Electrostatic solitary structures in a magnetized nonextensive plasma with q-distributed electrons

A rigorous theoretical investigation has been made of obliquely propagating electrostatic solitary structures in a magnetized plasma, taking into account the effect of nonextensive electrons. By employing the reductive perturbation method, the basic characteristics of obliquely propagating ion-acoustic (IA) solitary waves (SWs) in a cold magnetized electron-ion plasma (consisting of inertial ions and noninertial q-distributed electrons) have been addressed. The Korteweg-de Vries equation is derived and its numerical solution is obtained. It has been shown that the effects of electron nonextensivity and external magnetic field significantly modify the natures of the small but finite-amplitude IA SWs. The present analysis may be useful to understand and demonstrate the dynamical properties of IA SWs in different astrophysical and cosmological scenarios (viz. stellar polytropes, hadronic matter, quark-gluon plasma, protoneutron stars, dark-matter halos, etc.).     

Dust ion acoustic solitary structures in the presence of isothermal positrons

The Sagdeev potential technique has been employed to study the dust ion acoustic solitary waves and double layers in an unmagnetized collisionless dusty plasma consisting of negatively charged static dust grains, adiabatic warm ions, isothermally distributed electrons, and positrons. A computational scheme has been developed to draw the qualitatively different compositional parameter spaces or existence domains showing the nature of existence of different solitary structures with respect to any parameter of the present plasma system. The present system supports both positive and negative potential double layers. The negative potential double layer always restricts the occurrence of negative potential solitary waves, i.e., any sequence of negative potential solitary waves having monotonically increasing amplitude converges to a negative potential double layer. However, there exists a parameter regime for which the positive potential double layer is unable to restrict the occurrence of positive potential solitary waves. As a result, in this region of the parameter space, there exist solitary waves after the formation of positive potential double layer, i.e., positive potential supersolitons have been observed.     

Dust-acoustic waves in a nonuniform adiabatic dusty plasma in the presence of polarization force

The linear propagation of the dust-acoustic (DA) waves in a nonuniform adiabatic dusty plasma, which consists of inertialess adiabatic electrons, inertialess adiabatic ions, and inertial negatively charged dust by taking into account the effects of polarization force, is theoretically investigated. It is found that the linear dispersion properties of the DA waves are significantly modified by the dust density nonuniformity, adiabaticity of electrons and ions, and the effects of the polarization force. It is shown that the phase speed of the DA waves is increased with the increase of adiabaticity of electrons and ions but decreased with the increase of the effects of polarization force. It is also shown that the dust density is enhanced with the increase of adiabatic index but depleted with the increase of polarization force. The scenarios relevant to dust-ion plasma in space environments are briefly addressed.     

Cylindrical and spherical dust-ion-acoustic modified Gardner solitons in dusty plasmas with two-temperature superthermal electrons

A rigorous theoretical investigation has been performed on the propagation of cylindrical and spherical Gardner solitons (GSs) associated with dust-ion-acoustic (DIA) waves in a dusty plasma consisting of inertial ions, negatively charged immobile dust, and two populations of kappa distributed electrons having two distinct temperatures. The well-known reductive perturbation method has been used to derive the modified Gardner (mG) equation. The basic features (amplitude, width, polarity, etc.) of nonplanar DIA modified Gardner solitons (mGSs) have been thoroughly examined by the numerical analysis of the mG equation. It has been found that the characteristics of the nonplanar DIA mGSs significantly differ from those of planar ones. It has been also observed that kappa distributed electrons with two distinct temperatures significantly modify the basic properties of the DIA solitary waves and that the plasma system under consideration supports both compressive and rarefactive DIA mGSs. The present investigation should play an important role for understanding localized electrostatic disturbances in space and laboratory dusty plasmas where stationary negatively charged dust, inertial ions, and superthermal electrons with two distinct temperatures are omnipresent ingredients.     

Electrostatic Solitary Pulses in a Dusty Electronegative Magnetoplasma

The nonlinear characteristics of dust-electron-acoustic (DEA) waves in a dusty electronegative magnetoplasma system consisting of nonextensive hot electrons, inertial cold electrons, positively charged static ions, and negatively charged immobile dust grains has been investigated. In this observation, the well-known reductive perturbation technique is employed to determine different types of nonlinear dynamical equations, namely, magnetized Korteweg–de Vries (KdV), magnetized modified KdV (mKdV), and magnetized Gardner equations. The stationary solitary wave and double layer solution of these three equations, which describe the characteristics of solitary waves and double layers of DEA waves, are obtained and numerically analyzed. It is noticed that various plasma parameters (viz., hot electron nonextensivity, positive ion-to-cold electron number density ratio, dust-to-cold electron number density ratio, etc.) significantly affect the basic properties of DEA solitary waves (DEASWs) and Gardner solitons (GSs). The prodigious results found from this theoretical investigation may be useful for researchers to investigate the nonlinear structures in various space and laboratory plasmas.     

Properties of cylindrical and spherical heavy ion-acoustic solitary and shock structures in a multispecies plasma with superthermal electrons

A theoretical investigation on heavy ion-acoustic (HIA) solitary and shock structures has been accomplished in an unmagnetized multispecies plasma consisting of inertialess kappa-distributed superthermal electrons, Boltzmann light ions, and adiabatic positively charged inertial heavy ions. Using the reductive perturbation technique, the nonplanar (cylindrical and spherical) Kortewg–de Vries (KdV) and Burgers equations have been derived. The solitary and shock wave solutions of the KdV and Burgers equations, respectively, have been numerically analyzed. The effects of superthermality of electrons, adiabaticity of heavy ions, and nonplanar geometry, which noticeably modify the basic features (viz. polarity, amplitude, phase speed, etc.) of small but finite amplitude HIA solitary and shock structures, have been carefully investigated. The HIA solitary and shock structures in nonplanar geometry have been found to distinctly differ from those in planar geometry. Novel features of our present attempt may contribute to the physics of nonlinear electrostatic perturbation in astrophysical and laboratory plasmas.     

Small-amplitude shock waves and double layers in dusty plasmas with opposite polarity charged dust grains

Theoretical investigation is carried out for understanding the properties of nonlinear dust-acoustic (DA) waves in an unmagnetized dusty plasma whose constituents are massive, micron-sized, positive and negatively charged inertial dust grains along with q (nonextensive) distributed electrons and ions. The reductive perturbation method is employed in order to derive two types of nonlinear dynamical equations, namely, Burgers equation and modified Gardner equation (Gardner equation with dissipative term). They are also numerically analyzed to investigate the basic features (viz., polarity, amplitude, width, etc.) of shock waves and double layers. It has been observed that the effects of nonextensivity, opposite polarity charged dust grains, and different dusty plasma parameters have significantly modified the fundamental properties of shock waves and double layers. The results of this investigation may be used for researches of the nonlinear wave propagation in laboratory and space plasmas.     

Ion-acoustic Gardner solitons in a four-component nonextensive multi-ion plasma

The nonlinear propagation of ion-acoustic (IA) solitary waves (SWs) in a four-component non-extensive multi-ion plasma system containing inertial positively charged light ions, negatively charged heavy ions, as well as noninertial nonextensive electrons and positrons has been theoretically investigated. The reductive perturbation method has been employed to derive the nonlinear equations, namely, Korteweg?deVries (KdV), modified KdV (mKdV), and Gardner equations. The basic features (viz. polarity, amplitude, width, etc.) of Gardner solitons are found to exist beyond the KdV limit and these IA Gardner solitons are qualitatively different from the KdV and mKdV solitons. It is observed that the basic features of IA SWs are modified by various plasma parameters (viz. electron and positron nonextensivity, electron number density to ion number density, and electron temperature to positron temperature, etc.) of the considered plasma system. The results obtained from this theoretical investigation may be useful in understanding the basic features of IA SWs propagating in both space and laboratory plasmas.     

Effects of nonextensivity and nonthermality on dust-acoustic Gardner solitons in dusty plasmas with distinct ion temperatures

The effects of nonextensivity and nonthermality of ions of two distinct temperatures on dustacoustic Gardner solitons (DAGSs) in an unmagnetized dusty plasma system are investigated theoretically. The constituents of the dusty plasma under consideration are negatively charged mobile dust fluid, Boltzmann-distributed electrons, and ions of two distinct temperatures following nonextensive (q) and nonthermal distributions, respectively. The Korteweg-de Vries (KdV), modified KdV, and Gardner equations are derived by using the reductive perturbation technique, and thereby their characteristic features are compared. It is observed that both the nonextensive and nonthermal ions significantly modify the basic properties and polarities of dust-acoustic solitary waves. The present investigation may be of relevance to space and laboratory dusty plasma systems.     

Nonlinear dust-acoustic structures in space plasmas with superthermal electrons,positrons, and ions

Some features of nonlinear dust-acoustic (DA) structures are investigated in a space plasma consisting of superthermal electrons, positrons, and positive ions in the presence of negatively charged dust grains with finite-temperature by employing a pseudo-potential technique in a hydrodynamic model. For this purpose, it is assumed that the electrons, positrons, and ions obey a kappa-like (κ) distribution in the background of adiabatic dust population. In the linear analysis, it is found that the dispersion relation yield two positive DA branches, i.e., the slow and fast DA waves. The upper branch (fast DA waves) corresponds to the case in which both (negatively charged) dust particles and (positively charged) ion species oscillate in phase with electrons and positrons. On the other hand, the lower branch (slow DA waves) corresponds to the case in which only dust particles oscillate in phase with electrons and positrons, while ion species are in antiphase with them. On the other hand, the fully nonlinear analysis shows that the existence domain of solitons and their characteristics depend strongly on the dust charge, ion charge, dust temperature, and the spectral index κ. It is found that the minimum/maximum Mach number increases as the spectral index κ increases. Also, it is found that only solitons with negative polarity can propagate and that their amplitudes increase as the parameter κ increases. Furthermore, the domain of Mach number shifts to the lower values, when the value of the dust charge Z _d increases. Moreover, it is found that the Mach number increases with an increase in the dust temperature. Our analysis confirms that, in space plasmas with highly charged dusts, the presence of superthermal particles (electrons, positrons, and ions) may facilitate the formation of DA solitary waves. Particularly, in two cases of hydrogen ions H⁺ (Z _i = 1) and doubly ionized Helium atoms He²⁺ (Z _i = 2), the mentioned results are the same. Additionally, the mentioned dusty plasma does not support DA solitons with positive polarity (compressive solitons). Furthermore, our analysis confirms that DA double layers cannot exist in such a system. Moreover, the positron density has not a considerable effect on the behavior of DA solitons in our model.     

Effect of dust charge fluctuations on dust acoustic structures in magnetized dusty plasma containing nonextensive electrons and two-temperature isothermal ions

Effect of dust electrical charge fluctuations on the nature of dust acoustic solitary waves (DASWs) in a four-species magnetized dusty plasma containing nonextensive electrons and two-temperature isothermal ions has been investigated. In this model, the negative dust electric charge is considered to be proportional to the plasma space potential. The nonlinear Zakharov–Kuznetsov (ZK) and modified Zakharov–Kuznetsov (mZK) equations are derived for DASWs by using the standard reductive perturbation method. The combined effects of electron nonextensivity and dust charge fluctuations on the DASW profile are analyzed. The different ranges of the nonextensive q-parameter are considered. The results show that solitary waves the amplitude and width of which depend sensitively on the nonextensive q-parameter can exist. Due to the electron nonextensivity and dust charge fluctuation rate, our dusty plasma model can admit both positive and negative potential solitons. The results show that the amplitude of the soliton increases with increasing electron nonextensivity, but its width decreases. Increasing the electrical charge fluctuations leads to a decrease in both the amplitude and width of DASWs.     

Dust-acoustic Rogue Waves in Four-Component Plasmas

Plasma Physics Reports - A theoretical investigation has been made on modulational instability (MI) and dust-acoustic (DA) rogue waves (DARWs) in a four-component dusty plasma medium containing...     

Nonlinear screening of dust grains and structurization of dusty plasma

A review of theoretical ideas on the physics of structurization instability of a homogeneous dusty plasma, i.e., the formation of zones with elevated and depressed density of dust grains and their arrangement into different structures observed in laboratory plasma under microgravity conditions, is presented. Theoretical models of compact dust structures that can form in the nonlinear stage of structurization instability, as well as models of a system of voids (both surrounding a compact structure and formed in the center of the structure), are discussed. Two types of structures with very different dimensions are possible, namely, those smaller or larger than the characteristic mean free path of ions in the plasma flow. Both of them are characterized by relatively regular distributions of dust grains; however, the first ones usually require external confinement, while the structures of the second type can be self-sustained (which is of particular interest). In this review, they are called dust clusters and self-organized dust structures, respectively. Both types of the structures are characterized by new physical processes that take place only in the presence of the dust component. The role of nonlinearities in the screening of highly charged dust grains that are often observed in modern laboratory experiments turns out to be great, but these nonlinearities have not received adequate study as of yet. Although structurization takes place upon both linear and nonlinear screening, it can be substantially different under laboratory and astrophysical conditions. Studies on the nonlinear screening of large charges in plasma began several decades ago; however, up to now, this effect was usually disregarded when interpreting the processes occurring in laboratory dusty plasma. One of the aims of the present review was to demonstrate the possibility of describing the nonlinear screening of individual grains and take it into account with the help of the basic equations for the equilibrium between plasma components when analyzing equilibrium structures. The effect of plasma screening nonlinearity on both the diffusion processes and the forces of dust drag by plasma fluxes is analyzed. It is shown how self-organized dust structures form in these processes. In the limit of very small dust grain charges, the forces acting on the dusty plasma components and the set of basic equations for stationary dust structures (with allowance for nonlinear screening) take a standard form. New qualitative effects, such as the suppression of diffusion due to ion scattering from dust grains and the formation of structures of different configurations, are described. A detailed comparison with previous results is performed. It is shown that the solution of basic nonlinear equations for dust structures yields new qualitative effects. A number of new effects to be studied in future dusty plasma experiments with the formation of structures in spherical chambers are predicted (it is assumed that diffusion will play a significant role under microgravity conditions). Recent ground-based experiments, as well as experiments carried out onboard the International Space Station, directly confirm the nonlinear character of screening and the significant role played by this nonlinearity in the structurization of dusty plasma. Experiments on the formation of structures consisting of smaller dust grains within structures formed of larger grains are discussed. It is shown that those experiments can be interpreted only using the concept of nonlinear screening.     

Dust–Ion–Acoustic Solitary Wave Structure in Magnetized Plasma with Nonthermally Distributed Electrons and Positrons

Plasma Physics Reports - The dust–ion–acoustic (DIA) solitary wave (SW) propagation in a magnetized dusty plasma consisting of mobile positive and heavy negative ions, nonthermal...     

Properties of dust-plasma structures formed in a glow discharge above the lower wall of the discharge chamber

The properties are studied of dusty plasma structures formed in a glow discharge in a dust trap above the lower wall of the side branch of the discharge tube, near the turn of the discharge channel. The dust structure is three-dimensional with a characteristic size of up to 3 cm and contains about 30000 dust grains. Depending on the experimental conditions, dust-acoustic, dissipative, and charge-gradient instabilities can develop in such a structure. When using highly polydisperse dust grains of arbitrary shape, the effect of selection of dust grains by the plasma with respect to their mean size and shape was discovered. This effect was studied quantitatively in two gases by using the method of gathering and extraction of the dust grains levitating in the trap. The morphology of the dust structures was determined from the pair correlation functions of the horizontal cross sections containing long-range order peaks and elements of a hexagonal lattice. Stratification of a uniform structure accompanied by convective rotation caused by the grain charge gradient was observed. Applications of the dusty plasma created in this type of device are discussed.     

Solitary dust sound waves in a plasma with two-temperature ions and distributed grain size

The propagation of weakly nonlinear dust sound waves in a dusty plasma containing two different-temperature ion species is explored. The nonlinear equations describing both the quadratic and cubic plasma nonlinearities are derived. It is shown that the properties of dust sound waves depend substantially on the grain size distribution. In particular, for solitary dust sound waves with a positive potential to exist in a plasma with distributed grain size, it is necessary that the difference between the temperatures of two ion species be larger than that in the case of equal-size grains.     

Nonlinear screening of dust grains and structurization of dusty plasma: II. formation and stability of dust structures

The second part of the review on dust structures (the first part was published in Plasma Phys. Rep. 39, 515 (2013)) is devoted to experimental and theoretical studies on the stability of structures and their formation from the initially uniform dusty plasma components. The applicability limits of theoretical results and the role played by nonlinearity in the screening of dust grains are considered. The importance of nonlinearity is demonstrated by using numerous laboratory observations of planar clusters and volumetric dust structures. The simplest compact agglomerates of dust grains in the form of stable planar clusters are discussed. The universal character of instability resulting in the structurization of an initially uniform dusty plasma is shown. The fundamental correlations described in the first part of the review, supplemented with effects of dust inertia and dust friction by the neutral gas, are use to analyze structurization instability. The history of the development of theoretical ideas on the physics of the cluster formation for different types of interaction between dust grains is described.     

Ionization instability and dusty plasma structurization

In the presence of ionization processes, a homogeneous equilibrium dust distribution often appears as a balance between plasma generation by ionization and plasma absorption by dust particles. It is shown that such equilibrium, often present in laboratory plasmas, is generally unstable against the formation of dust clumps separated by dust-free regions (dust voids). The driving force that separates an initially homogeneous dusty plasma into dust clumps and dust voids is the drag force produced by ions flowing out from the regions with reduced dust density. The lower the dust density, the lower the electron absorption by dust particles and the larger the ionization rate proportional to the electron density. An increase in the ion drag force leads to a further decrease in the dust density and, thus, drives the instability. In the nonlinear stage, the instability creates structures—dust clouds separated by dust voids. The dependence of the instability growth rate on the wavenumber (or, in other words, on the size of the dust-free and dust-containing regions) is investigated. It is shown that, for sufficiently small wavenumbers, a homogeneous distribution is always unstable. An analogy with a gravitational-like instability related to shadowing of the plasma flux by dust particles is pointed out. This effect, which is due to collective shadowing of the plasma flux, dominates the shadowing by individual dust particles discussed previously. Similar to the usual gravitational instability, perturbations with the largest scales are always unstable. Contrary to the usual gravitational instability, the largest growth rate corresponds not to the largest possible scale but to the size close to the mean free path of plasma particles colliding with dust particles. A special investigation is undertaken to determine the influence of the ion-neutral collisions on the growth rate of the instability.     

Shock structure formation in dusty plasmas

The problem of the evolution of a perturbation in a dusty plasma and its transformation into a nonlinear wave structure is considered. A computational method that allows one to solve the set of nonlinear evolutionary equations describing variable-charge dust grains, Boltzmann electrons, and inertial ions is developed. Exact steady-state solutions corresponding to ion-acoustic shock structures associated with anomalous dissipation originating from dust grain charging are found taking into account the effect of electron and ion charge separation. The role of this effect increases with the speed of the shock. The evolutions of an initial soliton (which is a steady-state wave solution in a plasma containing dust grains with a constant charge) and an initially immobile perturbation with a constant increased ion density are investigated. In a charge-varying dusty plasma, the soliton evolves into a nonsteady shock wave structure that propagates at a constant speed and whose amplitude decreases with time. The initially immobile perturbation with a constant increased ion density evolves into a shock structure similar to a steady-state shock wave. In the latter case, the compression shock wave is accompanied by a rarefaction region (dilatation wave), which finally leads to the destruction of the shock structure. The solution of the problem of the evolution of a perturbation and its transformation into a shock wave in a charge-varying dusty plasma opens up the possibility of describing real phenomena (such as supernova explosions) and laboratory and active space experiments.     

Splitting of the modes of a low-frequency magnetosonic wave in a polydisperse dusty plasma

The properties of magnetosonic waves that propagate perpendicularly to the external magnetic field in a polydisperse dusty plasma and the frequencies of which are about the dust cyclotron frequency are analyzed. A dispersion relation containing integrals of functions of the dust grain radius is derived and investigated as a function of the parameters characterizing the polydisperse properties of dust. It is found that, in a polydisperse dusty plasma, the low-frequency magnetosonic mode splits into two branches. The first, lower frequency branch has a cutoff, while the higher frequency branch has a resonance. Between the two branches, there is a forbidden frequency range within which electromagnetic waves cannot propagate perpendicular to the magnetic field. The width of the forbidden frequency range is determined as a function of the slope of the distribution function of dust grains over radii and the interval within which the dust grain radii lie.