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.     

Effect of Bohm quantum potential in the propagation of ion–acoustic waves in degenerate plasmas

A theoretical investigation has been carried out on the propagation of the ion–acoustic(IA) waves in a relativistic degenerate plasma containing relativistic degenerate electron and positron fluids in the presence of inertial non-relativistic light ion fluid. The Korteweg-de Vries(K-dV), modified K-dV(m K-dV), and mixed m K-dV(mm K-dV) equations are derived by adopting the reductive perturbation method. In order to analyze the basic features(phase speed, amplitude, width,etc.) of the IA solitary waves(SWs), the SWs solutions of the K-dV, m K-dV, and mm K-d V are numerically analyzed. It is found that the degenerate pressure, inclusion of the new phenomena like the Fermi temperatures and quantum mechanical effects(arising due to the quantum diffraction) of both electrons and positrons, number densities, etc., of the plasma species remarkably change the basic characteristics of the IA SWs which are found to be formed either with positive or negative potential. The implication of our results in explaining different nonlinear phenomena in astrophysical compact objects, e.g.,white dwarfs, neutron stars, etc., and laboratory plasmas like intense laser–solid matter interaction experiments, etc., are mentioned.     

Ion waves driven by shear flow in a relativistic degenerate astrophysical plasma

We investigate the existence and propagation of low-frequency (in comparison to ion cyclotron frequency) electrostatic ion waves in highly dense inhomogeneous astrophysical magnetoplasma comprising relativistic degenerate electrons and non-degenerate ions. The dispersion equation is obtained by Fourier analysis under mean-field quantum hydrodynamics approximation for various limits of the ratio of rest mass energy to Fermi energy of electrons, relevant to ultra-relativistic, weakly-relativistic and non-relativistic regimes. It is found that the system admits an oscillatory instability under certain condition in the presence of velocity shear parallel to ambient magnetic field. The dispersive role of plasma density and magnetic field is also discussed parametrically in the scenario of dense and degenerate astrophysical plasmas.     

Modified dispersion properties of lower hybrid wave with exchange correlation potential in ultra-relativistic degenerate plasma

In this letter, the propagation characteristics of lower hybrid waves are investigated in electron–ion degenerate plasma with exchange effect considering non-relativistic, relativistic and ultra-relativistic regimes. The combined effect of Bohm force and exchange correlation potential are found to alter the dispersion properties of lower hybrid waves. The analytical and numerical results clearly show the influence of relativistic velocities of electrons, kinetic pressure of ions, Bohm force and exchange correlation potential on the frequency of the lower hybrid wave. The present work find its relevance for the dense astrophysical environments like white dwarfs and for laboratory fusion plasma experiments.     

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.     

Multi-dimensional instability of electrostatic solitary waves in ultra-relativistic degenerate electron-positron-ion plasmas

The basic features and multi-dimensional instability of electrostatic (EA) solitary waves propagating in an ultra-relativistic degenerate dense magnetized plasma (containing inertia-less electrons, inertia-less positrons, and inertial ions) have been theoretically investigated by reductive perturbation method and small-k perturbation expansion technique. The Zakharov-Kuznetsov (ZK) equation has been derived, and its numerical solutions for some special cases have been analyzed to identify the basic features (viz. amplitude, width, instability, etc.) of these electrostatic solitary structures. The implications of our results in some compact astrophysical objects, particularly white dwarfs and neutron stars, are briefly discussed.     

Interactions of ion acoustic multi-soliton and rogue wave with Bohm quantum potential in degenerate plasma

This work investigates the interactions among solitons and their consequences in the production of rogue waves in an unmagnetized plasmas composing non-relativistic as well as relativistic degenerate electrons and positrons, and inertial non-relativistic helium ions. The extended Poincare′–Lighthill–Kuo(PLK) method is employed to derive the two-sided Korteweg–de Vries(Kd V) equations with their corresponding phase shifts. The nonlinear Schr o¨dinger equation(NLSE) is obtained from the modified Kd V(m Kd V) equation, which allows one to study the properties of the rogue waves. It is found that the Fermi temperature and quantum mechanical effects become pronounced due to the quantum diffraction of electrons and positrons in the plasmas. The densities and temperatures of the helium ions, degenerate electrons and positrons, and quantum parameters strongly modify the electrostatic ion acoustic resonances and their corresponding phase shifts due to the interactions among solitons and produce rogue waves in the plasma.     

Cylindrical and Spherical Ion-Acoustic Shock Waves in a Relativistic Degenerate Multi-Ion Plasma

A rigorous theoretical investigation has been made to study the existence and basic features of the ion-acoustic (IA) shock structures in an unmagnetized, collisionless multi-ion plasma system (containing degenerate electron fluids, inertial positively as well as negatively charged ions, and arbitrarily charged static heavy ions). This investigation is valid for both non-relativistic and ultra-relativistic limits. The reductive perturbation technique has been employed to derive the modified Burgers equation. The solution of this equation has been numerically examined to study the basic properties of shock structures. The basic features (speed, amplitude, width, etc.) of these electrostatic shock structures have been briefly discussed. The basic properties of the IA shock waves are found to be significantly modified by the effects of arbitrarily charged static heavy ions and the plasma particle number densities. The implications of our results in space and interstellar compact objects like white dwarfs, neutron stars, black holes, and so on have been briefly discussed.     

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.     

Two-tone ion-acoustic waves in degenerate quantum plasma

Ion-acoustic waves (IAWs) in a quantum electron-ion plasma with degenerate components are theoretically investigated using a system of quantum equations of gas dynamics that allow for the quantum-size character of the object (Bohm’s quantum force is included in the equation of motion) and the Pauli exclusion principle (equations of state for degenerate Fermi gases of electrons and ions are used). Linear analysis and numerical solution of equations yielded an identical qualitative result: periodic IAWs in a quantum electron-ion plasma are always a superposition of two waves with equal phase velocities but different wavelengths. The high-frequency component of the IAW is identified with free quantum oscillations of ions. A solution in the form of an ion-sound soliton with free quantum oscillations of ions superposed on its profile is also found.     

Overtaking collisions of oblique isothermal ion-acoustic multisolitons in ultra-relativistic degenerate dense magnetoplasmas

Overtaking collisions of oblique isothermal ion-acoustic multisolitons are studied in an ultra-relativistic degenerate dense magnetoplasma, containing non-degenerate inertial warm ions and ultra-relativistic degenerate inertialess electrons and positrons. A non-linear Korteweg-de Vries (KdV) equation describing oblique isothermal ion-acoustic solitons (OIIASs) in such a plasma model is derived. By applying Hirota's bilinear method (HBM), the overtaking collisions of oblique isothermal ion-acoustic multisoliton solutions are investigated. An in-depth discussion shows that the amplitude, the width, and the phase shift of isothermal ion-acoustic multisolitons increase as the obliqueness and the chemical potential of electrons increase. The deviation of the trajectories decreases with increasing concentration of fermions and the ion cyclotron frequency. The present finding of this study is applicable in compact objects, such as white dwarfs and neutron stars, having degenerate ultra-relativistic dense electrons and positrons.     

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.     

Landau damping of ion-acoustic waves with simultaneous effects of non-extensivity and non-thermality in the presence of hybrid Cairns-Tsallis distributed electrons

The dispersion properties and Landau damping rate of ion-acoustic waves (IAWs) with the hybrid Cairns-Tsallis distributed (CTD) electrons and Maxwellian ions are investigated using the plasma kinetic model based on Vlasov-Poisson's equations. For both super-extensive (q < 1) and sub-extensive (q > 1) plasmas, the dielectric response function, real frequency, and Landau damping rate of IAWs are derived. By taking the effect of θ_{i, e} (ion-to-electron temperature ratio) into account, it is found that with the increase of ion temperature, the real frequency and wave dispersion effects increase as well (for both super-extensive and sub-extensive cases). Exploring the properties of the Landau damping rate of IAWs with the simultaneous presence of non-thermal parameter α and non-extensive parameter q, a comparison of numerical and analytical results is presented. It is found that in different ranges of θ_{e, i} (electron-to-ion temperature ratio), on decreasing the values of the non-extensive parameter and increasing values of the non-thermal parameter, the weak damping rate is observed (vice versa) in super-extensive or super-thermal plasma, although the trend of the damping rate in sub-thermal plasma is similar (as in the case of super-thermal plasma) but is less weak. It is further revealed that the damping rate of IAWs in thermal plasmas (Maxwellian) is stronger than the damping rate of IAWs in the case of non-thermal plasmas (CTD). The current study is applicable to provide deep insight and further allow the exploration of electrostatic plasma modes in different space and laboratory plasma environments where the hybrid CTD plasma exists.     

Magnetosonic Shocks in Ultra-Relativistic Dissipative Degenerate Plasmas

Magnetosonic shock structures in dissipative magnetized degenerate electron ion plasma are studied.The two fluid quantum magnetohydrodynamic equations for non-degenerate ions and ultra-relativistic degenerate electron fluids with the Maxwell equations are presented.Using the reductive perturbation technique the Korteweg de Vries Burgers(KdVB)equation is derived and its solution is presented with the tanh method.Astrophysical plasma parameters are used to study the effects of variation of plasma density,magnetic held intensity and kinematic viscosity on the propagation characteristics of nonlinear shock structures in such plasma systems.     

Head-on Collision of Ion-acoustic Multi-Solitons in e-p-i Plasma

The propagation and interaction between ion acoustic multi-solitons in an unmagnetized multicomponent plasma consisting of fluid hot ions, positrons and both hot and cold electrons, are investigated by employing the extended Poincare–Lighthill–Kuo(PLK) method. Two different Kortewege-de Vries(K-dV) equations are derived. The Hirota's method is applied to get the K-dV multi-solitons solution. The phase shift due to the overtaking and head- on collision of the multi-solitons is obtained.     

Interaction phenomena of ion‐acoustic quasi‐solitons and classical‐solitons in three component plasma

The space–time evolution of the cnoidal‐soliton solution, characteristics of the quasi‐soliton solution of Korteweg‐de‐Vries (KdV) equation, and the interaction phenomena of ion‐acoustic waves (IAWs) are investigated in a plasma system consisting of positive and negative ions with superthermal electrons. To do this, and (Ar⁺, F^?) plasmas are considered and two‐sided KdV equations (KdVEs) are derived applying the extended Poincaré‐Lighthill‐Kuo (ePLK) method. The effects on wave structures, potential profiles, and propagation characteristics with plasma parameters of the cnoidal‐wave, quasi‐soliton solution, and head‐on collision phenomena of IAWs are presented graphically. It was found that the superthermality parameter and the mass ratio of ions play a significant role in the head‐on collision between soliton and standing cnoidal wave and reveal that the collision is elastic and both waves change their phase shifts due to collision. Moreover, the superthermality parameters are also responsible for the production of compressive and rarefactive phase shifts in overtaking collision processes between right travelling classical soliton (CS) and cnoidal wave (CW) and reduced the amplitudes of IAWs. It was also found that a new wave is created with a high amplitude in the interacting region during collision depending on the plasma parameters.     

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.     

Dynamics of ion-acoustic rogue waves in electron-positron-ion magneto-plasmas

A more general and realistic four-component magnetized plasma medium consisting of opposite polarity ions and nonthermal distributed positrons and electrons is considered to investigate the stable/unstable frequency regimes of modulated ion-acoustic waves (IAWs) in the D-F regions of Earth's ionosphere. A (3 + 1) -dimensional nonlinear Schrödinger equation, which leads to the modulation instability (MI) of IAWs, is derived. The parametric regimes for the existence of the MI, first- and second-order rogue waves, and also their basic features (viz., amplitude, width, and speed) are found to be significantly modified by the effect of physical plasma parameters and external magnetic field. It is found that the nonlinearity of the different types of electronegative plasma system depends on the positive to negative ion mass ratio. It is also shown that the presence of nonthermal distributed electrons and positrons modifies the nature of the MI of the modulated IAWs. The implication of our results for the laboratory plasma [e.g., (Ar⁺, F⁻ ) electronegative plasma] and space plasma [e.g., (H⁺, H⁻ ), () electronegative plasma in D-F regions of Earth's ionosphere] are briefly discussed.     

Polarized Debye Sheath in Degenerate Plasmas

The force on a charged dust grain in a plasma due to polarization of thermal ions and degenerate electrons around the grain is derived in the limits of weakly relativistic and ultra-relativistic degeneracy of electrons. It is found that in both these cases, the magnitude of the polarization force is enhanced compared to that in classical plasmas. The influence of this force on dust-acoustic(DA) modes is examined and discussed. It is shown that the DA wave frequency in degenerate plasmas is significantly reduced compared to the classical DA mode.     

Nonplanar Electrostatic Solitary Waves in a Relativistic Degenerate Dense Plasma

By employing the reductive perturbation technique, the propagation of cylindrical and spherical ion acoustic solitary waves is studied in an unmagnetized dense relativistic plasma, consisting of relativistically degenerate electrons and cold fluid ions. A modified Korteweg-de-Vries equation is derived and its numerical solutions have been analyzed to identify the basic features of electrostatic solitary structures that may form in such a degenerate Fermi plasma. Different degrees of relativistic electron degeneracy are discussed and compared. It is found that increasing number density leads to decrease the amplitude the width of the ion acoustic solitary wave in both the cylindrical and spherical geometries. The relevance of the work to the compact astrophysical objects, particularly white dwarfs is pointed out.