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.     

Electrostatic Solitary Waves in Pair-ion Plasmas with Trapped Electrons

Electrostatic solitons in an unmagnetized pair-ion plasma comprising adiabatic fluid positive and negative ions and non-isothermal electrons are investigated using both arbitrary and small amplitude techniques. An energy integral equation involving the Sagdeev potential is derived, and the basic properties of large amplitude solitary structures are investigated. Various features of solitons differ in different existence domains. The effects of ion adiabaticity, particle concentration, and resonant electrons on the profiles of Sagdeev potential and corresponding solitary waves are investigated. The generalized Korteweg-de Vries equation with mixed-nonlinearity is derived by expanding the Sagdeev potential. Asymptotic solutions for different orders of nonlinearity are discussed for solitary waves. The present work is applicable to understanding the wave phenomena and associated nonlinear electrostatic perturbations in pair/bi-ion plasmas which may occur in space and laboratory plasmas.     

Large amplitude ion-acoustic double layers in a plasma havingvariable-charge dust grain particles

The dust grain charging effect on large amplitude ion-acoustic double layers in a dusty plasma are investigated by the numerical calculation. The nonlinear structures of ion-acoustic double layers are examined, showing that the characteristics of the double layer sensitively depend on the dust charging effect, the influence of the ion temperature, the electrostatic potential, and the Mach number. The flow of the plasma current to the surface of dust particles increases the dust charge numbers. The effect of the ion temperature decreases the propagation speed of the ion-acoustic double layers and decreases the dust charge numbers. It is found that rarefactive double layers can propagate in this system. New findings of large amplitude ion-acoustic double layers with the dust charging effect and finite ion temperature in a dusty plasma are predicted     

On some properties of linear and nonlinear waves in pair-ion plasmas

It is pointed out that the observation of the electrostatic ion acoustic wave frequency can be a suitable check to determine whether the produced plasma is a pure pair-ion plasma or whether it comprises some concentration of electrons. A theoretical model for the pair-ion plasma dynamics is presented along with a new electrostatic mode which can exist only in such systems. It can become unstable in the presence of shear flow and it can give rise to vortex structures in the nonlinear regime. The possibility of shocks and solitons, due to nonlinear drift waves in a pair-ion plasma comprising electrons, is also discussed. The relevance of this investigation to both laboratory and astrophysical plasmas is pointed out.     

Electrostatic solitons in unmagnetized hot electron-positron-ion plasmas

Linear and nonlinear electrostatic waves in unmagnetized electron-positron-ion (e-p-i) plasmas are studied. The electrons and positrons are assumed to be isothermal and dynamic while ions are considered to be stationary to neutralize the plasma background only. It is found that both upper (fast) and lower (slow) Langmuir waves can propagates in such a type of pair (e-p) plasma in the presence of ions. The small amplitude electrostatic Korteweg-de Vries (KdV) solitons are also obtained using reductive perturbation method. The electrostatic potential hump structures are found to exist when the temperature of the electrons is larger than the positrons, while the electrostatic potential dips are obtained in the reverse temperature conditions for electrons and positrons in e-p-i plasmas. The numerical results are also shown for illustration. The effects of different ion concentration and temperature ratios of electrons and positrons, on the formation of nonlinear electrostatic potential structures in e-p-i plasmas are also discussed.     

Electrostatic dust-acoustic envelope solitons in an electron-depleted plasma

A standard nonlinear Schrödinger equation has been established by using the reductive perturbation method to investigate the propagation of electrostatic dust-acoustic waves, and their modulational instability as well as the formation of localized electrostatic envelope solitons in an electron-depleted unmagnetized dusty plasma system comprising opposite polarity dust grains and super-thermal positive ions. The relevant physical plasma parameters (viz., charge, mass, number density of positive and negative dust grains, and super-thermality of the positive ions, etc.) have rigorous impact to recognize the stability conditions of dust-acoustic waves. The present study is useful for understanding the mechanism of the formation of dust-acoustic envelope solitons associated with dust-acoustic waves in the laboratory and space environments.     

Magnetoacoustic solitons in pair-ion fullerene plasma

ABSTRACT

The propagation of magnetoacoustic (fast magnetohydrodynamic) waves in pair-ion (PI) fullerene plasma is studied in the linear and nonlinear regimes. The pair-ion (PI) fullerene plasma is theorized as homogeneous, magnetized, warm and collisionless. Employing multi-fluid magnetohydrodynamic model, the dispersion relation is obtained and wave dispersion effects which appear through ion inertial length are discussed. Using reductive perturbation technique (RPT), the Korteweg–de Vries (KdV) equation is derived and its solution for small but finite amplitude magnetoacoustic solitons propagating in the direction perpendicular to the external magnetic field is presented. The compressive magnetoacoustic soliton (i.e. positive potential pulse) propagating with super Alfvénic speed is obtained in magnetized PI fullerene plasma. The variations in the amplitude and width of the magnetoacoustic soliton structures are also illustrated by using numerical values of the plasma parameters such as ions' density, temperature difference between fullerene ions and magnetic field intensity, which have been taken from the PI plasma experiments already published in the literature.     

Nonlinear Structures in an Ion-Beam Plasmas Including Dust Impurities with Nonthermal Nonextensive Electrons

The properties of dust ion acoustic waves are investigated in an unmagnetized multicomponent plasma system consisting of ion beam, charged positive and negative ions, electrons obeying nonthermal-Tsallis distribution and stationary negatively charged dust grains by the conventional Sagdeev pseudopotential method, through which the condition for existence of several nonlinear structures is analyzed theoretically. The dispersion relation for electrostatic waves is derived and analyzed and an expression of the energy integral equation is obtained. It is reported here that our plasma model supports solitions, double layers and supersoliton solutions for certain range of parameters. Finally, the effects of different physical plasma parameters on these nonlinear structures are studied numerically. The present theory should be helpful in understanding the salient features of the electrostatic waves in space and in laboratory plasmas where two distinct groups of ions and non-Maxwellian distributed electrons are present.     

Head-on collision of ion thermal solitary waves in pair-ion plasmas containing charged dust impurities

In the present research paper, the study of the head-on collision between two ion thermal solitary waves is investigated in a two-fluid (i.e., a pair-ion) plasma consisting of positive and negative ions as well as a fraction of stationary (positively/negatively) charged dust impurities, using the extended Poincaré-Lighthill-Kuo method. The effects of the concentration of charged dust impurities and the positive-to-negative ion temperature ratio on the solitary waves collisions are investigated. It is found that the phase shift is significantly affected by the presence of the positive-to-negative ion temperature ratio and positively/negatively charged dust grains.     

Dust ion-acoustic shock waves due to dust charge fluctuation in a superthermal dusty plasma

The nonlinear propagation of dust ion-acoustic (DIA) shock waves is studied in a charge varying dusty plasma with electrons having kappa velocity distribution. We use hot ions with equilibrium streaming speed and a fast superthermal electron charging current derived from orbit limited motion (OLM) theory. It is found that the presence of superthermal electrons does not only significantly modify the basic properties of shock waves, but also causes the existence of shock profile with only positive potential in such plasma with parameter ranges corresponding to Saturn?s rings. It is also shown that the strength and steepness of the shock waves decrease with increase of the size of dust grains and ion temperature.     

Electrostatic waves in a paired fullerene-ion plasma

Three kinds of electrostatic modes are experimentally observed to propagate along magnetic-field lines for the first time in the pair-ion plasma consisting of only positive and negative fullerene ions with an equal mass. It is found that the phase lag between the density fluctuations of positive and negative ions varies from 0 to pi depending on the frequency for ion acoustic wave and is fixed at pi for an ion plasma wave. In addition, a new mode with the phase lag about pi appears in an intermediate-frequency band between the frequency ranges of the acoustic and plasma waves.     

Effects of axial magnetic field and nonextensivity on small amplitude dust acoustic solitary waves in dusty plasma

The nonlinear propagation of small amplitude dust‐acoustic (DA) solitary waves in magnetized dusty plasma consisting of negatively charged mobile dust fluid, and Boltzmann‐distributed electrons and ions with two distinct temperatures following a q‐nonextensive distribution are investigated. In this article, a number of nonlinear equations, namely, the Korteweg–de‐Vries (K‐dV) equations, have been derived by employing the reductive perturbation technique that is valid for a small but finite amplitude limit. The effects of nonextensivity of ions with two distinct temperatures and dust concentration on the amplitude and width of DA solitary waves are investigated theoretically. It is observed that both the nonextensive and low‐temperatures ions significantly modify the basic properties and polarities of DA solitary waves. It is shown that both positive and negative potential DA solitons occur in this case. The implications of these results to some astrophysical environments and space plasmas (e.g., stellar polytropes, peculiar velocity distributions of galaxies, and collisionless thermal plasma), and laboratory dusty plasma systems are briefly mentioned.     

Effect of nonthermal ion distribution and dust temperature on nonlinear dust acoustic solitary waves

The effects of nonthermal ion distribution and finite dust temperature are incorporated in the investigation of nonlinear dust acoustic waves in an unmagnetized dusty plasma. Sagdeev pseudopotential method which takes into account the full nonlinearity of plasma equations, is used here to study solitary wave solutions. Possibility of co-existence of refractive and compressive solitons as a function of Mach number, dust temperature and concentration of nonthermal ions, is considered. For the fixed value of nonthermal ions, it is found that the effect of increase in dust temperature is to reduce the range of co-existence of compressive and refractive solitons. Particular concentration of nonthermal ions results in disappearance of refractive solitons while the decrease in dust temperature, at this concentration restores the lost refractive solitons.     

Large-amplitude dust acoustic solitons in an opposite polarity dusty plasma with generalized polarization force

Linear and nonlinear dust acoustic(DA)waves have been investigated in an opposite polarity dusty plasma comprising negatively and positively charged dust grains,Maxwellian electrons and ions,including the generalized polarization force effect.The properties of linear DA waves have been significantly altered by the dual dust polarity and polarization force.Large amplitude DA solitons have been discussed in the framework of the Sagdeev potential technique.Our results show that both rarefactive and compressive solitons can exist in such a dusty plasma.The basic features of the Sagdeev potential have been examined under the effect of the polarization force parameter R,the ratio of the charge number of the positive dust to that of the negative dust Z,and the Mach number M.The results show that these parameters play a significant role in determining the region of existence of large amplitude DA solitons.     

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.     

Rogue wave triplets in an ion-beam dusty plasma with superthermal electrons and negative ions

A new dust ion-acoustic wave structure called ‘Rogue wave triplets’ is investigated in an unmagnetized plasma consisting of stationary negatively charged dust grains, charged positive and negative ions, and electrons obeying kappa distribution, which is penetrated by an ion beam. The reductive perturbation theory is used to derive the nonlinear Schrödinger equation governing the dynamics as well as the modulation of wave packets. The rogue wave triplets which are composed of three separate Peregrine breathers can be generated in the modulation instability region. It has been suggested that a laboratory experiment be performed to test the theory presented here.     

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.     

Periodic and localized structures in a degenerate Thomas-Fermi plasma

The propagation of electrostatic ion-acoustic cnoidal waves (IACWs) and solitons in a degenerated electron-positron-ion plasma with cold inertial ions and Thomas-Fermi distributed electrons and positrons is investigated. Adopting a reductive perturbation technique (RPT), the Korteweg-de Vries (KdV) equation is obtained and its cnoidal waves (CWs) solution is analyzed. The plasma configuration parameters (namely, the positron concentration and the Fermi temperature ratio of electron-to-positron) are shown to affect remarkably the dynamical characteristics of IACWs and solitons. The relevance of the present work to superdense white dwarfs is pointed out.     

Effect of dust size distribution and dust charge fluctuation on dust ion-acoustic shock waves in a multi-ion dusty plasma

The effects of dust size distribution and dust charge fluctuation of dust grains on the small but finite amplitude nonlinear dust ion-acoustic shock waves, in an unmagnetized multi-ion dusty plasma which contains negative ions, positive ions and electrons, are studied in this paper. A Burgers equation and its stationary solutions are obtained by using the reductive perturbation method. The analytical and numerical results show that the height with polynomial dust size distribution is larger than that of the monosized dusty plasmas with the same dust grains, but the thickness in the case of different dust grains is smaller than that of the monosized dusty plasmas. Furthermore, the moving speed of the shock waves also depend on different dust size distributions.     

Weak dissipation of electrostatic solitary structures in warm collisional pair-ion plasmas with non-Maxwellian electron population

The localized electrostatic structures with dissipation due to ion-neutral collisions in a symmetric warm pair-ion plasma in the presence of non-Maxwellian population of electrons are studied. The analytical model for ion dynamics is based on fluid equations and the evolution equation is derived by using the reductive perturbation scheme in the form of a damped Korteweg-de Vries equation. The parameter regime relevant to space-based observations and laboratory plasmas is considered and time evolution of the propagating ion-acoustic soliton is discussed. The energetic-particles-driven properties of soliton for various spectral indices, dissipation, ion temperature, and density are illustrated with comparison to the thermal mode for Boltzmann distribution of electrons.