Ion‐Acoustic Waves Instability in a Three Components Magneto‐Plasma with Nonthermal Electrons

A theoretical investigation has been made on obliquely propagating ion‐acoustic (IA) solitary structures in a three components magneto‐plasma containing cold inertial ions, Boltzmann distributed positrons, and hot non‐thermal electrons. The Zakharov‐Kuznetsov equation has been derived by the reductive perturbation method, and its solitary wave solution has been analyzed. Multi‐dimensional instability has also studied by the small‐k (long wave‐length plane wave) perturbation expansion technique, which is found to exist in such a plasma. The effects of the external magnetic field, nonthermal electrons, obliqueness and temperature ratio have significantly modified the basic properties of small but finite‐amplitude IA solitary waves, such as amplitude, width, instability criterion and the growth rate. The present investigation contributes to the physics of the nonlinear IA waves in space and laboratory electron‐positron‐ion magneto‐plasmas in which wave damping produces an electron tail. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

Planar and Nonplanar Shock Waves in a Degenerate Quantum Plasma

The nonlinear propagation of modified electron‐acoustic (mEA) shock waves in an unmagnetized, collisionless, relativistic, degenerate quantum plasma (containing non‐relativistic degenerate inertial cold electrons, both nonrelativistic and ultra‐relativistic degenerate hot electron and inertial positron fluids, and positively charged static ions) has been investigated theoretically. The well‐known Burgers type equation has been derived for both planar and nonplanar geometry by employing the reductive perturbation method. The shock wave solution has also been obtained and numerically analyzed. It has been observed that the mEA shock waves are significantly modified due to the effects of degenerate pressure and other plasma parameters arised in this investigation. The properties of planar Burgers shocks are quite different from those of nonplanar Burgers shocks. The basic features and the underlying physics of shock waves, which are relevant to some astrophysical compact objects (viz. non‐rotating white dwarfs, neutron stars, etc.), are briefly discussed. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

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.     

Nonlinear ion‐acoustic cnoidal wave in electron‐positron‐ion plasma with nonextensive electrons

Effects of plasma nonextensivity on the nonlinear cnoidal ion‐acoustic wave in unmagnetized electron‐positron‐ion plasma have been investigated theoretically. Plasma positrons are taken to be Maxwellian, while the nonextensivity distribution function was used to describe the plasma electrons. The known reductive perturbation method was employed to extract the KdV equation from the basic equations of the model. Sagdeev potential, as well as the cnoidal wave solution of the KdV equation, has been discussed in detail. We have shown that the ion‐acoustic periodic (cnoidal) wave is formed only for values of the strength of nonextensivity (q). The q allowable range is shifted by changing the positron concentration (p) and the temperature ratio of electron to positron (σ). For all of the acceptable values of q, the cnoidal ion‐acoustic wave is compressive. Results show that ion‐acoustic wave is strongly influenced by the electron nonextensivity, the positron concentration, and the temperature ratio of electron to positron. In this work, we have investigated the effects of q, p, and σ on the characteristics of the ion‐acoustic periodic (cnoidal) wave, such as the amplitude, wavelength, and frequency.     

The (3+1)‐dimensional dust‐acoustic waves in multi‐components magneto‐plasmas

A three‐dimensional four components magneto‐plasma system consists of super‐thermal κ‐distributed electrons and positrons, Maxwellian ions, and inertial massive negatively charged dust grains is considered to examine the modulational instability (MI) of the dust‐acoustic waves (DAWs), which propagates in such a magneto‐plasma system. The reductive perturbation method, which is valid for small but finite amplitude DAWs, is employed to derive the (3 + 1)‐dimensional non‐linear Schrödinger equation (NLSE). The NLSE leads to the MI of DAWs as well as the formation of dust‐acoustic rogue waves (DARWs) which are formed due to the effects of non‐linearity in the propagation of the DAWs. It is found that the basic features (viz. amplitude and width) of the DAWs and DARWs (which is formed in the unstable region) are significantly modified by the various plasma parameters such as κ‐distributed electrons and positrons, temperatures, and number densities of plasma species, and so on. The application of the results in both space and laboratory magneto‐plasma systems is briefly discussed.     

Planar and non-planar ion acoustic shock waves in electron-positron-ion plasmas

Ion acoustic shock waves (IASW's) are studied in an unmagnetized plasma consisting of electrons, positrons and adiabatically hot positive ions. This is done by deriving the Kortweg-deVries-Burger (KdVB) equation under the small amplitude perturbation expansion method. The dissipation is introduced by taking into account the kinematic viscosity among the plasma constituents. It is found that the strength of ion acoustic shock wave is maximum for spherical, intermediate for cylindrical, and minimum for planar geometry. It is observed that the positron concentration, ratio of ion to electron temperature, and the plasma kinematic viscosity significantly modifies the shock structure. Finally, it is found that the temporal evolution of the non-planar IASW's is quite different by comparison with the planar geometry. The relevance of the present study with regard to the dense astrophysical environments is also pointed out.     

Radially ingoing and outgoing dispersive and dissipative structures in electron‐ion plasmas in the presence of electron trapping

In this article, non‐linear propagation of ingoing and outgoing electrostatic waves on the ion time scale in an unmagnetized, non‐relativistic electron‐ion (ei) plasma in the presence of warm ions, ion kinematic viscosity, and trapped Maxwellian electrons was examined in a non‐planar geometry. In the weak non‐linearity limit, modified soliton and shock equations were derived with the inclusion of electron trapping in cylindrical and spherical geometries. The finite difference method was used to solve all these equations in the non‐planar geometries using the planar versions of these equations as an initial input. The results were compared with their counterparts with quadratic non‐linearity and the main differences were expounded. It was shown that the spatio‐temporal scales over which the shocks form for the non‐planar trapped Burgers equation are much shorter by comparison with the shocks admitted by the non‐planar trapped Korteweg de Vries Burgers equation. It was also found that unlike their non‐linear shock counterparts, the solitary structures admitted by the non‐planar trapped Korteweg de Vries equation exhibit a phase shift.     

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.     

Dust‐ion‐acoustic solitary waves in a magnetized dusty pair‐ion plasma with Cairns‐Gurevich electrons and opposite polarity dust particles

The nonlinear dust‐ion‐acoustic (DIA) solitary structures have been studied in a dusty plasma, including the Cairns‐Gurevich distribution for electrons, both negative and positive ions, and immobile opposite polarity dust grains. The external magnetic field directed along the z‐axis is considered. By using the standard reductive perturbation technique and the hydrodynamics model for the ion fluid, the modified Zakharov–Kuznetsov equation was derived for small but finite amplitude waves and was provided the solitary wave solution for the parameters relevant. Using the appropriate independent variable, we could find the modified Korteweg–de Vries equation. By plotting some figures, we have discussed and emphasized how the different plasma values, such as the trapping parameter, the positive (or negative) dust number density, the non‐thermal electron parameter, and the ion cyclotron frequency, can influence the solitary wave structures. In addition, using the bifurcation theory of planar dynamical systems, we have extracted the centre and saddle points and illustrated the phase portrait of such a system for some particular plasma parameters. Finally, we have graphically investigated the behaviour of the solitary energy wave by changing the plasma values as well as by calculating the instability criterion; we have also discussed the growth rate of the solitary waves. The results could be useful for studying the physical mechanism of nonlinear propagation of DIA solitary waves in laboratory and space plasmas where non‐thermal electrons, pair‐ions, and dust particles can exist.     

Effect of positron density and temperature on the electron acoustic waves in a magnetized dissipative plasma

Zakharov–Kuznetsov–Burgers (ZKB) equation is derived for electron acoustic shock waves in magnetized e–p–i plasma. In the present model, magnetized plasma containing two electron population with kappa distributed positrons has been considered. The propagation characteristics of three dimensional electron acoustic (EA) shock waves have been studied under the influence of magnetic field. Our present plasma model supports the negative potential shocks. Combined action of dissipation (η), superthermality (κ), concentration of positrons (β), temperature ratio of cold electrons to positrons (σ), and magnetic field (ω_c) significantly modify the properties of EA shock waves. The width and amplitude of the shock structures are modified by various physical parameters. It is found that shock wave width decreases with increase in β, η₀, and ω_c whereas it becomes wider for κ and σ. Further, potential of the shock wave decreases as one departs away from superthermal distribution.     

Cylindrical and Spherical Electron-Acoustic Shock Waves in Electron-Positron-Ion Plasmas with Nonextensive Electrons and Positrons

Electron-acoustic shock waves (EASWs) in an unmagnetized four-component plasma (containing hot electrons and positrons following the q-nonextensive distribution, cold mobile viscous electron fluid, and immobile positive ions) are studied in nonplanar (cylindrical and spherical) geometry. With the help of the reductive perturbation method, the modified Burgers equation is derived. Analytically, the effects of nonplanar geometry, nonextensivity, relative number density and temperature ratios, and cold electron kinematic viscosity on the basic properties (viz. amplitude, width, speed, etc.) of EASWs are discussed. It is examined that the EASWs in nonplanar geometry significantly differ from those in planar geometry. The results of this investigation can be helpful in understanding the nonlinear features of EASWs in various astrophysical plasmas.     

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 ion‐acoustic solitons with trapped q‐non‐extensive electrons,dissipative processes,and streaming ions

The characteristics of dust ion‐acoustic waves (DIAWs) that are excited because of streaming ions and hot q‐non‐extensive electrons obeying a vortex‐like distribution are investigated. By exploiting a pseudo‐potential technique, we have derived an energy integral equation. The presence of non‐extensive q‐distributed hot trapped electrons and a streaming ion beam has been shown to influence soliton structure quite significantly. The evolution of the soliton‐like perturbations in complex plasmas, taking into account the dissipation processes, are also investigated, obtained by numerically solving the modified Schamel, equation whose widths are dependant on electron trapping efficiency β. Our illustrations indicate that compressive DIAWs develop in this plasma. As the plasmas in reality have a relative flow, such an analysis can be used to understand the DIA solitary structures observed in the mesospheric noctilucent clouds.     

Dissipative ion acoustic solitary waves in collisional,magneto‐rotating,non‐thermal electron–positron–ion plasma

The linear and non‐linear dynamics of ion acoustic waves are investigated in three‐component magnetized plasma consisting of cold inertial ions and non‐thermal electrons and positrons. The non‐thermal components are modelled by the hybrid distribution, representing the combination of two (kappa and Cairn's) non‐thermal distributions. The relevant processes, including the slow rotation of plasma along the magnetic field axis and collision between ions and neutrals, are taken into consideration. It is shown that the non‐linear dynamics of the considered system are governed by the Zakharov–Kuznetsov equation in modified form. In the general dissipation regime, the effects of the two non‐thermal distributions on the solitary waves are compared. The effects of other plasma parameters, such as collisional and rotational frequency, are also discussed in detail.     

Nonlinear Dynamics in a Nonextensive Complex Plasma with Viscous Electron Fluids

Cylindrical and spherical dust-electron-acoustic(DEA) shock waves and double layers in an unmagnetized,collisionless,complex or dusty plasma system are carried out.The plasma system is assumed to be composed of inertial and viscous cold electron fluids,nonextensive distributed hot electrons,Maxwellian ions,and negatively charged stationary dust grains.The standard reductive perturbation technique is used to derive the nonlinear dynamical equations,that is,the nonplanar Burgers equation and the nonplanar further Burgers equation.They are also numerically analyzed to investigate the basic features of shock waves and double layers(DLs).It is observed that the roles of the viscous cold electron fluids,nonextensivity of hot electrons,and other plasma parameters in this investigation have significantly modified the basic features(such as,polarity,amplitude and width) of the nonplanar DEA shock waves and DLs.It is also observed that the strength of the shock is maximal for the spherical geometry,intermediate for cylindrical geometry,while it is minimal for the planar geometry.The findings of our results obtained from this theoretical investigation may be useful in understanding the nonlinear phenomena associated with the nonplanar DEA waves in both space and laboratory plasmas.     

Shocks and Solitons in Ultradense Degenerate Electron-Positron-Ion Plasmas

The formation and propagation of shocks and solitons are investigated in anunmagnetized, ultradense plasma containing degenerate Fermi gas of electrons and positrons, and classical ion gas by employing Thomas-Fermi model. For this purpose, a deformed Korteweg-de Vries-Berger (dKdVB) equation is derived using the reductive perturbative technique for cold, adiabatic, and isothermal ions. Localized analytical solutions of dKdVB equation in planar geometry are obtained for dispersion as well as dissipation dominant cases. For nonplanar (cylindrical and spherical) geometry, time varying numerical shock wave solution of dKdVB equation is found. Its dispersion dominant case leading to the soliton solution is also discussed. The effect of ion temperature, positron concentration and dissipation is found significant on these nonlinear structures. The relevance of the results to the systems of scientific interest is pointed out.     

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.     

Rogue waves in multi‐pair plasma medium

The non‐linear propagation of ion acoustic (IA) waves, which is governed by the non‐linear Schrödinger equation, in multi‐pair plasmas (MPPs) containing adiabatic positive and negative ion fluids as well as non‐extensive (q‐distributed) electrons and positrons is theoretically investigated. It is observed that the MPP under consideration supports two types of modes, namely fast and slow IA modes, and the modulationally stable and unstable parametric regimes for the fast and slow IA modes are determined by the sign of the ratio of the dispersive coefficient to the non‐linear one. It is also found that the modulationally unstable regime generates highly energetic IA rogue waves (IARWs), and the amplitude as well as the width of the IARWs decreases with increase in the value of q (for both q > 0 and q < 0 limits). These new striking features of the IARWs are found to be applicable in the space (i.e., D‐region [], and F‐region [H⁺, H^?] of the Earth's ionosphere) and laboratory MPPs (i.e., fullerene [C⁺, C^?]).