Stationary Dust Research Articles

Roles of negatively-charged heavy ions and nonextensivity in cylindrical and spherical dust-ion-acoustic shock waves

A rigorous theoretical investigation has been carried out on the propagation of nonplanar (cylindrical and spherical) dust-ion-acoustic (DIA) waves in an unmagnetized dusty multi-ion plasma system containing nonextensive electrons, inertial negatively-charged heavy ions, positively-charged Maxwellian light ions, and negatively-charged stationary dust. The well-known reductive perturbation technique has been used to derive the modified Burgers-type equation (which describes the shock wave’s properties), and its numerical solution is obtained. The basic features (viz. polarity, amplitude, width, etc.) of the cylindrical and the spherical DIA shock waves are investigated. The basic features of the cylindrical and the spherical DIA shock waves are found to have been significantly modified in a way that depends on the intrinsic parameters (viz. electron nonextensivity, heavy-ion’s kinematic viscosity, heavy-to-light-ion number density ratio, electron-to-light-ion temperature ratio, etc.) of the considered plasma system. The characteristics of the cylindrical and the spherical DIA shock waves are observed to be qualitatively different from those of planar ones.

DEA Waves With Cold and Hot Electrons

The theoretical and numerical studies have been made to observe the planar and nonplanar geometries for the nonlinear propagation of the dust-electron-acoustic (DEA) in a dusty plasma (containing initially cold and hot Maxwellian electrons, stationary ions, and charge fluctuating stationary dust grains) using reductive perturbation method. It has also been found that the basic features of the DEA waves are significantly modified by the presence of dust charge fluctuation. The numerical solution to the K-dV equation indicates that the parameters those we have considered in our model blatantly influence the propagation speed and the structure of DEA solitary waves. The geometrical effects on the structure of DEA wave are discussed. It is shown that the amplitude and propagation speed in spherical geometry is larger compared with cylindrical and planar geometries for different values of the above-mentioned parameters. The implications of our results would be useful to understand some astrophysical and cosmological scenarios like stellar polytropes, hadronic matter and quark-gluon plasma, protoneutron stars, and dark-matter halos.

Compressive and rarefactive dust-ion-acoustic Gardner solitons in a multi-component dusty plasma

The linear and nonlinear propagations of dust-ion-acoustic solitary waves (DIASWs) in a collisionless four-component unmagnetized dusty plasma system containing nonextensive electrons, inertial negative ions, Maxwellian positive ions, and negatively charged static dust grains have been investigated theoretically. The linear properties are analyzed by using the normal mode analysis and the reductive perturbation method is used to derive the nonlinear equations, namely, the Korteweg-de Vries (K-dV), the modified K-dV (mK-dV), and the Gardner equations. The basic features (viz., polarity, amplitude, width, etc.) of Gardner solitons (GS) are found to exist beyond the K-dV limit and these dust-ion-acoustic GS are qualitatively different from the K-dV and mK-dV solitons. It is observed that the basic features of DIASWs are affected by various plasma parameters (viz., electron nonextensivity, negative-to-positive ion number density ratio, electron-to-positive ion number density ratio, electron-to-positive ion temperature ratio, etc.) of the considered plasma system. The findings of our results obtained from this theoretical investigation may be useful in understanding the nonlinear structures and the characteristics of DIASWs propagating in both space and laboratory plasmas.

Dust-ion-acoustic shock waves in nonextensive dusty multi-ion plasmas

A theoretical and numerical analysis of dust-ion-acoustic (DIA) shock waves has been carried out in an unmagnetized dusty multi-ion plasma containing nonextensive electrons, inertial negatively charged heavy ions, positively charged Maxwellian light ions, and negatively charged stationary dusts. The normal mode analysis is used to examine the linear properties of DIA waves (DIAWs). The reductive perturbation technique is employed in order to derive the nonlinear time evolution Burgers type equation (which describes the shock waves properties). The basic features (viz. polarity, amplitude, width, etc.) of the DIA shock waves are investigated. It is found that the basic features of DIA shock waves are significantly modified depending on the intrinsic parameters (viz. electron nonextensivity, heavy ions kinematic viscosity, heavy-to-light ion number density ratio, electron-to-light ion temperature ratio, etc.) of the considered plasma system. Both polarities (positive and negative potential) are also found to exist in the plasma under consideration in this paper. The findings of this investigation may be used in understanding the wave propagation in laboratory and space plasmas.

Grain-grain interaction in stationary dusty plasma

We present a particle-in-cell simulation study of the steady-state interaction between two stationary dust grains in uniform stationary plasma. Both the electrostatic force and the shadowing force on the grains are calculated explicitly. The electrostatic force is always repulsive. For two grains of the same size, the electrostatic force is very nearly equal to the shielded electric field due to a single isolated grain, acting on the charge of the other grain. For two grains of unequal size, the electrostatic force on the smaller grain is smaller than the isolated-grain field, and the force on the larger grain is larger than the isolated-grain field. In all cases, the attractive shadowing force exceeds the repulsive electrostatic force when the grain separation d is greater than an equilibrium separation d0. d0 is found to be between 6λD and 9λD in all cases. The binding energy is estimated to be between 19 eV and 900 eV for various cases.

Time Evolution of Localized Waves in Non thermal Distributed Plasmas: Considering Dissipation Effects

Recent observations show the existence of high energy electrons in various astrophysical plasmas which their distribution functions are highly non thermal. The presence of dust ion acoustic localized waves in plasmas which contain non thermal electrons and ions with kinematic viscosity along with stationary charged dust is investigated. Solitary shock waves are derived as solutions of nonlinear wave equation of the medium using the reductive perturbation method by employing suitable stretching coordinates. Both rarefactive and compressive shock profiles are created in the medium according to the initial values of the medium parameters. We report that increasing the electron number density makes a growth in the amplitude of negative shock waves while it decreases the amplitude of positive shock profile. Some behavior of observed transience in the plasma waves can be explained using the presented results.

Dust-ion acoustic shock waves in a dusty multi-ion plasma with negatively dust-charge fluctuation

The nonlinear propagation of dust-ion acoustic shock waves in a collisionless, unmagnetized multi-ion dusty plasma contains Botlzemann-distributed electrons, negative and positive ions with extremely massive and stationary negative charge dust grains with dust charge fluctuations is investigated. By employing the reductive perturbation method, we obtain a Burgers equation that describes the two-ion fluid dynamics. The dust charge variation is found to play an important role in the formation of such dust-ion acoustic shock structures. The viscosity only affects the thickness of the shock waves. The dependences of the shock wave’s velocity, height and thickness on the system parameters are investigated.

Nonlinear features of ion acoustic shock waves in dissipative magnetized dusty plasma

The nonlinear propagation of small as well as arbitrary amplitude shocks is investigated in a magnetized dusty plasma consisting of inertia-less Boltzmann distributed electrons, inertial viscous cold ions, and stationary dust grains without dust-charge fluctuations. The effects of dissipation due to viscosity of ions and external magnetic field, on the properties of ion acoustic shock structure, are investigated. It is found that for small amplitude waves, the Korteweg-de Vries-Burgers (KdVB) equation, derived using Reductive Perturbation Method, gives a qualitative behaviour of the transition from oscillatory wave to shock structure. The exact numerical solution for arbitrary amplitude wave differs somehow in the details from the results obtained from KdVB equation. However, the qualitative nature of the two solutions is similar in the sense that a gradual transition from KdV oscillation to shock structure is observed with the increase of the dissipative parameter.

Dust-ion acoustic waves modulation in dusty plasmas with nonextensive electrons

The nonlinear amplitude modulation of dust-ion acoustic wave (DIAW) is studied in the presence of nonextensive distributed electrons in dusty plasmas with stationary dust particles. Using the reductive perturbation method (RPM), the nonlinear Schrodinger equation (NLSE) which governs the modulational instability (MI) of the DIAWs is obtained. Modulational instability regions and the growth rate of nonlinear waves are discussed. It is shown that the wave characters are affected by the value of nonextensive parameter and also relative density of plasma constituents.

Dust-ion-acoustic Gardner double layers in a dusty plasma with two-temperature electrons

The properties of dust-ion-acoustic Gardner double layers (DIA GDLs) in an unmagnetized dusty plasma, whose constituents are negatively-charged stationary dust, inertial ions, and Boltzmann electrons of two distinct temperatures, are rigorously investigated by employing the reductive perturbation method: Gardner approach. The standard Gardner equation is derived, and its double layer (DL) solution is obtained. It has been shown that the properties of the DIA GDLs are significantly modified by some plasma parameters (viz. σ=Te1/Te2, μe1=ne10/ni0, and μe2=ne20/ni0, where Te1 (Te2) is the cold (hot) electron temperature, ne10 (ne20) is the cold (hot) electron number density at equilibrium, and ni0 is the ion number density at equilibrium). The implications of our investigation in understanding the basic features of nonlinear electrostatic perturbations observed in many space plasma systems and laboratory devices are briefly discussed.

Higher-order corrections to nonlinear dust-ion-acoustic shock waves in a degenerate dense space plasma

A reductive perturbation technique is employed to investigate the contribution of higher-order nonlinearity and dissipation to nonlinear dust-ion-acoustic (DIA) shock waves in a three-component degenerate dense space plasma. The model consists of degenerate electron (being either ultrarelativistic or nonrelativistic), nonrelativistic ion fluid and stationary heavy dust grains. A nonlinear Burger equation and a linear inhomogeneous Burger-type equation are derived. The present model admits only compressive DIA shocks. Including these higher-order corrections results in creating new solitary wave structures “humped DIA shock” waves. For the case of ultrarelativistic (nonrelativistic) electrons, one (two) humped DIA shock is (are) created. The DIA shock wave amplitude and velocity is larger in case of ultrarelativistic electrons than of nonrelativistic electrons. It is shown that the effects of kinematic viscosity, heavy dust grains number density, and equilibrium ion number density have important roles in the basic features of the produced DIA shocks and the associated electric fields. The implications of our results to dense plasmas in astrophysical objects (e.g., non-rotating white dwarf stars) are briefly discussed.

The effects of vortex like distributed electron in magnetized multi-ion dusty plasmas

Abstract The nonlinear propagation of small but finite amplitude dust-ion-acoustic solitary waves in a magnetized, collisionless dusty plasma is investigated theoretically. It has been assumed that the electrons are trapped following the vortex-like distribution and that the negatively and positively charged ions are mobile with the presence of charge fluctuating stationary dusts, where ions mass provide the inertia and restoring forces are provided by the thermal pressure of hot electrons. A reductive perturbation method was employed to obtain a modified Korteweg-de Vries (mK-dV) equation for the first-order potential and a stationary solution is obtained. The effect of the presence of trapped electrons, negatively and positively charged ions and arbitrary charged dust grains are discussed.

A scaling law for the dust cloud in radio frequency discharge under microgravity conditions

We employ the approximation of overlapped scattering potentials of charged dust particles exposed to streaming ions to deduce the “equation of state” for a stationary dust cloud in the radio frequency discharge apart from the void-dust boundary. The obtained equation defines the potential of a dust particle as a function of the ion number density, the mass of a carrier gas atom, and the electron temperature. A scaling law that relates the particle number density to the particle radius and electron temperature in different systems is formulated. Based on the proposed approach, the radius of a cavity around a large particle in the bulk of a cloud is estimated. The results of calculation are in a reasonable agreement with the experimental data available in literature.

On the characteristics of head on collision of dust ion acoustic solitons in the adiabatic dusty plasmas

Based on a one-dimensional mode, the characteristics of the head on collision between two dust ion acoustic solitons (DIASs), propagating in opposite directions in adiabatic dusty plasmas composed of adiabatic non-inertial electrons, adiabatic inertial ions and immersed (negatively/positively) charged dust grains have been investigated. The extended Poincaré–Lighthill–Kuo (PLK) method has been used to obtain two side Korteweg-de Vries (KdV) equations for DIASs. The analytical phase shifts and trajectories after collision of two solitons are given. The effects of adiabaticity of electron and ion fluids, concentration of negatively/positively charged static dust particles and ion temperature to electron temperature ratio on the phase shift are studied. It is found that these factors significantly affect the phase shifts.

Effect of Anisotropic Ion Pressure on Solitary Waves in Magnetized Dusty Plasmas

AbstractThe propagation of linear and nonlinear dust ion acoustic waves (DIAWs) are studied in a collisionless magnetized plasma which consists of warm ions having anisotropic thermal pressure, nonthermal (energetic) electrons and static dust particles of positive and negative charge polarity. The anisotropic ion pressure is defined using double adiabatic Chew‐Golberger‐Low (CGL) theory. In the linear regime, the propagation properties of the two possible modes are investigated via ion pressure anisotropy, dust particle polarity and nonthermality of electrons. Using reductive method Zakharov‐Kuznetsov (ZK) equation is derived for the propagation of two dimensional electrostatic dust ion acoustic solitary waves in dusty plasmas. It is found that both compressive and rarefactive solitons are formed in presence of nonthermal electrons using Cairn's distribution [R.A. Cairns, A.A. Mamun, R. Bingham, R.O. Dendy, R. Bostrom, C.M.C. Nairn and P.K. Shukla, Geophys.Res. Lett. 22, 2709 (1995)] in the system. The ion pressure anisotropy, nonthermality of electrons and charge polarity of the dust particles have significant effects on the amplitude and width of the dust ion acoustic solitary waves in such anisotropic nonthermal magnetized dusty plasmas. The numerical results are also presented for illustration. Our finding is applicable to space dusty plasma regimes having anisotropic ion pressure and nonthermal electrons. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

The roles of non-extensivity and dust concentration as bifurcation parameters in dust-ion acoustic traveling waves in magnetized dusty plasma

Dust ion-acoustic traveling waves are studied in a magnetized dusty plasma in presence of static dust and non-extensive distributed electrons in the framework of Zakharov-Kuznesstov-Burgers (ZKB) equation. System of coupled nonlinear ordinary differential equations is derived from ZKB equation, and equilibrium points are obtained. Nonlinear wave phenomena are studied numerically using fourth order Runge-Kutta method. The change from unstable to stable solution and consequently to asymptotic stable of dust ion acoustic traveling waves is studied through dynamical system approach. It is found that some dramatical features emerge when the non-extensive parameter and the dust concentration parameters are varied. Behavior of the solution of the system changes from unstable to stable and stable to asymptotic stable depending on the value of the non-extensive parameter. It is also observed that when the dust concentration is increased the solution pattern is changed from oscillatory shocks to periodic solution. Thus, non-extensive and dust concentration parameters play crucial roles in determining the nature of the stability behavior of the system. Thus, the non-extensive parameter and the dust concentration parameters can be treated as bifurcation parameters.

Dust ion acoustic solitary waves and their multi-dimensional instability in a weakly relativistic adiabatic magnetized dusty plasma with two different types of adiabatic electrons

Obliquely propagating dust ion-acoustic solitary waves in a collisionless, weakly relativistic, adiabatic, magnetized dusty plasma which consist of two different types of adiabatic inertia-less electrons, weakly relativistic adiabatic inertial ions fluid and negatively charged stationary dust particles have been studied. A nonlinear Zakharov–Kuznetsov equation has been derived by using reductive perturbation method. Solitary wave solution of this equation has been obtained. Combined effects of the external magnetic field, obliqueness, relativistic factor and two-temperature adiabatic electrons, which are found to significantly modify the basic properties of dust ion acoustic solitary waves, are explicitly examined. Multi-dimensional instability of dust ion acoustic solitary waves has been analyzed using small-k perturbation expansion technique. The results show that the external magnetic field, propagation angle, relativistic factor and temperature ratio between low and high temperatures adiabatic electrons have strong effects on instability criterion as well as growth rate of instability.

Modulational instability of dust ion acoustic waves in dusty plasmas with superthermal electrons

The propagation of dust ion acoustic waves is studied in plasmas composed of superthermal distributed electrons and stationary dust particles. The nonlinear Schrodinger equation is derived using the reductive perturbation technique and the modulational instability of dust ion acoustic waves is analyzed. Parametric investigations indicate that the presence of superthermal distributed electrons significantly modify the modulational instability and its growth rate. The effect of particle relative density on the wave characters is also investigated.

Coupling of the Okuda–Dawson model with a shear current-driven wave and the associated instability

AbstractIt is pointed out that the Okuda–Dawson mode can couple with the newly proposed current-driven wave. It is also shown that the Shukla–Varma mode can couple with these waves if the density inhomogeneity is taken into account in a plasma containing stationary dust particles. A comparison of several low-frequency electrostatic waves and instabilities driven by shear current and shear plasma flow in an electron–ion plasma with and without stationary dust is also presented.

Nonplanar Dust-Ion Acoustic Solitary Waves in Warm Plasma With Superthermal Electrons

Using the reductive perturbation technique, a cylindrical/spherical Korteweg-de Vries (KdV) equation is derived for dust-ion acoustic solitary wave (DIASW) in an unmagnetized dusty plasma, whose constituents are adiabatic ion fluid, superthermal electrons, and negatively charged static dust particles. The solution of modified KdV equation in nonplanar geometry is numerically analyzed. The change of the DIASW structure due to the effect of the geometry, superthermal parameter, dust density, and ion temperature is investigated by numerical calculation of the cylindrical/spherical KdV equation.