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.     

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)     

Modified Ion-Acoustic Shock Waves and Double Layers in a Degenerate Electron-Positron-Ion Plasma in Presence of Heavy Negative Ions

A general theory for nonlinear propagation of one dimensional modified ion-acoustic waves in an unmagnetized electron-positron-ion (e-p-i) degenerate plasma is investigated. This plasma system is assumed to contain relativistic electron and positron fluids, non-degenerate viscous positive ions, and negatively charged static heavy ions. The modified Burgers and Gardner equations have been derived by employing the reductive perturbation method and analyzed in order to identify the basic features (polarity, width, speed, etc.) of shock and double layer (DL) structures. It is observed that the basic features of these shock and DL structures obtained from this analysis are significantly different from those obtained from the analysis of standard Gardner or Burgers equations. The implications of these results in space and interstellar compact objects (viz. non-rotating white dwarfs, neutron stars, etc.) are also briefly mentioned.     

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.     

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.     

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.     

Electrostatic Solitary Structures in a Relativistic Degenerate Multispecies Plasma

The nonlinear propagation of cylindrical and spherical modified ion-acoustic (mIA) waves in an unmagnetized, collisionless, relativistic, degenerate multispecies plasma has been investigated theoretically. This plasma system is assumed to contain both relativistic degenerate electron and positron fluids, nonrelativistic degenerate positive and negative ions, and positively 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 positive and negative ions. The positively charged static heavy ions participate only in maintaining the quasi-neutrality condition at equilibrium. The nonplanar K-dV and mK-dV equations are derived by using reductive perturbation technique and numerically analyzed to identify the basic features (speed, amplitude, width, etc.) of mIA solitary structures. The basic characteristics of mIA solitary 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 states of heavy ions. The implications of our results to dense plasmas in astrophysical compact objects (e.g., nonrotating white dwarfs, neutron stars, etc.) are briefly mentioned.     

Nonlinear propagation of dust-acoustic solitary waves in a dusty plasma with arbitrarily charged dust and trapped electrons

A theoretical investigation of dust-acoustic solitary waves in three-component unmagnetized dusty plasma consisting of trapped electrons, Maxwellian ions, and arbitrarily charged cold mobile dust was done. It has been found that, owing to the departure from the Maxwellian electron distribution to a vortex-like one, the dynamics of small but finite amplitude dust-acoustic (DA) waves is governed by a nonlinear equation of modified Korteweg–de Vries (mKdV) type (instead of KdV). The reductive perturbation method was employed to study the basic features (amplitude, width, speed, etc.) of DA solitary waves which are significantly modified by the presence of trapped electrons. The implications of our results in space and laboratory plasmas are briefly discussed.     

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)     

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 Korteweg-de Vries (K-dV) 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.     

Dust ion-acoustic solitary waves in a hot adiabatic magnetized dusty plasma

The basic features of obliquely propagating dust ion-acoustic (DIA) solitary waves in a hot adiabatic magnetized dusty plasma (containing adiabatic inertia-less electrons, adiabatic inertial ions, and negatively charged static dust) have been investigated. The reductive perturbation method has been employed to derive the Korteweg-de Vries (KdV) equation which admits a small amplitude solitary wave solution. The combined effects of plasma particle (electron and ion) adiabaticity, ion-dust collision, and external magnetic field (obliqueness), which are found to significantly modify the basic features of the small but finite-amplitude DIA solitary waves are explicitly examined. The implications of our results in space and laboratory dusty plasmas are briefly discussed.     

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.     

Complex Burgers’ Equation: Evolution of Shock Waves with a Pair of Non-isothermal Ions in an Arbitrarily Charged Dusty Plasma

The evolution characteristics of dust-acoustic shock wave phenomenon in an arbitrarily charged dusty plasma in presence of pair-ion are investigated by deriving modified Complex Burgers’ equation. In this work, the effect of state of both the ions on the shock wave potential is analysed and discussed in detail. It has been observed that the variation of the non-linear coefficient is more consistent with the non-isothermal positive ions moving toward thermal equilibrium than with non-isothermal negative ions. A significant effect on the amplitude of the shock wave potential is observed as the distribution of the non-isothermal positive and negative ions changes from a hump shape through the flat-topped to Boltzmann type. A weighty effect on the height of the shock wave is observed as and when the Mach number of positive and negative ions changes. The shock wave potential shows a greater (lesser) value with negative (positive) ions moving ahead for thermal equilibrium.     

Obliquely propagating ion-acoustic shock waves in a degenerate quantum plasma

A theoretical investigation has been carried out on the propagation of non-linear ion-acoustic shock waves (IASHWs) in a magnetized degenerate quantum plasma system composed of inertial non-relativistic positively charged light and heavy ions, inertialess non-relativistically or ultra-relativistically degenerate electrons and positrons. The reductive perturbation method has been employed to derive the Burgers' equation. It has been observed that under consideration, our plasma model supports only positive potential shock structure. It is also found that the amplitude and steepness of the IASHWs have been significantly modified by the variation of ion kinematic viscosity, oblique angle, number density, and charge state of the plasma species. The results of our present investigation will be helpful for understanding the propagation of IASHWs in white dwarfs and neutron stars.     

Propagation properties of dust-electron-acoustic waves in weakly magnetized dusty nonthermal plasmas

The linear and nonlinear properties of dust-electron acoustic waves (DEAWs) propagating in magnetized, collisionless, dusty plasma system containing inertial cold electrons, Maxwellian hot electrons, nonthermal ions, and arbitrarily (positively or negatively) charged stationary dust are investigated. The reductive perturbation technique is employed to reduce the basic set of fluid equations to the modified Korteweg-de Vries equation or Ostrovsky's equation, which governs the dynamics of small amplitude DEAWs in a weakly magnetized dusty nonthermal plasma. The approximate analytical as well as numerical solutions reveal that the basic characteristics of DEA nonlinear structures are found to be significantly modified by the key plasma configuration parameters. It is found that the leading compressive or rarefactive solitary wave structure separates from a trailing wave packet during a considerable time under the influence of magnetic field-induced Lorentz force.     

Effect of viscosity on dust–ion acoustic shock wave in dusty plasma with negative ions

The properties of dust–ion acoustic (DIA) shock wave in a dusty plasma containing positive and negative ions is investigated. The reductive perturbation method has been used to derive the Korteweg–de Vries–Burgers equation for dust acoustic shock waves in a homogeneous, unmagnetized and collisionless plasma whose constituents are Boltzmann distributed electrons, singly charged positive ions, singly charged negative ions and cold static dust particles. The KdV–Burgers equation is derived and its stationary analytical solution is numerically analyzed where the effect of viscosity on the DIA shock wave propagation is taken into account. It is found that the viscosity in the dusty plasma plays as a key role in dissipation for the propagation of DIA shock.     

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)     

Effects of polarization force and nonthermal ions on dust-acoustic (DA) shock waves in a strongly coupled dusty plasma with positively charged dust

The nonlinear propagation of the dust-acoustic (DA) waves in a strongly coupled dusty plasma containing Maxwellian electrons, nonthermal ions, and positively charged dust is theoritically investigated by a Burgers equation. The effects of the polarization force (which arises due to the interaction between electrons and highly positively charged dust grains) and nonthermal ions are studied. DA shock waves are found to exist with positive potential only. It represents that the strong correlation among the charged dust grains is a source of dissipation, and is responsible for the formation of DA shock waves. The effects of polarization force and nonthermal ions significantly modified the basic features of DA shock waves in strongly coupled dusty plasma.     

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.     

Nonlinear propagation of ion-acoustic waves in a degenerate dense plasma

Nonlinear propagation of ion-acoustic (IA) waves in a degenerate dense plasma (with all the constituents being degenerate, for both the non-relativistic or ultrarelativistic cases) have been investigated by the reductive perturbation method. The linear dispersion relation and Korteweg–de Vries (KdV) equation have been derived, and the numerical solutions of KdV equation have been analysed to identify the basic features of electrostatic solitary structures that may form in such a degenerate dense plasma. The implications of our results in compact astrophysical objects, particularly, in white dwarfs and neutron stars, have been briefly discussed.