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.     

Cylindrical and spherical electron-acoustic Gardner solitons and double layers in a two-electron-temperature plasma with nonthermal ions

Cylindrical and spherical Gardner solitons (GSs) and double layers (DLs) in a two-electron-temperature plasma system (containing cold electrons, hot electrons obeying a Boltzmann distribution, and hot ions obeying a nonthermal distribution) are studied by employing the reductive perturbation method. The modified Gardner equation describing the nonlinear propagation of the electron-acoustic (EA) waves is derived, and its nonplanar GS and DL solutions are numerically analyzed. The parametric regimes for the existence of GSs, which are associated with both positive and negative potential, and DLs which are associated with positive potential, are obtained. The basic features of nonplanar EA GSs, and DLs, which are found to be different from planar ones, are also identified. The implications of our results in space and laboratory plasmas are briefly discussed.     

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)     

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.     

Parametric study of cylindrical and spherical dust ion acoustic shock waves with two temperature electrons in dusty plasma relevant to Saturn's E ring

We have performed numerical analysis of the one-dimensional dynamics of the cylindrical/spherical dust ion acoustic shock waves in unmagnetized dusty plasma consisting of positive ions, immobile dust particles, and nonextensive distributed cold and hot electrons. A multiple-scale expansion method is used to derive Burgers Equation (BE) and modified Burgers equation (MBE) by including higher order nonlinearity. The basic characteristics of the shock waves have been analysed numerically and graphically for different physical parameters relevant to Saturn' E ring through 2D figures. The parametric dependence of dust ion acoustic shock waves on some plasma parameters nonextensive index, density, and temperature of cold and hot electrons, concentration of dust particles, thermal effects and kinematic viscosity of ions is explored. Furthermore, it is found that the nonplanar geometry effects have an important impact on the establishment of shock waves. The amplitude of the wave decreases faster as one departs away from the axis of the cylinder or centre of the sphere. Such decaying behaviour continues as time progresses. It is also found that an increasing dust concentration decreases the amplitude of the dust ion acoustic shock waves.     

Time-Dependent Cylindrical and Spherical Solitary Structures and Double Layers of Dust Ion-Acoustic Waves in Ultra-Relativistic Dense Plasma

Cylindrical and spherical (nonplanar) solitary waves (SWs) and double layers (DLs) in a multi-ion plasma system (containing inertial positively as well as negatively charged ions, non-inertial degenerate electrons, and negatively charged static dust) are studied by employing the standard reductive perturbation method. The modified Gardner (MG) equation describing the nonlinear propagation of the dust ion-acoustic (DIA) waves is derived, and its nonplanar SWs and DLs solutions are numerically analyzed. The parametric regimes for the existence of SWs, which are associated with both positive and negative potential, and DLs which are associated with negative potential, are obtained. The basic features of nonplanar DIA SWs, and DLs, which are found to be different from planar ones, are also identified.     

Nonplanar double layers in plasmas with opposite polarity dust

Nonplanar (cylindrical and spherical) double layers (DLs) in a four-component dusty plasma (composed of inertial positively and negatively charged dust, Boltzmann electrons and ions) are studied by employing the reductive perturbation method. The modified Gardner equation describing the nonlinear propagation of the dust-acoustic (DA) waves is derived, and its nonplanar double layer solutions are numerically analyzed. The parametric regimes for the existence of the DLs, which are found to be associated with positive potential only, are obtained. The basic features of nonplanar DA DLs, which are found to be different from planar ones, are also identified. The implications of our results to different space and laboratory dusty plasma situations, where opposite polarity dust are observed, are discussed.     

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.     

Theoretical analysis of planar and non‐planar electron ‐ acoustic shock waves in electron‐positron‐ion plasma

The propagation properties of planar and non‐planar electron acoustic shock waves composed of stationary ions, cold electrons, and q‐non‐extensive hot electrons and positrons are studied in unmagnetized electron‐positron‐ion plasma. In this model, the Korteweg‐de Vries Burgers equation is obtained in the planar and non‐planar coordinates. We have investigated the combined action of the dissipation, non‐extensivity, density ratio of hot to cold electrons, concentration of positrons, and temperature difference of cold electrons, hot electrons, and positrons. It was found that the amplitude of shock wave in e‐p‐i plasma increases when the positron concentration and temperature increase. The same effect is observed in the case of kinematic viscosity η. Furthermore, it is noticed that spherical wave moves faster in comparison to the shock waves in cylindrical geometry. This difference arises due to the presence of the geometry term m/2τ. It should be noted that the contribution of the geometry factor comes through the continuity equation. Results of our work may be helpful to illustrate the different properties of shock wave features in different astrophysical and space environments like supernova, polar regions, and in the vicinity of black holes.     

Nonplanar Shocks and Solitons in a Strongly Coupled Adiabatic Plasma: the Roles of Heavy Ion Dynamics and Nonextensitivity

An investigation has been made on heavy ion‐acoustic (HIA) nonplanar shocks and solitons in an unmagnetized, collisionless, strongly coupled plasma whose constituents are strongly correlated adiabatic inertial heavy ions, weakly correlated nonextensive distributed electrons and Maxwellian light ions. By using appropriate nonlinear equations for our strongly coupled plasma system and the well‐known reductive perturbation technique, a modified Burgers (mB) equation and a modified Korteweg‐de Vries (mK‐dV) equation have been derived. They are also numerically solved in order to investigate the basic features (viz. polarity, amplitude, width, etc.) of cylindrical and spherical shock/solitary waves in such a strongly coupled plasma system. The roles of heavy ion dynamics, nonextensivity of electrons, and other plasma parameters arised in this investigation have significantly modified the basic features of the cylindrical and spherical HIA solitary and shock waves. The findings of our results obtained from this theoretical investigation may be useful in understanding the nonlinear phenomena associated with the cylindrical and spherical HIA waves both in space and laboratory plasmas. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Spherical Kadomtsev-Petviashvili Solitons in a Suprathermal Complex Plasma

The nonlinear aspects of nonplanar dust acoustic (DA) solitary waves are investigated in an unmagnetized complex plasma comprising of cold dust grains,kappa-distributed ions as well as electrons.The nonplanar DA solitons are studied based on the reductive perturbation technique.It is shown that the evolution of DA solitons is governed by a spherical Kadomtsev-Petviashvili (sKP) equation and then the impact of suprathermality on the spatial structure as well as the nature of DA soliton is studied.It seems that the properties of DA solitons in nonplanar geometry are quite different from that of the planar solitons.     

Spherical Kadomtsev-Petviashvili Solitons in a Suprathermal Complex Plasma

The nonlinear aspects of nonplanar dust acoustic (DA) solitary waves are investigated in an unmagnetized complex plasma comprising of cold dust grains, kappa-distributed ions as well as electrons. The nonplanar DA solitons are studied based on the reductive perturbation technique. It is shown that the evolution of DA solitons is governed by a spherical Kadomtsev-Petviashvili (sKP) equation and then the impact of suprathermality on the spatial structure as well as the nature of DA soliton is studied. It seems that the properties of DA solitons in nonplanar geometry are quite different from that of the planar solitons.     

Nonplanar Electron - Acoustic Shock Waves with Superthermal Hot Electrons

Nonplanar electron-acoustic shock waves having superthermal hot electrons are investigated with two temperature electrons model in unmagnetized plasma. Using reductive perturbation method, Korteweg-de Vries-Burgers (KdVB) equation is obtained in the cylindrical/spherical coordinates. Dissipation effect is introduced in the model by means of kinematic viscosity term. On the basis of the solutions of KdVB equation, variation of shock waves features (amplitude, velocity and width) with different plasma parameters are analysed. KdV-Burgers equation always leads to monotonic solitons and no oscillatory peak may appear. The combined effect of particle density (α), superthermal parameter (κ), electron temperature ratio (??) and kinetic viscosity (η₀) is numerically studied, and it is observed that these parameters significantly change the properties of the shock waves in nonplanar geometry especially in spherical coordinates. Results could be helpful to analyse the soliton features in laboratory as well as in the space environments.     

Planar and nonplanar ion-acoustic envelope solitary waves in a very dense electron-positron-ion plasma

Ion-acoustic envelope solitary waves in a very dense plasma comprised of the electrons, positrons and ions are investigated. For this purpose, the quantum hydrodynamic model and the Poisson equation are used. A modified nonlinear Schrödinger equation is derived by employing the reductive perturbation method. The effects of the quantum correction and of the positron density on the propagation and stability of the envelope solitary waves are examined. The nonplanar (cylindrical/spherical) geometry gives rise to an instability period. The latter cannot exist for planar case and it affected by the quantum parameters, as well as the positron density. The present investigation is relevant to white dwarfs.     

Propagation of Electron Acoustic Soliton,Periodic and Shock Waves in Dissipative Plasma with a q-Nonextensive Electron Velocity Distribution

The nonlinear properties of small amplitude electron-acoustic(EA) solitary and shock waves in a homogeneous system of unmagnetized collisionless plasma with nonextensive distribution for hot electrons have been investigated.A reductive perturbation method used to obtain the Kadomstev-Petviashvili-Burgers equation.Bifurcation analysis has been discussed for non-dissipative system in the absence of Burgers term and reveals different classes of the traveling wave solutions.The obtained solutions are related to periodic and soliton waves and their behavior are shown graphically.In the presence of the Burgers term,the EXP-function method is used to solve the Kadomstev-Petviashvih-Burgers equation and the obtained solution is related to shock wave.The obtained results may be helpful in better conception of waves propagation in various space plasma environments as well as in inertial confinement fusion laboratory plasmas.     

Propagation of Electron Acoustic Soliton,Periodic and Shock Waves in Dissipative Plasma with a q-Nonextensive Electron Velocity Distribution

The nonlinear properties of small amplitude electron-acoustic (EA) solitary and shock waves in a homogeneous system of unmagnetized collisionless plasma with nonextensive distribution for hot electrons have been investigated. A reductive perturbation method used to obtain the Kadomstev-Petviashvili-Burgers equation. Bifurcation analysis has been discussed for non-dissipative system in the absence of Burgers term and reveals different classes of the traveling wave solutions. The obtained solutions are related to periodic and soliton waves and their behavior are shown graphically. In the presence of the Burgers term, the EXP-function method is used to solve the Kadomstev-Petviashvili-Burgers equation and the obtained solution is related to shock wave. The obtained results may be helpful in better conception of waves propagation in various space plasma environments as well as in inertial confinement fusion 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.     

Nonplanar Shock Structures in a Relativistic Degenerate Multi-Species Plasma

A nonlinear propagation of cylindrical and spherical modified ion-acoustic (mIA) waves in an unmagnetized, collisionless, relativistic, degenerate multi-species plasma has been investigated theoretically. This plasma system is assumed to contain non-relativistic degenerate light ions, both non-relativistic and ultra-relativistic degenerate electron and positron fluids, and arbitrarily charged static heavy ions. The restoring force is provided by the degenerate pressures of the electrons and positrons, whereas the inertia is provided by the mass of ions. The arbitrarily charged static heavy ions participate only in maintaining the quasi-neutrality condition at equilibrium. The modified Burgers (mB) equation is derived by using reductive perturbation technique and numerically analyzed to identify the basic features of mIA shock structures. The basic characteristics of mIA shock 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 ions. The implications of our results to dense plasmas in astrophysical compact objects (e.g., non-rotating white dwarfs, neutron stars, etc.) are briefly discussed.     

Ion-acoustic shock waves in multi-electron temperature collisional plasma

The nonlinear propagation of ion-acoustic waves in a collision-dominated double electron temperature plasma is considered. Accounting for the ion viscosity and the ion heat conductivity, it is shown by means of two-warm fluid equations that the nonlinear evolution of the ion-acoustic waves is governed by the Korteweg—de Vries—Burgers equation. Stationary shock solution of the KdV—Burgers equation is presented.