Dust-ion-acoustic Research Articles

Dust–ion–acoustic damped solitary waves and shocks in laboratory and Saturn's E-ring magnetized nonthermal dusty plasmas with anisotropic ion pressure and dust-charge fluctuation

We study the oblique propagation of weakly nonlinear dust–ion–acoustic (DIA) solitary waves (SWs) and shocks in collisional magnetized nonthermal dusty plasmas that are relevant in laboratory and space (Saturn's E-ring) environments. We consider plasmas to be composed of q-nonextensive hot electrons, thermal positive ions, and immobile negatively charged dust grains immersed in a static magnetic field and take into account the effects of ion creation (source), ion loss (sink), ion–neutral and ion–dust collisions, anisotropic ion pressure, and dust-charge fluctuations on the evolution of small-amplitude SWs and shocks. The ion–neutral collision enhancement equilibrium dust-charge number is self-consistently determined using Newton–Raphson method. We found that in laboratory dusty plasmas with adiabatic dust-charge variation [i.e., when the dust charging frequency (νch) is much higher than the dust–plasma oscillation frequency (ωpd)], the DIA solitary waves (DIASWs) get damped by the effects of the ion–dust and ion–neutral collisions, whereas the ion creation and ion loss lead to the amplification of solitary waves, and they appear as only compressive types with positive potential. On the other hand, in Saturn's E-ring plasmas, where the collisional and ion creation or ion loss effects are insignificant, the non-adiabaticity of dust-charge variation can give rise to the evolution of either damped DIASWs or DIA shocks, depending on the smallness of the ratios νch/ωpd or ωpd/νch, respectively. Furthermore, two critical values of the nonextensive parameter q exist, below (or above) which, the DIASWs and shocks can appear as rarefactive (or compressive) types. The characteristics of DIASWs and shocks are also analyzed numerically for parameters relevant to the laboratory and Saturn's E-ring plasmas.

Modified Korteweg–de Vries solitons with quartic nonlinearity in a dusty plasma

The present multicomponent dusty plasma with ions, Cairns distributed electrons and immobile dusts has been investigated first time through modified Korteweg–de Vries (mKdV) equation of quartic nonlinearity derived by reductive perturbation technique. In this new investigation, it is found that the dust ion-acoustic (DIA) solitary waves have smaller amplitudes compared to the amplitudes of mKdV-DIA compressive solitons of our previous investigation []. Roles of non-thermal parameter (β), dust to ion density ratio (σ), number of dust charge (Z d ) and initial streaming speed of ion (u i0) in the growth of amplitudes and widths of this new mKdV-DIA solitons are investigated.

Oblique Arbitrary Amplitude Dust Ion Acoustic Solitary Waves in Anisotropic Non-Maxwellian Plasmas with Kappa-Distributed Electrons

In this paper, we investigate the behavior of dust ion acoustic solitary waves (DIASWs) with arbitrary amplitudes in a magnetized anisotropic dusty plasma that includes inertial hot ion fluid, electrons following a Kappa distribution, and negatively charged dust particles in the background. An ambient magnetic field aligns with the x-direction, while the wave propagation occurs obliquely to the ambient magnetic field. In the linear regime, two distinct modes, namely fast and slow modes, are observed. We employ the Sagdeev pseudo-potential method to analyze the fundamental properties of arbitrary amplitude DIASWs. Additionally, we examine how various physical parameters influence the existence and characteristics of symmetric planar dust ion acoustic solitary structures (DIASs). The characteristics of the solitary structures are greatly influenced by the dust concentration, the electrons superthermality (spectral) index, the obliquity parameter, the magnetic field, the parallel ion pressure and the perpendicular ion pressure. The results show that the amplitude and width of both compressive and rarefactive DIASWs are sensitive to the degree of electron superthermality and dust concentration. Additionally, it is shown that the propagation features of DIASWs are highly affected by the parallel component of ion pressure as compared to perpendicular component of ion pressure.

(3+1)-dimensional cylindrical dust ion-acoustic solitary waves in dusty plasma

The basic properties of (3+1)-dimensional cylindrical dust ion-acoustic (DIA) solitary waves have been studied in a multi-component plasma medium consisting of inertial ions, Maxwellian electrons, and stationary negative dust particles. The reductive perturbation method has been used to derive a cylindrical (3+1)-dimensional Kadomtsev–Petviashvili equation for small but finite amplitude of dust ion-acoustic waves. The impacts of nonplanar geometry and presence of static negative dust particles on the dust ion-acoustic solitary structures have been investigated. DIA solitary waves with both positive and negative polarity is observed to generate for this existing multi-component and complex plasma medium. The changes in the DIA wave structure in radial, azimuthal, and axial coordinates over time have been presented analytically. The results of this present investigation may contribute to a better understanding of laboratory plasma events as well as nonlinear electrostatic excitations in astrophysical environments.

Oblique dust-ion acoustic shock and oscillatory periodic wave excitations in space magnetized complex plasma regimes

The collisionless magnetized complex plasma (MCP) is considered to describe the nonlinear oblique propagation of dust-ion acoustic (DIA) shock wave and oscillatory wave having periodicity due to the impact of plasma parameters. Such plasma is composed of the dynamic ions having viscous influence, (α, q)-velocity distributed electrons, and static positive or negative dust charged particles. By implementing only the expansion of perturb quantities, the Burgers equation (BE) having quadratic nonlinearity (QN), cubic nonlinearity (CN), and composition of QN and CN are derived. Based on the useful exact solutions of these equations, the effect of physical parameters on the propagation of DIA shock wave, DIA oscillatory wave having periodicity and DIA double layer are discussed. It is found that the plasma system supports the shock and periodic wave excitations with both positive and negative polarity described by BE having QN. In addition, BE having CN supports shock and periodic wave excitations with only positive polarity. BE having a composition of QN and CN supports both shock wave excitations and double layer as well as both left to right and right to left propagating oscillatory waves having periodicity. The presented results would be applicable to space MCP regimes and further experimental verification.

Higher-order nonlinear dust ion acoustic (DIA) solitary waves in plasmas with weak relativistic effects in electrons and ions

Higher-order nonlinear dust ion acoustic (DIA) solitary waves in plasmas with weak relativistic effects in electrons and ions

Simulation Studies on the Dissipative Modified Kawahara Solitons in a Complex Plasma

In this work, a damped modified Kawahara equation (mKE) with cubic nonlinearity and two dispersion terms including the third- and fifth-order derivatives is analyzed. We employ an effective semi-analytical method to achieve the goal set for this study. For this purpose, the ansatz method is implemented to find some approximate solutions to the damped mKE. Based on the proposed method, two different formulas for the analytical symmetric approximations are formally obtained. The derived formulas could be utilized for studying all traveling waves described by the damped mKE, such as symmetric solitary waves (SWs), shock waves, cnoidal waves, etc. Moreover, the energy of the damped dressed solitons is derived. Furthermore, the obtained approximations are used for studying the dynamics of the dissipative dressed (modified Kawahara (mK)) dust-ion acoustic (DIA) solitons in an unmagnetized collisional superthermal plasma consisting of inertia-less superthermal electrons and inertial cold ions as well as immobile negative dust grains. Numerically, the impact of the collisional parameter that arises as a result of taking the ion-neutral collisions into account and the electron spectral index on the profile of the dissipative structures are examined. Finally, the analytical and numerical approximations using the finite difference method (FDM) are compared in order to confirm the high accuracy of the obtained approximations. The achieved results contribute to explaining the mystery of several nonlinear phenomena that arise in different plasma physics, nonlinear optics, shallow water waves, oceans, and seas, and so on.

Cubic nonlinearity driven dust ion acoustic solitons with superthermal two-temperature electrons in the Saturn’s magnetosphere

Nonlinear propagation of electrostatic waves with cubic nonlinearity has been investigated in a multicomponent dusty plasma with inertial ions, superthermal two temperature electrons and stationary dust. In this regard, single and multi-soliton solutions of modified Korteweg–de Vries (mKdV) equation for dust ion acoustic waves (DIAWs) have been investigated implementing Hirota’s bilinear method. Plasma parameters affecting the amplitude of dust ion acoustic (DIA) mKdV single soliton have been thoroughly investigated based on the data from Saturn’s magnetosphere. The overtaking interaction of two mKdV solitons has been investigated by changing the percentage of propagation vectors to observe bipolar structure reducing to a single humped structure for a particular value of the ratio of propagation vectors. The most significant outcome of this study has been the investigation of interaction of a compressive and rarefactive dust ion acoustic soliton forming a peculiar composite shape at the interaction point.

Modulational Instability Analysis of Four-Component Dusty Plasma System

Dust in plasma is a major hindrance for many scientific activities that occur in space, fusion, and so on. One of the crucial properties that makes sense for such hindrance is its nonlinearity. Existence of solitons proves the condition of nonlinearity and by enabling the significance of such solitons, nonlinearity can be minimized to an extent. Our own selves conceptually probed the four-component dusty plasma system and the four components are positive and negative dust components, two components of electrons and non-thermal ions modeled by Boltzmann distributions. The nonlinear reductive perturbation technique is employed and we derived the nonlinear Schrödinger equation (NLSE), which governs the nonlinear dynamics of the plasmic system. Furthermore, we invoke the modulational instability (MI) analysis to inspect the stability of plasmic solitons and the instability/stability regions of dust ion acoustic (DIA) waves are highly explored.

On the stability of 2D modulated electrostatic wavepackets in non-Maxwellian dusty plasma – application in Saturn’s magnetosphere

ABSTRACT Motivated by observations of localized electrostatic wavepackets by the Voyager 1 and 2 and Cassini missions in Saturn’s magnetosphere, we have investigated the evolution of modulated electrostatic wavepackets in a dusty plasma environment. The well-known dust-ion acoustic (DIA) mode was selected to explore the dynamics of multidimensional structures, by means of a Davey–Stewartson (DS) model, by taking into account the presence of a highly energetic (suprathermal, kappa-distributed) electron population in combination with heavy (immobile) dust in the background. The modulational (in)stability profile of DIA wavepackets for both negative as well as positive dust charge is investigated. A set of explicit criteria for modulational instability (MI) to occur is obtained. Wavepacket modulation properties in 3D dusty plasmas are shown to differ from e.g. Maxwellian plasmas in 1D. Stronger negative dust concentration results in a narrower instability window in the K (perturbation wavenumber) domain and to a suppressed growth rate. In the opposite manner, the instability growth rate increases for higher positive dust concentration and the instability window gets larger. In a nutshell, negative dust seems to suppress instability while positive dust appears to favour the amplitude modulation instability mechanism. Finally, stronger deviation from the Maxwell–Boltzmann equilibrium, i.e. smaller κe values, lead(s) to stronger instability growth in a wider wavenumber window – hence suprathermal electrons favour MI regardless of the dust charge sign (i.e. for either positive or negative dust). The wavepacket modulation properties in 2D dusty plasmas thus differ from e.g. Maxwellian plasmas in 1D, both quantitatively and qualitatively, as indicated by a generalized dispersion relation explicitly derived in this paper (for the amplitude perturbation). Our results can be compared against existing experimental data in space, especially in Saturn’s magnetosphere.

Bifurcation analysis for dust ion acoustic waves in magnetized four-component plasmas with superthermal electrons

In collisionless, dissipative, and magnetized dusty plasma, the propagation of nonlinear dust-ion-acoustic (DIA) solitary and shock waves has been studied, whose constituents are cold positive ions, negative ions obeying the Boltzmann distribution, superthermally distributed electrons and positively charged stationary dust particles. The Korteweg-de Vries–Burgers (KdVB) equation is derived using the reductive perturbation method. This equation is solved using the tangent hyperbolic method, yielding a shock wave solution. Also, other interesting physical solutions and the corresponding electric field are determined. By applying the bifurcation theory to the planar dynamical system of the derived KdVB equation under two conditions and , the presence of solitary wave solutions and periodic traveling wave solutions has been established. According to both numerical and analytical investigations, The basic properties of dust ion acoustic waves are significantly modified by the influence of superthermal electrons, viscosity coefficients, and the existence of an external magnetic field. The current results could help in a full understanding and studying of plasma waves in both space and astrophysical environments (such as the magnetospheres of Saturn and pulsars) and also in the laboratory.

Spike-Like Traveling Waves at the Critical Point of Bifurcation in a Nonextensive Dusty Plasma With Dust Polarity

This article presents a detailed study on the basic features of bifurcation of dust ion acoustic (DIA) traveling waves in a dusty plasma comprising warm adiabatic ions, nonextensive electrons, and arbitrarily charged dust particles. A reduced dynamical system is obtained for plasma waves’ evolution, and the global dynamics of local bifurcation of waves’ motion are determined on the equilibrium points’ dust concentrations’ plane with respect to all possible plasma parametric combinations. The stability and phase portrait analysis indicate a sudden emergence of nonlinear periodic and solitary waves for critical values of negative (positive) dust concentration. At these critical values, waves’ dynamics exhibit a transcritical bifurcation with half-stable fixed points which support new spike-like traveling waves. The analytical and numerical solutions reveal that the decay rate of this localized structure is much slower than ordinary solitary waves that decay exponentially fast. Furthermore, the existence domain of bifurcation parameters and transitions between modes are found for different values of nonextensive electrons and arbitrarily charged dust concentrations. Our results could be applicable to different space and astrophysical plasma systems, particularly in earth atmosphere.

KP, MKP, and CKP dust ion acoustic solitons in a multispecies non-Maxwellian plasma

Characteristics of small amplitude dust ion acoustic (DIA) solitons under transverse perturbations in a multispecies plasma with dust impurity and Vasyliunas–Cairns distributed two temperature electrons are presented. Using a reductive perturbation technique, the Kadomtsev–Petviashivili (KP), modified KP, and coupled KP equations are derived. Furthermore, considering single variable transformation, solutions of different equations are derived to investigate the influence of various plasma parameters and higher order effects on the characteristics of DIA solitons. From the nonlinear coefficient of the KP equation, the parametric range for the existence of positive and negative potential solitons is also determined. Furthermore, the stability analysis of the soliton solution of the KP equation is discussed. It is remarked that all different physical parameters have much influence on the characteristics of different types of small amplitude DIA solitons.

Two-component plasma and electron trapping’s influence on the potential of a solitary electrostatic wave with the dust-ion-acoustic speed

In this paper, the ion-acoustic waves’ dynamic behavior in plasma and dusty plasma is investigated to explain the electron trapping’s effect on the potential of a solitary electrostatic wave with the dust-ion-acoustic speed in two-components plasma. This study investigates the soliton wave solutions of the Schamel–Korteweg–de Vries (S–KdV) equation that Hans Schamel derived in 1973. In a nonlinear dispersive medium, the S–KdV equation is used to describe a coherent localized wave structure propagates are demonstrated. One-dimensional, unmagnetized plasma with positive ions, negative ions, trapped electrons, and stationary dust grains with both positive and negative charges is studied for the nonlinear propagation of dust-ion-acoustic (DIA) waves. The Bernoulli sub-equation function (BSEF) method is applied to the S–KdV equation for constructing some novel soliton wave solutions that explain the effect of the plasma parameters on the DIA solitary waves. The obtained solitary wave solutions are represented through some different graphs by Mathematica 12 software. Additionally, the axisymmetric pulse propagation is demonstrated in some stream plots. All the obtained solutions are checked by putting them back into the original model.

Dust-ion acoustic waves in magnetized plasmas with a varying external magnetic field

The problem of small amplitude dust-ion acoustic (DIA) solitary waves (SWs) is discussed using the reductive perturbation theory in a plasma containing thermal electrons, inertial ions, and negatively charged stationary dust grains under the influence of a varying magnetic field. Presented investigation shows that the effects of non-uniform magnetic fields and dust particles significantly modify the basic properties of the DIA solitary waves.

Higher-order nonlinear and dispersive effects on dust-ion-acoustic solitary waves in magnetized dusty plasmas

We deal with the theoretical investigation of the higher-order nonlinear and dispersive effects on the basic features of dust-ion-acoustic (DIA) solitary waves in a magnetized dusty plasma. Also, we examine the impacts of the external magnetic field and adiabaticity, obliquity, etc. in changing solitary wave structures. The waves of small but finite amplitude propagate obliquely through the dusty plasma where the system comprises adiabatic positively charged ions (mobile), negatively charged trapped light ions, Maxwellian distributed electrons and stationary dust particles with arbitrary charges. The reductive perturbation method is extensively used for incorporating the higher-order terms into the modified Korteweg-de Vries (mKdV) equation, and the procedure yields an inhomogeneous mKdV-type equation. It is observed that the inclusion of higher-order nonlinear and dispersion effects increases the wave’s amplitude and width. Furthermore, in the presence of higher-order effects, the magnetic field and adiabaticity have decreasing and increasing effects respectively on the wave features. It is expected that the results will be useful to describe higher-order effects on DIA solitary waves.

Dust-ion acoustic solitons in superthermal dusty plasmas

In this research, the properties of dust- ion-acoustic (DIA) solitons in an unmagnetized dusty plasma, whose constituents are inertial ions, superthermal electrons, and stationary dust particles, are studied by using the Pseudopotential method. As an important result it is shown that DIA solitons are accepted beyond a certain critical value of the electron-to-ion density ratio (μ) as well as the superthermal parameter of electrons. We show that Mach permissible numbers shift to lower values in supethermal dusty plasmas. The results of this study help to gain a better understanding of the dust-ion wave behavior propagated in various spaces such as the Earth's atmosphere, Venus ionosphere and solar winds.

Weakly Nonlinear Dust-Ion-Acoustic Solitons in an Electronegative Collisionless Dusty Plasma With Cairns–Gurevich Distributed Electrons

The problem of dust-ion-acoustic (DIA) solitons is addressed in an electronegative collisionless dusty plasma with the presence of trapped-nonthermal electrons. To do this, we revisited the Cairns–Gurevich distribution that describes, concurrently, the evolution of the energetic electrons and those trapped in the plasma potential and analytically expressed its corresponding density. The modifications, due to the presence of this trapped nonthermal density, arising in small-amplitude DIA solitons propagation associated with both space and experimental plasmas are analyzed. In particular, we have found that, in both cases, a proportion of trapped nonthermal electrons relatively significant makes the solitary structure less spiky. Besides, we have shown that the amplitude and width of the experimental plasma soliton seem more affected due to the low ionic mass ratio.

Positron nonextensivity effect on the propagation of dust ion acoustic Gardner waves

Abstract Propagation of dust ion-acoustic (DIA) Gardner wave in a dusty electron–positron–ion (e–p–i) plasma is investigated. This plasma consists of q-distributed electrons and positrons, warm ions, and dust grains. The effects of the electron nonextensivity, positron nonextensivity, and fractional parameter on the properties of DIA Gardner wave are investigated. Space fractional Gardner (SFG) equation is derived using the semi inverse technique. An efficient modified G′/G-expansion method is presented to solve the SFG equation. It is found that the amplitude of the DIA Gardner wave increases with an increase in space fractional parameter β $\left(\beta \right)$ and spatial parameter ζ $\left(\zeta \right)$ . On other hands, the DIA Gardner wave shape can be modulated using the space fractional parameter β $\left(\beta \right)$ . Our results may help understand the astrophysical environments such as star magnetospheres, solar flares, and galactic nuclei.

Dust-Ion-Acoustic Rogue Waves in a Dusty Plasma Having Super-Thermal Electrons

The standard nonlinear Schrödinger Equation (NLSE) is one of the elegant equations to find detailed information about the modulational instability criteria of dust-ion-acoustic (DIA) waves and associated DIA rogue waves (DIARWs) in a three-component dusty plasma medium with inertialess super-thermal kappa distributed electrons, and inertial warm positive ions and negative dust grains. It can be seen that the plasma system supports both fast and slow DIA modes under consideration of inertial warm ions along with inertial negatively charged dust grains. It is also found that the modulationally stable parametric regime decreases with κ. The numerical analysis has also shown that the amplitude of the first and second-order DIARWs decreases with ion temperature. These results are to be considered the cornerstone for explaining the real puzzles in space and laboratory dusty plasmas.