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.     

Investigation of Ion-Acoustic Solitons in Magnetosphere and Tokamak Warm Plasma with Two-Temperature Electrons

The properties of oblique propagation of small amplitude ion-acoustic soliton are investigated in a plasma containing weakly relativistic ions and two-temperature electrons (cold and hot electrons). The reductive perturbation method is used to derive the Korteweg?de Vries equation for the present plasma model. It is found that the parameters determining the nature of soliton are different for compressive or rarefactive structures. Moreover, the effects of weakly relativistic ions, the temperature ratio, and the density ratio of hot-to-cold electron species on soliton characters are studied. The theory is applied on the case of relativistic ions observed in the magnetosphere and in the case of nonrelativistic ions observed in tokamaks.     

Nonlinear ion modes in a strongly coupled plasma in the presence of nonthermal ion fluids and polarization force

The nonlinear propagation of ion-acoustic (IA) waves in a strongly coupled plasma system containing Maxwellian electrons and nonthermal ions has been theoretically and numerically investigated. The well-known reductive perturbation technique is used to derive both the Burgers and Korteweg?de Vries (KdV) equations. Their shock and solitary wave solutions have also been numerically analyzed in understanding localized electrostatic disturbances. It has been observed that the basic features (viz. polarity, amplitude, width, etc.) of IA waves are significantly modified by the effect of polarization force and other plasma parameters (e.g., the electron-to-ion number density ratio and ion-to-electron temperature ratio). This is a unique finding among all theoretical investigations made before, whose probable implications are discussed in this investigation. The implications of the results obtained from this investigation may be useful in understanding the wave propagation in both space and laboratory plasmas.     

3D Burgers Equation in Relativistic Plasma in the Presence of Electron and Negative Ion Trapping: Evolution of Shock Wave

The characteristics of shock waves in a relativistic plasma in the presence of nonisothermal electrons and nonisothermal negative ions is investigated by deriving the evolution equation in terms of a modified 3D Burgers equation, or trapped 3D Burgers equation. The solution of this equation is examined analytically to study the salient characteristics of shock waves in such plasma. The nonlinear coefficient is found to have the lowest (highest) value when the negative ions move toward thermal equilibrium with a dip-shaped electron distribution (when both electrons and negative ions follow a dip-shaped distribution) for a particular value of relativistic factor, and it remains in an intermediate state when both electrons and negative ions follow a flat-topped distribution. On the other hand, the dissipative coefficient is found to decrease (increase) with increasing relativistic parameter (viscous parameter). A profound effect of the trapped state of both electrons and negative ions and the temperature ratio between positive ions and electrons (negative ions and electrons) on the structure of the shock wave is also seen. However, it has been noticed that the trapped parameter of electrons has a dominating control over the shock potential profile than the trapped parameter of negative ions.     

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.     

Ion-Scale Excitations in a Strongly Coupled Astrophysical Plasma with Nuclei of Heavy Elements

The linear and nonlinear propagation of ultrarelativistic and nonrelativistic analysis on modified ion-acoustic (MIA) waves in a strongly coupled unmagnetized collisionless relativistic space plasma system is carried out. Plasma system is assumed to contain strongly coupled nonrelativistic ion fluids, both nonrelativistic and ultrarelativistic degenerate electron and positron fluids, and positively charged static heavy elements. The restoring force is provided by the degenerate pressure of the electron and positron fluids, whereas the inertia is provided by the mass of ions. The positively charged static heavy elements participate only in maintaining the quasineutrality condition at equilibrium. The well-known reductive perturbation method is used to derive the Burgers and Korteweg–de Vries equations. Their shock and solitary wave solutions are numerically analyzed to understand the localized electrostatic disturbances. The basic characteristics of MIA shock and solitary waves are found to be significantly modified by the effects of degenerate pressures of electron, positron, and ion fluids, their number densities, and various charge state of heavy elements. The implications of our results to dense plasmas in compact astrophysical objects (e.g., nonrotating white dwarfs, neutron stars, etc.) are briefly discussed.     

Relativistic Ion-Acoustic Solitary Waves in a Magnetized Pair Ion Dense Plasma with Nuclei of Heavy Elements

The propagation of ion-acoustic solitary waves (IASWs) in a magnetized collisionless degenerate plasma system for describing collective plasma oscillations in dense quantum plasmas with relativistically degenerate electrons, oppositely charged inertial ions, and positively charged immobile heavy elements is investigated theoretically. The perturbations of the magnetized quantum plasma are studied employing the reductive perturbation technique to derive the Korteweg–de Vries (KdV) and the modified KdV (mKdV) equations that admit solitary wave solutions. Chandrasekhar limits are used to investigate the degeneracy effects of interstellar compact objects through the equation of state for degenerate electrons in nonrelativistic and ultrarelativistic cases. The basic properties of small but finite-amplitude IASWs are modified significantly by the combined effects of the degenerate electron number density, pair ion number density, static heavy element number density, and magnetic field. It is found that the obliqueness affects both the amplitude and width of the solitary waves, whereas the other parameters mainly influence the width of the solitons. The results presented in this paper can be useful for future investigations of astrophysical multi-ion plasmas.     

Nonlinear ion flux caused by a periodic ion-acoustic wave in plasma with two-temperature electrons

The propagation of periodic ion-acoustic waves in plasma with two-temperature electrons and cold ions is analyzed. The equations for the wave potential are derived in the first- and second-orders of the perturbation theory, and their nonsecular periodic solutions are obtained. The average nonlinear ion flux is determined, and its properties are studied as functions of the ratios between the densities and temperatures of the cold and hot electron components. The conditions are analyzed under which the ion flux is co- or counter-directed to the wave propagation direction. For the case in which, depending on the plasma parameters, the ion flux at a given wave amplitude can be either positive or negative, the domains of existence of positive and negative ion fluxes in the “temperature ratio-density ratio” plane are determined.     

Slow electromagnetic solitons in electron-ion plasmas

A set of nonlinear differential equations that describe moving relativistic solitons is investigated analytically and solved numerically. The influence of the ion motion on the soliton structure is investigated. It is demonstrated that, depending on the propagation velocity, relativistic solitary waves can occur in the form of bright solitons, dark solitons, or collisionless electromagnetic shock waves. In the limit of a low propagation velocity, a dark soliton can trap the ions and accelerate them. In the case of a bright soliton, the effects of ion dynamics limit the soliton amplitude. The constraint on the maximum amplitude is related to either the breaking of ion motion or the intersection of electron trajectories. The soliton breaking provides a new mechanism for ion and electron acceleration in the interaction of high-intensity laser pulses with 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.     

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.     

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.     

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.     

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.     

Ion flux associated with an ion-acoustic cnoidal wave in magnetized dusty plasma

The oblique propagation of nonlinear periodic ion-acoustic waves in magnetized dusty plasma is investigated. The equations describing the dynamics of the wave potential in the first and second orders of the perturbation theory are derived, and their nonsecular periodic solutions are found. The average nonlinear ion flux caused by the propagation of a cnoidal wave is estimated. The magnitude and direction of the ion flux are analyzed as functions of the dust charge density and the angle between the wave propagation direction and the magnetic field.     

Influence of electromagnetic radiation on the shock structure formation in complex plasmas

Electromagnetic radiation effects are calculated for the case of the solar radiation spectrum in the vicinity of the Earth. The influence of the photoelectric effect on the propagation of nonlinear waves in complex plasmas is studied when the dust grains acquire large positive charges. Exact solutions to nonlinear equations in the form of steady-state shocks that do not involve electron-ion collisions are found, and the conditions for their existence are obtained. In contrast to the classical collisionless shock waves, the dissipation due to the dust charging involves the interaction of the electrons and ions with the dust grains in the form of microscopic grain currents and the photoelectric current. The nonsteady problem of the evolution of a perturbation and its transformation into a nonlinear wave structure is considered. The evolution of an intense, initially nonmoving region with a constant increased ion density is investigated. It is shown that the evolution of a rather intense nonmoving region with a constant increased ion density can result in the formation of a shock wave. In addition to the compressional wave, a rarefaction region (dilatation wave) appears. The presence of a dilatation wave finally leads to the destruction of the shock structure. The possibility is discussed of the observation of shock waves related to dust charging in the presence of electromagnetic radiation in active rocket experiments, which involve the release of a gaseous substance in the Earth's ionosphere in the form of a high-speed plasma jet at altitudes of 500–600 km.     

Dust−ion acoustic freak wave propagation in a nonthermal mesospheric dusty plasma

Nonlinear properties of dust?ion acoustic freak waves have been studied in homogeneous unmagnetized dusty plasmas consisting of ions, nonthermal fast electrons, and positive and negative dust grains. By using derivative expansion method under the assumption of strongly dispersive medium, the basic equations are reduced to nonlinear Schrödinger equation (NLSE). One of NLSE solutions in the unstable region is the rational one which is responsible for creation of the freak waves. The dependence of the freak wave profile on the dust grain charge, carrier wavenumber, and energetic nonthermal electron population is discussed.     

Heavy Ion-Acoustic Solitary Waves and Double Layers in a Multi-Ion Plasma

The formation and propagation of small-amplitude heavy-ion-acoustic (HIA) solitary waves and double layers in an unmagnetized collisionless multicomponent plasma system consisting of superthermal electrons, Boltzmann distributed light ions, and adiabatic positively charged inertial heavy ions are theoretically investigated. The reductive perturbation technique is employed to derive the modified Korteweg–de Vries (mKdV) and standard Gardner (SG) equations. The solitary wave (SW) solution of mKdV and SG equations, as well as double layers (DLs) solution of SG equation, is studied for analysis of higher order nonlinearity. It is found that the plasma system under consideration supports positive and negative potential Gardner solitons, but only positive potential mKdV solitons. In addition, it is shown that, the basic properties of HIA mKdV and Gardner solitons and DLs (viz. polarity, amplitude, width, and phase speed) are incomparably influenced by the adiabaticity effect of heavy ions and the superthermality effect of electrons. The relevance of the present findings to the system of space plasmas, as well as to the system of researchers interest, is specified.     

Study of Electromagnetic Electron Cyclotron Waves for Kappa Distribution with AC Field in the Magnetosphere of Saturn

Parallel propagating electromagnetic electron cyclotron (EMEC) waves in the extended plasma sheet (~12R_S) and in the outer magnetosphere (~18R_S) of Saturn have been studied. A dispersion relation for parallel propagating relativistic EMEC waves has been applied to the magnetosphere of Saturn, and comparisons have been made with the data of Voyager 1 at these radial distances. The detailed investigations for EMEC waves have been done in the presence of the perpendicular AC electric field, using the kappa distribution function. The relativistic temporal growth rate is calculated by the method of characteristic solution with the data provided by Voyager 1. The effect of the suprathermal electron density, temperature anisotropy, frequency of AC electric field, thermal energy of ions, and relativistic factor on the temporal growth rate of EMEC wave emission has been studied. The simulation results show that the growth of parallel propagating EMEC waves is significantly affected by variations in the temperature anisotropy, electron density, ion thermal energy, and relativistic factor in both the extended plasma sheet and the outer magnetosphere of Saturn. The temperature anisotropy (T⊥/T_║), ion thermal energy (K_BT_║i), and electron density (n₀) have been found to be a major source of free energy for parallel propagating EMEC waves in both regions.