerre–Gauss distribution function, as well as the electrostatic and gravitational potentials in the limit of paraxial approximation. For plane wave solution, the wavefronts of the dust‐acoustic (DA) wave are assumed to have a constant phase with electric and gravitational field lines propagating straight along the propagation axis. On the other hand, non‐planar wave solutions show helical (twisted) wavefronts, in which field lines spiral around the propagation axis owing to the azimuthal velocity component to account for the finite orbital angular momentum (OAM) states. The dispersion relation and damping rate for twisted DA waves are studied both analytically and numerically. It is shown that finite OAM states, the dust to electron temperature ratio, and dust self‐gravitation effects significantly affect the linear dispersion and Landau damping frequencies. In particular, the phase speed of twisted DA waves is reduced with the variation of the twist parameter η (= k/lqϕ), dust concentration δ (= nd0/ni0), and dust self‐gravitation α (= ωJd/ωpd). The relevance of our findings to interstellar dust clouds is also discussed for micrometre‐sized massive dust grains.

Effects of two-temperature ions on head-on collision and phase shifts of dust acoustic single- and multi-solitons in dusty plasma

Propagation characteristics and interaction phenomena among the dust acoustic (DA) solitons in unmagnetized dusty plasmas are studied. The plasma is composed of negatively charged mobile dust, Boltzmann distributed electrons, and nonthermally distributed cold and hot ions. The extended Poincaré-Lighthill-Kuo method is employed to derive the two-sided Korteweg–de Vries (KdV) equations. The solutions of the KdV equations are constructed using the Hirota bilinear method both for single- and multi-solitons. The phase shifts are determined for the interactions among the two-, four-, and six-DA solitons. The effects of plasma parameters on the head-on collisions of the DA single- and multi-solitons and their corresponding phase shifts are investigated.

Low-frequency shock waves in a magnetized superthermal dusty plasma

The characteristics of low-frequency shocks in a magnetized dusty plasma comprising of negatively charged dust fluid, kappa-distributed electrons and ions have been investigated. Using the reductive perturbation method, the nonlinear Korteweg de–Vries–Burgers (KdV–B) equation which governs the dynamics of the dust acoustic (DA) shock waves is derived. The characteristics of shock structures are studied under the influence of various plasma parameters, viz. superthermality of ions, magnetic field, electron-to-dust-density ratio, kinematic viscosity, ion-to-electron-temperature ratio and obliqueness. The combined effects of these physical parameters significantly influence the characteristics of DA shock structures. It is observed that only negative potential shocks exist in a plasma environment comprising of dust fluid and superthermal electrons and ions such as that of Saturn’s magnetosphere.