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.     

Effects of nonextensivity on the electron-acoustic solitary structures in a magnetized electron−positron−ion plasma

Obliquely propagating electron-acoustic solitary waves (EASWs) in a magnetized electron?positron?ion plasma (containing nonextensive hot electrons and positrons, inertial cold electrons, and immobile positive ions) are precisely investigated by deriving the Zakharov–Kuznetsov equation. It is found that the basic features (viz. polarity, amplitude, width, phase speed, etc.) of the EASWs are significantly modified by the effects of the external magnetic field, obliqueness of the system, nonextensivity of hot positrons and electrons, ratio of the hot electron temperature to the hot positron temperature, and ratio of the cold electron number density to the hot positron number density. The findings of our results can be employed in understanding the localized electrostatic structures and the characteristics of EASWs in various astrophysical 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.     

Characteristics of Electronegative Plasma Sheath with <Emphasis Type="Italic">q</Emphasis>-Nonextensive Electron Distribution

The characteristics of sheath in a plasma system containing q-nonextensive electrons, cold fluid ions, and Boltzmann-distributed negative ions are investigated. A modified Bohm sheath criterion is derived by using the Sagdeev pseudopotential technique. It is found that the proposed Bohm velocity depends on the degree of nonextensivity (q), negative ion temperature to nonextensive electron temperature ratio (σ), and negative ion density (B). Using the modified Bohm sheath criterion, the sheath characteristics, such as the spatial distribution of the potential, positive ion velocity, and density profile, have been numerically investigated, which clearly shows the effect of negative ions, as well as the nonextensive distribution of electrons. It is found that, as the nonextensivity parameter and the electronegativity increases, the electrostatic sheath potential increases sharply and the sheath width decreases.     

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.     

Rogue Waves in Multi-Ion Cometary Plasmas

The effect of pair ions on the formation of rogue waves in a six-component plasma composed of two hot and one colder electron component, hot ions, and pair ions is studied. The kappa distribution, which provides an unambiguous replacement for a Maxwellian distribution in space plasmas, is connected with nonextensive statistical mechanics and provides a continuous energy spectrum. Hence, the colder and one component of the hotter electrons is modeled by kappa distributions and the other hot electron component, by a q-nonextensive distribution. It is found that the rogue wave amplitude is different for various pair-ion components. The magnitude, however, increases with increasing spectral index and nonextensive parameter q. These results may be useful in understanding the basic characteristics of rogue waves in cometary plasmas.     

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.).     

Nonlinear propagation of ion-acoustic waves through the Burgers equation in weakly relativistic plasmas

The Burgers equation is obtained to study the characteristics of nonlinear propagation of ionacoustic shock, singular kink, and periodic waves in weakly relativistic plasmas containing relativistic thermal ions, nonextensive distributed electrons, Boltzmann distributed positrons, and kinematic viscosity of ions using the well-known reductive perturbation technique. This equation is solved by employing the (G'/G)-expansion method taking unperturbed positron-to-electron concentration ratio, electron-to-positron temperature ratio, strength of electrons nonextensivity, ion kinematic viscosity, and weakly relativistic streaming factor. The influences of plasma parameters on nonlinear propagation of ion-acoustic shock, periodic, and singular kink waves are displayed graphically and the relevant physical explanations are described. It is found that these parameters extensively modify the shock structures excitation. The obtained results may be useful in understanding the features of small but finite amplitude localized relativistic ion-acoustic shock waves in an unmagnetized plasma system for some astrophysical compact objects 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.     

Dust-acoustic solitary waves in a four-component adiabatic magnetized dusty plasma

Theoretical investigation has been made on obliquely propagating dust-acoustic (DA) solitary waves (SWs) in a magnetized dusty plasma which consists of non-inertial adiabatic electron and ion fluids, and inertial negatively as well as positively charged adiabatic dust fluids. The reductive perturbation method has been employed to derive the Korteweg-de Vries equation which admits a solitary wave solution for small but finite amplitude limit. It has been shown that the basic features (speed, height, thickness, etc.) of such DA solitary structures are significantly modified by adiabaticity of plasma fluids, opposite polarity dust components, and the obliqueness of external magnetic field. The SWs have been changed from compressive to rarefactive depending on the value of μ (a parameter determining the number of positive dust present in this plasma model). The present investigation can be of relevance to the electrostatic solitary structures observed in various dusty plasma environments (viz. cometary tails, upper mesosphere, Jupiter’s magnetosphere, etc.).     

Dynamics of dust grains in a two-component dusty plasma induced by solar radiation under microgravity conditions

Results are presented from experimental studies of the dynamics of dust grains charged via photoemission under microgravity conditions. The experiments are performed with bronze grains exposed to solar radiation on board the Mir space station. The velocity distribution, temperature, mean charge, and friction and diffusion coefficients of dust grains are determined. An analysis of the data obtained shows that the polarization caused by the separation of opposite charges can significantly affect the transport processes in a two-component dusty plasma consisting of dust grains and the electrons emitted by them.     

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.     

Solitary waves in dusty plasmas with weak relativistic effects in electrons and ions

Two distinct classes of dust ion acoustic (DIA) solitary waves based on relativistic ions and electrons, dust charge Z _d and ion-to-dust mass ratio Q’ = m _i /m _d are established in this model of multicomponent plasmas. At the increase of mass ratio Q’ due to increase of relativistic ion mass and accumulation of more negative dust charges into the plasma causing decrease of dust mass, relativistic DIA solitons of negative potentials are abundantly observed. Of course, relativistic compressive DIA solitons are also found to exist simultaneously. Further, the decrease of temperature inherent in the speed of light c causes the nonlinear term to be more active that increases the amplitude of the rarefactive solitons and dampens the growth of compressive solitons for relatively low and high mass ratio Q’, respectively. The impact of higher initial streaming of the massive ions is observed to identify the point of maximum dust density N _d to yield rarefactive relativistic solitons of maximum amplitude.     

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.     

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.     

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.     

Effect of Dust Charge Fluctuation on Ion Acoustic Waves in a Plasma with Nonextensive Electrons

Plasma Physics Reports - The linear dispersion for ion acoustic waves (IAWs) including the effects of dust charge fluctuation and electron nonextensivity is derived. It is shown that the presence...     

Effect of dust size distribution on ion-acoustic solitons in dusty plasmas with different dust grains

Theoretical studies are carried out for ion acoustic solitons in multicomponent nonuniform plasma considering the dust size distribution. The Korteweg?de Vries equation for ion acoustic solitons is given by using the reductive perturbation technique. Two special dust size distributions are considered. The dependences of the width and amplitude of solitons on dust size parameters are shown. It is found that the properties of a solitary wave depend on the shape of the size distribution function of dust grains.     

Experimental studies of the dynamics of dust grains in gas-discharge plasmas

Results of the experimental studies of the dynamics of dust grains in the plasmas of an rf capacitive discharge and a dc glow discharge are presented. The dusty plasma of a dc glow discharge was investigated in both ground-based experiments and experiments carried out under microgravity conditions (on board the Mir space station). The pair correlation function, temperature, and diffusion coefficient of dust grains are measured in a wide range of the dusty-plasma parameters. Dimensionless parameters responsible for the microscopic transport of dust-grains in a gas-discharge plasma are determined. A nonintrusive diagnostic technique for determining the dust-grain charges and screening lengths under the assumption of screened interaction between the grains is proposed. This technique is used to estimate the surface potential of dust grains of different size in a gas-discharge plasma.