Modulational Instability Of Dust Acoustic Waves Research Articles

Dust–Acoustic Envelope Solitons in an Electron-Depleted Plasma

A theoretical investigation of the modulational instability (MI) of dust–acoustic waves (DAWs) by deriving a nonlinear Schrodinger equation in an electron-depleted opposite polarity dusty plasma system containing non-extensive positive ions is presented. The conditions for MI of DAWs and formation of envelope solitons are investigated. The sub-extensivity and super-extensivity of positive ions are seen to change the stable and unstable parametric regimes of DAWs. The addition of dust grains causes changes the width of both bright and dark envelope solitons. The findings of this study can help understanding the nonlinear features of DAWs in Martian atmosphere, cometary tails, solar system, laboratory experiments, etc.

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.

Dust-acoustic envelope solitons and rogue waves in an electron depleted plasma

A theoretical investigation of the modulational instability (MI) of dust-acoustic waves (DAWs) by deriving a nonlinear Schr\"{o}dinger equation in an electron depleted opposite polarity dusty plasma system containing non-extensive positive ions has been presented. The conditions for MI of DAWs and formation of envelope solitons have been investigated. The sub-extensivity and super-extensivity of positive ions are seen to change the stable and unstable parametric regimes of DAWs. The addition of dust grains causes to change the width of both bright and dark envelope solitons. The findings of this study may be helpful to understand the nonlinear features of DAWs in Martian atmosphere, cometary tail, solar system, and in laboratory experiments, etc.

Dust-Acoustic Rogue Waves in Opposite Polarity Dusty Plasma Featuring Nonextensive Statistics

Modulational instability of dust-acoustic waves, which propagate in an opposite polarity dusty plasma system containing inertial warm negatively and positively charged massive dust grains as well as nonextensive q-distributed electrons and ions has been theoretically investigated. The nonlinear Schrodinger equation is derived by employing the reductive perturbation method. The nonlinear Schrodinger equation predicts the conditions of the modulational instability of dust-acoustic waves and the formation of dust-acoustic rogue waves in a nonlinear and dispersive plasma medium. It is observed that the basic features of the dust-acoustic rogue waves (viz., amplitude and width) are significantly modified by the various plasma parameters such as nonextensivity of electrons and ions, electron number density, electron temperature, ion number density, ion temperature, the mass and number density of the dust grains, etc. The application of the results in space and laboratory opposite polarity dusty plasma is briefly discussed.

The (3+1)‐dimensional dust‐acoustic waves in multi‐components magneto‐plasmas

A three‐dimensional four components magneto‐plasma system consists of super‐thermal κ‐distributed electrons and positrons, Maxwellian ions, and inertial massive negatively charged dust grains is considered to examine the modulational instability (MI) of the dust‐acoustic waves (DAWs), which propagates in such a magneto‐plasma system. The reductive perturbation method, which is valid for small but finite amplitude DAWs, is employed to derive the (3 + 1)‐dimensional non‐linear Schrödinger equation (NLSE). The NLSE leads to the MI of DAWs as well as the formation of dust‐acoustic rogue waves (DARWs) which are formed due to the effects of non‐linearity in the propagation of the DAWs. It is found that the basic features (viz. amplitude and width) of the DAWs and DARWs (which is formed in the unstable region) are significantly modified by the various plasma parameters such as κ‐distributed electrons and positrons, temperatures, and number densities of plasma species, and so on. The application of the results in both space and laboratory magneto‐plasma systems is briefly discussed.

Existence and stability of modulated dust-acoustic wave packets in the presence of nonthermal ions

The effects of dust temperature and energetic (nonthermal) ions are incorporated in the study of modulated instability of dust-acoustic (DA) waves in a dusty plasma containing warm adiabatic dust grains, isothermal electrons and hot ions obeying a nonthermal distribution. Based on the multiple space and time scales perturbation, a nonlinear Schrödinger equation is derived with a solution showing a new relationship between the modulated DA wave packets and ion nonthermality. It is shown that as the population of fast ions increases, the transition from stable dark envelope solitons to unstable ones shifts to the smaller wavelength regions. The instability growth rate reduces owing to the presence of nonthermal ions. It is also found that the effects of dust temperature and electron concentration modify the criteria for the modulational instability of DA waves. The results could be useful for understanding the properties of modulated wave packets and their evolution in space and laboratory dusty plasmas, such as those in and around the Earth’s foreshock.

Cylindrical and spherical dust-acoustic wave modulations in dusty plasmas with non-extensive distributions

The nonlinear wave modulation of planar and non-planar (cylindrical and spherical) dust-acoustic waves (DAW) propagating in dusty plasmas, in the presence of non-extensive distributions for ions and electrons is investigated. By employing multiple scales technique, a cylindrically and spherically modified nonlinear Schrodinger equation (NLSE) is derived. The presence of hot non-extensive q-distributed ions and electron is shown to influence the modulational instability (MI) of the waves. It is shown that the properties of the MI of DAW in cylindrical and spherical geometry differ from those in a planar one-dimensional geometry. Furthermore, it is observed that the non-extensive distributed ions have more effect on the MI of the DAW than electrons. Also, it is found that there is a MI period for cylindrical and spherical wave modulations, which does not exist in the one-dimensional case.

Modulational instability of dust acoustic waves in dusty plasmas: Modulation obliqueness, background ion nonthermality, and dust charging effects

The oblique modulational instability of dust acoustic (DA) waves in an unmagnetized warm dusty plasma with nonthermal ions, taking into account dust grain charge variation (charging), is investigated. A nonlinear Schrödinger-type equation governing the slow modulation of the wave amplitude is derived. The effects of dust temperature, dust charge variation, ion deviation from Maxwellian equilibrium (nonthermality) and constituent species’ concentration on the modulational instability of DA waves are examined. It is found that these parameters modify significantly the oblique modulational instability domain in the k-θ plane. Explicit expressions for the instability rate and threshold have been obtained in terms of the dispersion laws of the system. The possibility and conditions for the existence of different types of localized excitations are also discussed. The findings of this investigation may be useful in understanding the stable electrostatic wave packet acceleration mechanisms close to the Moon, and also enhances our knowledge on the occurrence of instability associated to pickup ions around unmagnetized bodies, such as comets, Mars, and Venus.

Three-dimensional nonlinear Schrödinger equation for dust-acoustic waves and its stability in magnetized dusty plasma with two-temperature nonthermal ions and dust charge variation

The effect of two-temperature nonthermal ions and variable dust charge on small-amplitude nonlinear dust-acoustic waves (DAW) is investigated. By using the reductive perturbation technique, the three-dimensional nonlinear Schrödinger equation (3D-NLSE) is first derived. The modulational instability of DAW in the magnetized dusty plasma is investigated as well. Meanwhile, some new and important stability regions are given. The effect of the nonthermal parameter a is shown to play a significant role in the determination of the normalized dust charge. Further, setting this parameter to zero degenerates the system into one in the magnetized dusty plasma consisting of the isothermal ions.

Propagation of nonplanar dust-acoustic envelope solitary waves in a two-ion-temperature dusty plasma

The evolution of the cylindrical and spherical dust-acoustic envelope solitary wave (DAESW) in an unmagnetized dusty plasma consisting of negatively charged dust fluid and ions of two different temperatures is investigated. By using the reductive perturbation method, the cylindrical and spherical geometry-modified nonlinear Schrödinger equation (GMNLSE) is obtained. The change of the DAESW amplitude due to the cylindrical and spherical geometry effects is deduced analytically. It is shown that there exist two time ranges. On the other hand, the wave amplitude changes with time τ as (τ0/τ)m/2 when the geometry effect is stronger and as (τ0/τ)m when the geometry effect is weaker, where τ0 is the initial time, and m=1 (2) refers to the cylindrical (spherical) case. The theoretical results are verified by the numerical calculation for the GMNLSE. The modulational instability of dust-acoustic waves governed by the GMNLSE is also presented. It is shown that the propagation of the DAESW in cylindrical geometry, spherical geometry, and planar one-dimensional geometry are very different. The presence of a second component of ions would modify the nature of the modulation instabilities.