Multi-dimensional instability of electrostatic solitary waves in a warm multi-ion dust plasma

Study of dust ion acoustic waves in a magnetized dusty plasmas composed of negatively or positively charged static dust, positive and negative ions, as well as kappa distribution electrons is presented. The Zakharov–Kuznetsov (ZK) equation is derived via reductive perturbation technique. The solitary wave solution of ZK equation is given and the multi-dimensional instability of these solitary waves is investigated via small k perturbation method. The instability criterion and growth rate relying on obliqueness, superthermality, positive ion thermal pressure, relative ion number density, magnetic field strength, and direction cosines are discussed for five cases. The results are beneficial to understand different nonlinear characteristics of unstable electrostatic disturbances in laboratory and space plasmas.     

New interior solution describing relativistic fluid sphere

Nonlinear low-frequency electrostatic waves in a magnetized, three-component plasma consisting of hot electrons, hot positrons and warm ions have been investigated. The electrons and positrons are assumed to have Boltzmann density distributions while the motion of the ions are governed by fluid equations. The system is closed with the Poisson equation. This set of equations is numerically solved for the electric field. The effects of the driving electric field, ion temperature, positron density, ion drift, Mach number and propagation angle are investigated. It is shown that depending on the driving electric field, ion temperature, positron density, ion drift, Mach number and propagation angle, the numerical solutions exhibit waveforms that are sinusoidal, sawtooth and spiky. The introduction of the Poisson equation increased the Mach number required to generate the waveforms but the driving electric field E ₀ was reduced. The results are compared with satellite observations.     

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)     

On the linear and nonlinear characteristics of electrostatic solitary waves propagating in magnetized electron-positron-ion plasmas

Both linear and nonlinear propagation of electrostatic solitary waves (ESWs) in magnetized electron-positron-ion (e-p-i) plasmas are analyzed. The electrons and positrons are assumed to be dynamic, whereas positively charged ions are considered stationary. Using the reductive perturbation method, a Zakharov-Kuznetsov (ZK) equation is derived and exact soliton solutions are presented. It is found that both compressive and rarefactive ESWs can propagate. The conditions of transitions from compressive to rarefactive ESWs are specified. The nature of these electrostatic solitary waves structures which depends on the magnetic field, the obliqueness, the ion-to-electron number density ratio, and the positron-to-electron temperature ratio, are discussed.     

Nonplanar ion-acoustic shocks in electron–positron–ion plasmas: Effect of superthermal electrons

Ion-acoustic shock waves (IASWs) in a homogeneous unmagnetized plasma, comprising superthermal electrons, positrons, and singly charged adiabatically hot positive ions are investigated via two-dimensional nonplanar Kadomstev–Petviashvili–Burgers (KPB) equation. It is found that the profiles of the nonlinear shock structures depend on the superthermality of electrons. The influence of other plasma parameters such as, ion kinematic viscosity and ion temperature, is discussed in the presence of superthermal electrons in nonplanar geometry. It is also seen that the IASWs propagating in cylindrical/spherical geometry with transverse perturbation will be deformed as time goes on.     

Ion‐ and positron‐acoustic solitons in magnetized dusty plasma with q‐non‐extensive electron and positron velocity distribution

In this study, the properties of ion‐ and positron‐acoustic solitons are investigated in a magnetized multi‐component plasma system consisting of warm fluid ions, warm fluid positrons, q‐non‐extensive distributed positrons, q‐non‐extensive distributed electrons, and immobile dust particles. To drive the Korteweg–de Vries (KdV) equation, the reductive perturbation method is used. The effects of the ratio of the density of positrons to ions, the temperature of the positrons, and ions to electrons, the non‐extensivity parameters q_e and q_p , and the angle of the propagation of the wave with the magnetic field on the potential of ion‐ and positron‐acoustic solitons are also studied. The present investigation is applicable to solitons in fusion plasmas in the edge of tokamak.     

Dynamical behaviour of non-linear quantum ion acoustic wave in weakly magnetized electron–positron–ion plasma

In order to investigate the propagation characteristics of linear and non-linear ion acoustic waves (IAWs) in electron–positron–ion quantum plasma in the presence of external weak magnetic field, we have used a quantum hydrodynamic model, and degenerate statistics for the electrons and positrons are taken into account. It is found that the linear dispersion relation of the IAW was modified by the externally applied magnetic field. By using the reductive perturbation technique, a gyration-modified Korteweg-de Vries equation is derived for finite amplitude non-linear IAWs. Time-dependent numerical simulation shows the formation of an oscillating tail in front of the ion acoustic solitons in the presence of a weak magnetic field. It is also seen that the amplitude and width of solitons and oscillating tails are affected by the relevant plasma parameters such as quantum diffraction, positron concentration, and magnetic field. We have performed our analysis by extending it to account for approximate soliton solution by asymptotic perturbation technique and non-linear analysis via a dynamical system approach. The analytical results show the distortion of the shape of the localized soliton with time, and the non-linear analysis confirms the generation of oscillating tails.     

Multidimensional Instability of Dust‐Acoustic Solitary Waves in a Magnetized Hot Dusty Plasma with Superthermal Electrons and Ions

Multidimensional instability of dust‐acoustic solitary wave (DASW) in magnetized dusty plasma with superthermal electrons and ions and micron size hot dust particles is investigated. The Zakharov‐Kuznetsov (ZK) equation, describing the small but finite amplitude DASW, was derived using the reductive perturbation method and its solitary answers was introduced. Effects of electrons and ions superthermality as well as the external magnetic field on the nature of DASW are discussed in detail. Dispersion relation, threshold condition, and growth rate of multidimensional instability of DASW were derived using small‐k (long wavelength plane wave) perturbation expansion method. We found that the direction and strength of external magnetic field extremely affect the growth rate and instability criterion. Results show that growth rate of instability decreases with increasing the number of superthermal electrons and increases with increasing the number of superthermal ions. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonlinear Propagation of Positron-Acoustic Periodic Travelling Waves in a Magnetoplasma with Superthermal Electrons and Positrons

The nonlinear propagation of positron acoustic periodic(PAP) travelling waves in a magnetoplasma composed of dynamic cold positrons, superthermal kappa distributed hot positrons and electrons, and stationary positive ions is examined. The reductive perturbation technique is employed to derive a nonlinear Zakharov-Kuznetsov equation that governs the essential features of nonlinear PAP travelling waves. Moreover, the bifurcation theory is used to investigate the propagation of nonlinear PAP periodic travelling wave solutions. It is found that kappa distributed hot positrons and electrons provide only the possibility of existence of nonlinear compressive PAP travelling waves. It is observed that the superthermality of hot positrons, the concentrations of superthermal electrons and positrons, the positron cyclotron frequency, the direction cosines of wave vector k along the z-axis,and the concentration of ions play pivotal roles in the nonlinear propagation of PAP travelling waves. The present investigation may be used to understand the formation of PAP structures in the space and laboratory plasmas with superthermal hot positrons and electrons.     

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.     

Dissipative ion‐acoustic waves in collisional electron‐positron‐ion plasmas with Kappa distribution

In this work, linear and non‐linear structures of ion‐acoustic waves (IAWs) are investigated in a collisional plasma consisting of warm ions, superthermal electrons, and positrons. A dissipative effect is assumed due to ion‐neutral collisions. The linear properties of IAWs are investigated. It is shown that the dynamics of the IAWs is governed by the damped Korteweg‐de Vries (K‐dV) equation. It is seen that the ion‐neutral collisions modify the basic features of ion‐acoustic solitary waves significantly. Also, the effect of the plasma parameters on the dissipative IAWs is discussed in detail.     

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.     

Dust-ion-acoustic solitary waves in magnetized plasmas with positive and negative ions: The role of electrons superthermality

The formation of dust-ion-acoustic solitary waves (DIASWs), and their basic properties in a magnetized dusty plasma system containing inertial, hot positively and negatively charged ion fluids, κ-distributed superthermal electrons, and negatively charged stationary dust species are investigated theoretically. An ambient magnetic field is assumed along z-direction, and the wave propagation is considered obliquely to the direction of that ambient magnetic field. Two types of modes, the fast and the slow modes, are shown to exist in the linear regime. The reductive perturbation method (which is valid for small but finite amplitude DIASWs) as well as pseudo-potential approach (which is valid for arbitrary amplitude DIASWs) are employed to identify the basic properties of the DIASWs. The effects of key plasma composition parameters, namely the superthermality effect of electrons, the temperature of positive and negative ions, the number density of positive and negative ions, on the dynamics of small amplitude as well as on large amplitude DIASWs, are investigated. The influence of the obliquity parameter and the magnetic field on the propagation characteristics of DIASWs are also examined.     

Ion acoustic solitary waves in magnetized electron–positron–ion plasmas with Tsallis distributed electrons

The propagation of ion acoustic (IA) solitary waves is investigated in a magnetized electron-positron-ion (EPI) plasma with Tsalli distributed electrons and Maxwellian positrons. A non-linear Korteweg–de Vries (KdV)-type equation is derived for the potential by using the reductive perturbation method (RPM), and its solitary wave solution is analysed. For a given set of plasma parameters, the present model supports only compressive IA solitary structures. It is found that the variation of various relevant plasma parameters, like the nonextensive parameter q, temperature ratio σ , direction cosine l_z , the positron concentration γ and the magnetic field strength Ω significantly alter the characteristic properties of IA solitary waves.     

Electrostatic Nonplanar Positron-Acoustic Shock Waves in Superthermal Electron-Positron-Ion Plasmas

The basic properties of the nonlinear propagation of the nonplanar(cylindrical and spherical) positronacoustic(PA) shock waves(SHWs) in an unmagnetized electron-positron-ion(e-p-i) plasma containing immobile positive ions,mobile cold positrons,and superthermal(kappa distributed) hot positrons and electrons are investigated both analytically and numerically.The modified Burgers equation(mBE) is derived by using the reductive perturbation method.The basic features of PA SHWs are significantly modified by the cold positron kinematic viscosity(η),superthermal parameter of electrons(κ_e),superthermal parameter of hot positrons(κ_p),the ratio of the electron temperature to hot positron temperature(σ),the ratio of the electron number density to cold positron number density(μ_e),and the ratio of the hot positron number density to cold positron number density(μ_(ph)).This study could be useful to identify the basic properties of nonlinear electrostatic disturbances in dissipative space and laboratory plasmas.     

Obliquely propagating quantum solitary waves in quantum‐magnetized plasma with ultra‐relativistic degenerate electrons and positrons

The oblique propagation of the quantum electrostatic solitary waves in magnetized relativistic quantum plasma is investigated using the quantum hydrodynamic equations. The plasma consists of dynamic relativistic degenerate electrons and positrons and a weakly relativistic ion beam. The Zakharov‐Kuznetsov equation is derived using the standard reductive perturbation technique that admits an obliquely propagating soliton solution. It is found that two types of quantum acoustic modes, that is, a slow acoustic mode and fast acoustic mode, could be propagated in our plasma model. The parameter that determines the nature of soliton, that is, compressive or rarefactive soliton, for slow mode is investigated. Our numerical results show that for the slow mode, the determining parameter is ion beam velocity in the case of relativistic degenerate electrons. We also have examined the effects of plasma parameters (like the beam velocity, the density ratio of positron to electron, the relativistic factor, and the propagation angle) on the characteristics of solitary waves.     

Two‐dimensional magnetosonic shock wave propagation in dense electron–positron–ion plasmas

Two‐dimensional (2D) magnetosonic wave propagation in magnetized quantum dissipative plasmas is studied. The plasma system is comprised of inertial ions, inertia‐less electrons, and positrons. The multi‐fluid quantum hydrodynamic model is used, in which quantum statistical and quantum tunnelling effects of electrons and positrons are included. Reductive perturbation analysis is performed to derive the Zabolotskaya–Khokhlov equation for the 2D propagation of a magnetosonic shock wave in a magnetized qauntum plasma. The effects of varying the different plasma parameters such as positron density and magnetic field intensity on the propagation characteristics of magnetosonic shock waves are discussed with non‐relativistic degenerate plasma parameters in astrophysical plasma situations.     

Dust ion‐acoustic solitons collision in weakly relativistic plasmas with superthermality‐distributed electrons and positrons: Higher‐order phase shifts

The higher‐order (H‐O) phase shift of dust ion‐acoustic solitons (DIASs) in a weakly relativistic plasma is examined considering the influence of both superthermality‐distributed electrons and positrons. Employing the extended Poincaré–Lighthill–Kuo method (EPLKM), the Korteweg–de Vries equations (KdVEs) and the deviation in trajectories of DIASs (i.e., phase shifts) are obtained after the collision. For obtaining H‐O phase shifts of DIASs, the fifth‐order dispersion terms are added into KdVEs. The effects of the relativistic factor for a weakly relativistic regime and the superthermality of both electrons and positrons on the H‐O phase shifts are discussed. Numerical analysis gives rise to important highlights on the excitation and the collision of DIASs in astrophysical situations such as a pulsar magnetosphere.     

Slow electron acoustic double layer (SEADL) structures in bi-ion plasma with trapped electrons

The properties of ion acoustic double layer (IADL) structures in bi-ion plasma with electron trapping are investigated by using the quasi-potential analysis. The κ-distributed trapped electrons number density expression is truncated to some finite order of the electrostatic potential. By utilizing the reductive perturbation method, a modified Schamel equation which describes the evolution of the slow electron acoustic double layer (SEADL) with the modified speed due to the presence of bi-ion species is investigated. The Sagdeev-like potential has been derived which accounts for the effect of the electron trapping and superthermality in a bi-ion plasma. It is found that the superthermality index, the trapping efficiency of electrons, and ion to electron temperature ratio are the inhibiting parameters for the amplitude of the slow electron acoustic double layers (SEADLs). However, the enhanced population of the cold ions is found to play a supportive role for the low frequency DLs in bi-ion plasmas. The illustrations have been presented with the help of the bi-ion plasma parameters in the Earth's ionosphere F-region.     

Heavy ion–acoustic rogue waves in magnetized electron–positron multi-ion plasmas

Non-linear heavy ion-acoustic waves (HIAWs) are studied in a homogeneous magnetized four-component multi-ion plasma composed of inertial heavy negative ions, light positive ions, and inertia-less non-extensive electrons and positrons. The non-linear Schrödinger equation is derived in this model using the perturbation method. The criteria for modulational instability of HIAWs and the basic features of finite-amplitude heavy ion acoustic rogue waves (HIARWs) are investigated. The presence of the magnetic field was found to reduce the amplitude of HIARWs and enhances the stability. It is interesting to note that increasing positive ion mass causes decreases in the amplitude and width of rogue waves, which is opposite behaviour to that demonstrated in the previous study of these waves in an unmagnetized plasma. Furthermore, it is also shown that striking parameters, such as the non-extensive parameter, the positron number density, the electron number density, the electron temperature, and the magnetic field parameter, play an undeniable role on the stability of waves packets. The findings of the present investigation may be of wide relevance to some plasma environments, such as active galactic nuclei, pulsar magnetospheres, and other magnetic confinement systems.