Effects of bi-kappa distributed electrons on dust-ion-acoustic shock waves in dusty superthermal plasmas

The basic properties of dust-ion-acoustic （DIA） shock waves in an unmagnetized dusty plasma （containing inertial ions, kappa distributed electrons with two distinct temperatures, and negatively charged immobile dust grains） are investi- gated both numerically and analytically. The hydrodynamic equation for inertial ions has been used to derive the Burgers equation. The effects of superthermal bi-kappa electrons and ion kinematic viscosity, which are found to modify the basic features of DIA shock waves significantly, are briefly discussed.

Nonplanar Shock Excitations in a Four Component Degenerate Quantum Plasma:the Effects of Various Charge States of Heavy Ions

A theoretical study on the nonlinear propagation of nonplanar （cylindrical and spherical） electrostatic modified ion-acoustic （mIA） shock structures has been carried out in an unmagnetized, collisionless four component degenerate plasma system （containing degenerate electron fluids, inertial positively as well as negatively charged light ions, and positively charged static heavy ions）. This investigation is valid for both non-relativistic and ultra-relativistic limits. The modified Burgers （mB） equation has been derived by employing the reductive perturbation method, and used to numerically analyze the basic features of shock structures. It has been found that the effects of degenerate pressure and number density of electron and inertial positively as well as negatively charged light ion fluids, and various charging state of positively charged static heavy ions significantly modify the basic features of mIA shock structures. The implications of our results to dense plasmas in astrophysical compact objects （e.g., non-rotating white dwarfs, neutron stars, etc.） are briefly discussed.

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.

Modulated Dust-Acoustic Wave Packets in an Opposite Polarity Dusty Plasma System

The nonlinear propagation of the dust-acoustic bright and dark envelope solitons in an opposite polarity dusty plasma(OPDP) system(composed of non-extensive q-distributed electrons, iso-thermal ions, and positively as well as negatively charged warm dust) has been theoretically investigated. The reductive perturbation method(which is valid for a small, but finite amplitude limit) is employed to derive the nonlinear Schr¨odinger equation. Two types of modes, namely, fast and slow dust-acoustic(DA) modes, have been observed. The conditions for the modulational instability(MI) and its growth rate in the unstable regime of the DA waves are significantly modified by the effects of non-extensive electrons, dust mass, and temperatures of different plasma species, etc. The implications of the obtained results from our current investigation in space and laboratory OPDP medium are briefly discussed.

Ion-Acoustic Rogue Waves in Multi-ion Plasmas

The basic properties of nonlinear ion-acoustic(IA) waves(IAWs), particularly finite amplitude IA rogue waves(IARWs) in a plasma medium(containing pair ions, iso-thermal positrons, and non-thermal electrons) are theoretically investigated by deriving the nonlinear Schr¨odinger equation(NLSE).The criteria for the modulational instability of IAWs, and the basic features of finite amplitude IARWs are identified.The modulationally stable and unstable regions are determined by the sign of the ratio of the dispersive coefficient to the nonlinear coefficient of NLSE.The latter is analyzed to obtain the region for the existence of the IARWs, which corresponds to the unstable region.The shape of the profile of the rogue waves depends on the non-thermal parameter α and the ratio of electron temperature to positron temperature.It is found that the increase in the value of the non-thermal parameter enhances both the amplitude and width of IARWs, and that the enhancement of electron(positron) temperature reduces(enhances) the amplitude and width of IARWs.It is worth to mention that our present investigation may be useful for understanding the salient features of IARWs in space(viz., upper region of Titan’s atmosphere, cometary comae, and Earth’s ionosphere, etc.)and laboratory(viz., plasma processing reactor and neutral beam sources, etc.) plasmas.

Ion-Acoustic Shock Waves in Nonextensive Multi-Ion Plasmas

The nonlinear propagation of ion-acoustic(IA) shock waves(SHWs) in a nonextensive multi-ion plasma system(consisting of inertial positive light ions as well as negative heavy ions, noninertial nonextensive electrons and positrons) has been studied. The reductive perturbation technique has been employed to derive the Burgers equation.The basic properties(polarity, amplitude, width, etc.) of the IA SHWs are found to be significantly modified by the effects of nonextensivity of electrons and positrons, ion kinematic viscosity, temperature ratio of electrons and positrons, etc.It has been observed that SHWs with positive and negative potential are formed depending on the plasma parameters.The findings of our results obtained from this theoretical investigation may be useful in understanding the characteristics of IA SHWs both in laboratory and space plasmas.

Nonplanar Shock Structures in a Relativistic Degenerate Multi-Species Plasma

A nonlinear propagation of cylindrical and spherical modified ion-acoustic(m IA) 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(m B) equation is derived by using reductive perturbation technique and numerically analyzed to identify the basic features of m IA shock structures. The basic characteristics of m IA 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.

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 （roBE） is derived by using the reductive perturbation method. The basic features of PA SHWs are significantly modified by the cold positron kinematic viscosity （U）, superthermal parameter of electrons （ke）, superthermal parameter of hot positrons （kp）, the ratio of the electron temperature to hot positron temperature （or）, the ratio of the electron number density to cold positron number density （μe）, and the ratio of the hot positron number density to cold positron number density （μph）. This study could be useful to identify the basic properties of nonlinear electrostatic disturbances in dissipative space and laboratory plasmas.

Roles of Superthermal Electrons and Adiabatic Heavy Ions on Heavy-Ion-Acoustic Solitary and Shock Waves in a Multi-Component Plasma

Heavy-ion-acoustic(HIA) waves in an unmagnetized collisionless plasma system comprising superthermal electrons, Boltzmann distributed light ions, and adiabatic positively charged inertial heavy ions have been investigated both numerically and analytically. The well-known reductive perturbation method has been used to derive the Kortewegde Vries(K-d V) and Burgers(BG) equations. The parametric regimes for the existence of both the positive and negative solitary and shock waves have been obtained. The effects of adiabaticity of heavy ions and superthermality of electrons,which are found to notably modify the fundamental features(viz. polarity, amplitude, phase speed, etc.) of HIA solitary and shock waves, are precisely studied. The results of our theoretical investigation can be applicable to understand the characteristics and basic nonlinear structures of HIA waves both in space and laboratory plasma situations.

Instability Analysis of Positron-Acoustic Waves in a Magnetized Multi-Species Plasma

The nonlinear propagation of electrostatic excitations and their multi-dimensional instability in a magnetized, degenerate electron-positron-ion(EPI) plasma system(containing inertial cold positrons, relativistic degenerate electrons and hot positrons, and negatively charged immobile heavy ions) are theoretically investigated. The reductive perturbation method is employed to derive the Zakharov–Kuznetsov equation which admits a localized solitary wave solution for small but finite amplitude limit, and the multi-dimensional instability of the positron acoustic solitary waves(PASWs) is studied by the small-k perturbation expansion method. It is found that the basic characteristics(viz. phase speed, amplitude, width) of the PASWs are significantly affected by the degree of obliqueness, relativistic degeneracy,and plasma particle number densities. The instability criterion and its growth rate, which are depending on the magnetic field and the propagation directions of both the PASWs, and their perturbation modes are discussed. The present analysis can be helpful in understanding the nonlinear phenomenon in dense astrophysical as well as space plasma systems,especially in pulsar environments.

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 elec- trons and positrons following the q-nonextensiv.e 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 exarmined 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.

Solitary Potential in a Space Plasma Containing Dynamical Heavy Ions and Bi-Kappa Distributed Electrons of Two Distinct Temperatures

The heavy ion-acoustic solitary waves(HIASWs) in a magnetized, collisionless, space plasma system(containing dynamical heavy ions and bi-kappa distributed electrons of two distinct temperatures) have been theoretically investigated. The Korteweg-de Vries(K-dV), modified K-dV(MK-dV), and higher-order MK-dV(HMK-dV) equations are derived by employing the reductive perturbation method. The basic features of HIASWs(viz. speed, polarity,amplitude, width, etc.) are found to be significantly modified by the effects of number density and temperature of different plasma species, and external magnetic field(obliqueness). The K-dV and HM-Kd V equations give rise to both compressive and rarefactive solitary structures, whereas the MK-dV equation supports only the compressive solitary structures. The implication of our results in some space and laboratory plasma situations are briefly discussed.