Dust‐acoustic envelope solitons in super‐thermal plasmas

The modulational instability (MI) of the dust‐acoustic waves (DAWs) in an electron‐positron‐ion‐dust plasma (containing super‐thermal electrons, positrons, and ions along with negatively charged adiabatic dust grains) is investigated by the analysis of the non‐linear Schrödinger equation (NLSE). To derive the NLSE, the reductive perturbation method was employed. Two different parametric regions for stable and unstable DAWs are observed. The presence of super‐thermal electrons, positrons, and ions significantly modifies both the stable and unstable regions. The critical wave number k_c (at which MI sets in) depends on the super‐thermal electron, positron, and ion, and adiabatic dust concentrations.     

尘埃等离子体中朗缪尔波的非线性调制

研究了尘埃等离子体中尘埃声波（ＤＡＷ）和尘埃离子声波（ＤＩＡＷ）对朗缪尔波的非线性调制。在小而有限振幅极限下,得到了朗缪尔波的包络孤立子。对于朗缪尔波与尘埃声波的非线性耦合,包络孤立子存在两个速度传播区;而对于与尘埃离子声波的耦合,只有一个传播区     

Effect of non‐extensivity parameter q on the damping rate of dust ion acoustic waves in non‐extensive dusty plasma

Kinetic theory has been applied to study the damping characteristics of dust ion acoustic waves (DIAWs) in a dusty plasma comprising q‐non‐extensive distributed electrons and ions, while the dust particles are considered extensive following the Maxwellian velocity distribution function. It is found that the results of the three‐dimensional velocity distribution function are more accurate compared to the results of the one‐dimensional velocity distribution function. The numerical solution of the dispersion relation is carried out to study the effect of the non‐extensivity parameter q on the dispersion, the damping rate, and the range of the values of the normalized wavenumber ( k λ_D) for which the DIAWs are weakly damped. It is found that the change in the value of the electron non‐extensivity parameter q_e has a minor effect on the dispersion, the damping rate, and the range of the values of the normalized wavenumber ( k λ_D) for which the DIAWs are weakly damped, while on the other hand, ion non‐extensivity parameter q_i has a strong effect on these arguments. The effect of other parameters, such as the ratio of electron to ion number density and ratio of electron to ion temperature, on the damping characteristics of DIAWs is also highlighted.     

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

The 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 (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.     

Influence of external magnetic field on dust acoustic waves in a capacitive RF discharge

This paper reports experiments on self-excited dust acoustic waves (DAWs) and its propagation characteristics in a magnetized rf discharge plasma. The DAWs are spontaneously excited in dusty plasma after adding more particles in the confining potential well and found to propagate in the direction of streaming ions. The spontaneous excitation of such low-frequency modes is possible due to the instabilities associated with streaming ions through the dust grain medium. The background E-field and neutral pressure determine the stability of excited DAWs. The characteristics of DAWs strongly depend on the strength of external magnetic field. The magnetic field of strength B < 0.05 T only modifies the characteristics of propagating waves in dusty plasma at moderate power and pressure, P = 3.5 W and p = 27 Pa, respectively. It is found that DAWs start to be damped with increasing the magnetic field beyond B > 0.05 T and get completely damped at higher magnetic field B ∼ 0.13 T. After lowering the power and pressure to 3 W and 23 Pa respectively, the excited DAWs in the absence of B are slightly unstable. In this case, the magnetic field only stabilizes and modifies the propagation characteristics of DAWs while the strength of B is increased up to 0.1 T or even higher. The modification of the sheath electric field where particles are confined in the presence of the external magnetic field is the main cause of the modification and damping of the DAWs in a magnetized rf discharge plasma.     

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 /lq_ϕ ), dust concentration δ (= n_{d 0}/n_{i 0}), and dust self‐gravitation α (= ω_Jd /ω_pd ). The relevance of our findings to interstellar dust clouds is also discussed for micrometre‐sized massive dust grains.     

Weakly dissipative dust acoustic solitons in the presence of superthermal particles

An investigation of the linear and non‐linear properties of low‐frequency electrostatic (dust acoustic) waves in a collisional dusty plasma with negative dust grains, Maxwellian electrons, and κ ‐distributed ions is carried out. Low dust–neutral collisions accounting for dissipation (wave damping effect) is considered. The linear properties of dust acoustic excitations are discussed for varying values of relevant plasma parameters. It is shown that large wavelengths (beyond a critical value) are overdamped. In the limit of low dust–neutral collision rate, we have derived a damped Korteweg de Vries (KdV) equation by using the reductive perturbation technique. Supplemented by vanishing boundary conditions, the time‐varying solution of damped KdV equation leads to a weakly dissipative negative potential soliton. The soliton evolution with the damping parameter and other physical plasma parameters (superthermality, dust concentration, ion temperature) is delineated.     

Dust ion‐acoustic solitons with trapped q‐non‐extensive electrons,dissipative processes,and streaming ions

The characteristics of dust ion‐acoustic waves (DIAWs) that are excited because of streaming ions and hot q‐non‐extensive electrons obeying a vortex‐like distribution are investigated. By exploiting a pseudo‐potential technique, we have derived an energy integral equation. The presence of non‐extensive q‐distributed hot trapped electrons and a streaming ion beam has been shown to influence soliton structure quite significantly. The evolution of the soliton‐like perturbations in complex plasmas, taking into account the dissipation processes, are also investigated, obtained by numerically solving the modified Schamel, equation whose widths are dependant on electron trapping efficiency β. Our illustrations indicate that compressive DIAWs develop in this plasma. As the plasmas in reality have a relative flow, such an analysis can be used to understand the DIA solitary structures observed in the mesospheric noctilucent clouds.     

Variable‐size dust grains with generalized (r,q) electrons in a dusty plasma

The effect of the generalized (r, q) distribution on the non‐linear propagation of dust acoustic waves (DAWs) in a dusty plasma consisting of variable‐size dust grains is discussed. A Korteweg–de Vries (KdV) equation is derived using the reductive perturbation technique (RPT). The dust size obeys the power‐law dust size distribution (DSD). The present results reveal that rarefactive and compressive waves can propagate in the proposed plasma model. It is found that the spectral indices r and q influence the main properties of DAWs. Especially, the velocity, amplitude, and width of the DAW change drastically with r compared to changes in q.     

Dust ion acoustic waves in non-thermal Cairns bi-Maxwellian plasma

Using kinetic theory approach, the dispersion relation ω_r and Landau damping rate γ for dust ion acoustic waves are investigated numerically and analytically in an unmagnetized collisionless dusty plasma considering Cairns distribution for electrons and ions in stationary dust particles background. The phase velocity and Landau damping rate are calculated in the limits v_td∥ < v_ti∥ << ω/k << v_te∥ . The electrons and ions non-thermality effects are incorporated via the non-thermality parameter (0 ≤ α < 1) . The real frequency ω_r and Landau damping rate γ of the mode in Cairns bi-Maxwellian distributed plasma are graphically shown to depend on plasma parameters namely non-thermality index α , ion to electron temperature ratio T_i∥/T_e∥ and the dust concentration parameter δ (=1 − ηZ_d) .     

Effects of adiabaticity of electrons and ions on dust-ion-acoustic solitary waves

The nonlinear propagation of dust-ion-acoustic (DIA) waves in an adiabatic dusty plasma (containing adiabatic inertial-less electrons, adiabatic inertial ions, and negatively charged static dust) is investigated by the pseudo-potential approach. The combined effects of adiabatic electrons and negatively charged static dust on the basic properties (critical Mach number, amplitude, and width) of small as well as arbitrary amplitude DIA solitary waves are explicitly examined. It is found that the combined effects of adiabatic electrons and negatively charged static dust significantly modify the basic properties (critical Mach number, amplitude, and width) of the DIA solitary waves. It is also found that due to the effect of adiabaticity of electrons, negative DIA solitary waves [which are found to exist in a dusty plasma (containing isothermal electrons, cold ions, and negatively charged static dust) for α=zdnd0/ni0>2/3, where zd is the number of electrons residing onto a dust grain surface, nd0 is the constant (static) dust number density and ni0 is the equilibrium ion number density] disappears, i.e. due to the effect of adiabatic electrons, one cannot have negative DIA solitary waves for any possible set of dusty plasma parameters [0?α<1 and 0?σ=Ti0/Te0?1, where Ti0 (Te0) is electron (ion) temperature at equilibrium].     

Modulational instability of dust-ion-acoustic waves in pair-ion plasma having non-thermal non-extensive electrons

The modulational instability (MI) criteria of dust-ion-acoustic (DIA) waves (DIAWs) have been investigated in a four-component pair-ion plasma having inertial pair ions, inertialess non-thermal non-extensive electrons, and immobile negatively charged massive dust grains. A nonlinear Schrödinger equation (NLSE) is derived by using reductive perturbation method. The nonlinear and dispersive coefficients of the NLSE can predict the modulationally stable and unstable parametric regimes of DIAWs and associated first and second-order DIA rogue waves (DIARWs). The MI growth rate and the configuration of the DIARWs are examined, and it is found that the MI growth rate increases (decreases) with increasing the number density of the negatively charged dust grains in the presence (absence) of the negative ions. It is also observed that the amplitude and width of the DIARWs increase (decrease) with the negative (positive) ion mass. The implications of the results to laboratory and space plasmas are briefly discussed.     

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).     

Dust‐ion‐acoustic solitary waves in a magnetized dusty pair‐ion plasma with Cairns‐Gurevich electrons and opposite polarity dust particles

The nonlinear dust‐ion‐acoustic (DIA) solitary structures have been studied in a dusty plasma, including the Cairns‐Gurevich distribution for electrons, both negative and positive ions, and immobile opposite polarity dust grains. The external magnetic field directed along the z‐axis is considered. By using the standard reductive perturbation technique and the hydrodynamics model for the ion fluid, the modified Zakharov–Kuznetsov equation was derived for small but finite amplitude waves and was provided the solitary wave solution for the parameters relevant. Using the appropriate independent variable, we could find the modified Korteweg–de Vries equation. By plotting some figures, we have discussed and emphasized how the different plasma values, such as the trapping parameter, the positive (or negative) dust number density, the non‐thermal electron parameter, and the ion cyclotron frequency, can influence the solitary wave structures. In addition, using the bifurcation theory of planar dynamical systems, we have extracted the centre and saddle points and illustrated the phase portrait of such a system for some particular plasma parameters. Finally, we have graphically investigated the behaviour of the solitary energy wave by changing the plasma values as well as by calculating the instability criterion; we have also discussed the growth rate of the solitary waves. The results could be useful for studying the physical mechanism of nonlinear propagation of DIA solitary waves in laboratory and space plasmas where non‐thermal electrons, pair‐ions, and dust particles can exist.     

Kadomtsev–Petviashvili equation for dust ion-acoustic solitons in pair-ion plasmas

Using the reductive perturbation method, we have derived the Kadomtsev-Petviashvili (KP) equation to study the nonlinear properties of electrostatic collisionless dust ion-acoustic solitons in the pair-ion (p-i) plasmas. We have chosen the fluid model for the positive ions, the negative ions, and a fraction of static charged (both positively and negatively) dust particles. Numerical solutions of these dust ion-acoustic solitons are plotted and their characteristics are discussed. It is found that only the amplitudes of the electrostatic dust ion-acoustic solitons vary when the dust is introduced in the pair-ion plasma. It is also noticed that the amplitude and the width of these solitons both vary when the thermal energy of the positive or negative ions is varied. It is shown that potential hump structures are formed when the temperature of the negative ions is higher than that of the positive ions, and potential dip structures are observed when the temperature of the positive ions supersedes that of the negative ions. As the pair-ion plasma mimics the electron-positron plasma, thus our results might be helpful in understanding the nonlinear dust ion acoustic solitary waves in super dense astronomical bodies.     

Effect of viscosity on dust–ion acoustic shock wave in dusty plasma with negative ions

The properties of dust–ion acoustic (DIA) shock wave in a dusty plasma containing positive and negative ions is investigated. The reductive perturbation method has been used to derive the Korteweg–de Vries–Burgers equation for dust acoustic shock waves in a homogeneous, unmagnetized and collisionless plasma whose constituents are Boltzmann distributed electrons, singly charged positive ions, singly charged negative ions and cold static dust particles. The KdV–Burgers equation is derived and its stationary analytical solution is numerically analyzed where the effect of viscosity on the DIA shock wave propagation is taken into account. It is found that the viscosity in the dusty plasma plays as a key role in dissipation for the propagation of DIA shock.     

Nonlinear structures for extended Korteweg–de Vries equation in multicomponent plasma

Using the fluid hydrodynamic equations of positive and negative ions, as well as q-nonextensive electron density distribution, an extended Korteweg–de Vries (EKdV) equation describing a small but finite amplitude dust ion-acoustic waves (DIAWs) is derived. Extended homogeneous balance method is used to obtain a new class of solutions of the EKdV equation. The effects of different physical parameters on the propagating nonlinear structures and their relevance to particle acceleration in space plasma are reported.     

Spherical Kadomtsev–Petviashvili equation for dust acoustic waves with dust size distribution and two-charges-ions

The nonlinear dust acoustic waves in dusty plasmas with negative as well as positive ions and the combined effects of bounded spherical geometry and the transverse perturbation and the size distribution of dust grains are studied. Using the perturbation method, a spherical Kadomtsev–Petviashvili (SKP) equation that describes the dust acoustic waves is deduced.     

Effects of double spectral electron distribution and polarization force on dust acoustic waves in a negative dusty plasma

The nonlinear features of dust acoustic waves (DAWs) propagating in a multicomponent dusty plasma with negative dust grains, Maxwellian ions, and double spectral electron distribution (DSED) are investigated. A Korteweg de Vries Burgers equation (KdVB) is derived in the presence of the polarization force using the reductive perturbation technique (RPT). In the absence of the dissipation effect, the bifurcation analysis is introduced and various types of solutions are obtained. One of these solutions is the rarefactive solitary wave solution. Additionally, in the presence of the dissipation effects, the tanh method is employed to find out the solution of KdVB equation. Both of the monotonic and the oscillatory shock structures are numerically investigated. It is found that the correlation between dissipation and dispersion terms participates strongly in creating the dust acoustic shock wave. The limit of the DSED to the Maxwell distribution is examined. The distortional effects in the profile of the shock wave that result by increasing the values of the flatness parameter, r, and the tail parameter, q, are investigated. In addition, it has been shown that the proportional increase in the value of the polarization parameter R enhances in both of the strength of the monotonic shock wave and the amplitude of the oscillatory shock wave. The effectiveness of non-Maxwellian distributions, like DSED, in several of plasma situations is discussed as well.