Ion Acoustic Shock Waves Research Articles

Nonlinear quantum ion acoustic shock wave dynamics with exchange-correlation effects

The dynamics of linear and nonlinear electrostatic shock excitations is studied in homogeneous, unmagnetized, unbounded and dissipative quantum plasma consisting of electrons and ions. The dissipation in the system is taken into account by incorporating the ion kinematic viscosity. The system is modelled using the quantum hydrodynamic equations in which the electrons are significantly affected by the quantum forces, viz., the quantum statistical pressure, the quantum Bohm potential and electron exchange-correlations due to electron spin. In the weakly nonlinear limit, using reductive perturbation method deformed Korteweg-de Vries Burgers’s (KdVB) equation, which elegantly combines the effects of nonlinearity, dispersion and dissipation is derived. It is found that the present model predicts the existence of both nonlinear oscillatory and monotonic shock structures. The temporal evolution, stability and phase-space dynamics of nonlinear ion acoustic shocks are investigated numerically to elucidate the effects of quantum diffraction, electron exchange correlation and ion kinematic viscosity.

Ion-acoustic shocks in magnetized quantum plasmas with relative density effects of spin-up and spin-down degenerate electrons

Ion-acoustic shock wave propagation in dense magnetized plasmas with relative density effects of spin-up and spin-down degenerate electrons is studied. The ions are classical, and their dissipative effects on plasma dynamics are included via kinematic viscosity. The electrons with spin-up and spin-down states are taken as separate species. The quantum tunneling effects of electrons are also considered in equations of motions of electrons. The Korteweg de Vries Burgers (KdVB) equation is derived, which admits the shock solution. The KdVB equation is solved numerically to study the transition from shock with oscillatory trails at its wave fronts to the monotonic shock structure with respect to variations in different plasma parameters. The parametric role of the spin density polarization ratio in the propagation characteristics of the shock wave structure is discussed.

Oblique ion-acoustic shock waves in a magnetized, multi-species plasma

Ion-Acoustic (IA) shock waves are studied in a magnetized, five component cometary plasma consisting of positively and negatively charged oxygen ions, kappa described hydrogen ions, hot solar electrons and slightly colder cometary electrons. The Korteweg–de Vries–Burgers (KdVB) equation is derived and the variation of the shock profile is studied. It is found that the obliqueness of shock wave propagation significantly varies the basic properties like amplitude and width of the shock.

Nonlinear propagation of ion-acoustic waves through the Burgers equation in weakly relativistic plasmas

The Burgers equation is obtained to study the characteristics of nonlinear propagation of ionacoustic shock, singular kink, and periodic waves in weakly relativistic plasmas containing relativistic thermal ions, nonextensive distributed electrons, Boltzmann distributed positrons, and kinematic viscosity of ions using the well-known reductive perturbation technique. This equation is solved by employing the (G'/G)-expansion method taking unperturbed positron-to-electron concentration ratio, electron-to-positron temperature ratio, strength of electrons nonextensivity, ion kinematic viscosity, and weakly relativistic streaming factor. The influences of plasma parameters on nonlinear propagation of ion-acoustic shock, periodic, and singular kink waves are displayed graphically and the relevant physical explanations are described. It is found that these parameters extensively modify the shock structures excitation. The obtained results may be useful in understanding the features of small but finite amplitude localized relativistic ion-acoustic shock waves in an unmagnetized plasma system for some astrophysical compact objects and space plasmas.

Ion acoustic shock waves in a degenerate relativistic plasma with nuclei of heavy elements

Based on the quantum hydrodynamics theory, a rigorous model for ion acoustic shock waves (IASWs) in a degenerate relativistic plasma with heavy ion nuclei is presented. Two cases are considered: the ultra-relativistic case and the non-relativistic case. A Korteweg-de Vries-Burger's (KdVB) equation describing IASWs in such plasma is derived, then its explicit as well as oscillatory solutions are deduced. It is found that the shape of IASWs is influenced by the particle density of degenerate electrons, the concentration of heavy elements, the viscosity coefficient, and the quantum Bohm potential term. The results should be useful in understanding the shock wave characteristics in degenerate plasma which is found in compact astrophysical objects.

New: Variational principle–exact solutions and conservation laws for modified ion-acoustic shock waves and double layers with electron degenerate in plasma

The nonlinear propagation of modified ion acoustic shock waves and double layers in a relativistic degenerate plasma is considered. This plasma system is proposed for containing inertial viscous positive and negative ion fluids, relativistic electron fluids, and negatively charged immobile heavy ions. The basic set of fluid equations is reduced to modified Burgers (MB) and further modified Burgers (FMB) or (Gardner) or Mamun and Zobaer (M-Z) equations by using the reductive perturbation method. The basic features of these shocks obtained from this analysis are observed to be significantly different from those obtained from the standard Burgers equation. By introducing two special functions and He's semi-inverse method, a variational principle and conservation laws for the Gardner (FmB) equation are obtained. A set of new exact solutions for the Gardner (FmB) equation are obtained by the auto-Bäcklund transformations. Finally, we will study the physical meanings of solutions.

Dust-Charge Variation Effects on Dust ion Acoustic Shock Waves in Four Component Quantum Plasma

The behavior of nonlinear quantum dust ion acoustic (QDIA) shock waves in a collisionless, unmagnetized plasma consisting of inertialess quantum electrons and positrons, classical cold ions and stationary negatively charged dust grains with dust charge variation is investigated using quantum hydrodynamic (QHD) equations. The propagation of small amplitude QDIA shock waves is governed by Burgers equation. It is shown that the dust charge variation plays an important role in the formation of such QDIA shock structures. The dependence of the shock wave’s amplitude and thickness on the chemical potential is investigated. The present theory is applicable to analyze the formation of nonlinear structures at quantum scales in dense astrophysical objects.

Ion acoustic shock and periodic waves through Burgers equation in weakly and highly relativistic plasmas with nonextensivity

A comparative study is carried out for the nonlinear propagation of ion acoustic shock waves both for the weakly and highly relativistic plasmas consisting of relativistic ions and q-distributed electrons and positions. The Burgers equation is derived to reveal the physical phenomena using the well known reductive perturbation technique. The integration of the Burgers equation is performed by the method. The effects of positron concentration, ion–electron temperature ratio, electron–positron temperature ratio, ion viscosity coefficient, relativistic streaming factor and the strength of the electron and positron nonextensivity on the nonlinear propagation of ion acoustic shock and periodic waves are presented graphically and the relevant physical explanations are provided.

Dust ion acoustic solitary and shock waves in strongly coupled dusty plasma in presence of attractive interparticle interaction potential

The streaming of ions through the dust particles significantly modifies the repulsive Debye-Hückel type of interaction in the sheath and pre-sheath regions and leads to the appearance of oscillatory and attractive wake type interaction. In this paper, we investigate the formation of dust-ion acoustic solitary and shock waves in the presence of streaming ions in a strongly coupled dusty plasma. The generalized hydrodynamic equation is used to describe the dust dynamics, and the dust-dust interaction has been taken into account via the electrostatic pressure term. The novel feature of the present study is the incorporation of both the repulsive and attractive interactions in the electrostatic pressure term. The flow of ions along the vertical direction in the sheath/presheath region of the plasma brings asymmetry to the dust dynamics, which has been carefully handled while considering the effect of strong coupling in the formation of nonlinear structures in such plasma. The study reveals that the ion streaming velocity has a crucial role in controlling the nonlinear coherent structures.

K–P–Burgers equation in negative ion-rich relativistic dusty plasma including the effect of kinematic viscosity

The stationary solution is obtained for the K–P–Burgers equation that describes the nonlinear propagations of dust ion acoustic waves in a multi-component, collisionless, un-magnetized relativistic dusty plasma consisting of electrons, positive and negative ions in the presence of charged massive dust grains. Here, the Kadomtsev–Petviashvili (K–P) equation, three-dimensional (3D) Burgers equation, and K–P–Burgers equations are derived by using the reductive perturbation method including the effects of viscosity of plasma fluid, thermal energy, ion density, and ion temperature on the structure of a dust ion acoustic shock wave (DIASW). The K–P equation predictes the existences of stationary small amplitude solitary wave, whereas the K–P–Burgers equation in the weakly relativistic regime describes the evolution of shock-like structures in such a multi-ion dusty plasma.

Oblique propagation of ion acoustic shock waves in weakly and highly relativistic plasmas with nonthermal electrons and positrons

This work investigates the oblique nonlinear propagation of ion acoustic (IA) shock waves for both weakly and highly relativistic plasmas composed of nonthermal electrons and positrons with relativistic thermal ions. The KdVB-like equation, involving dispersive, weakly transverse dispersive, nonlinearity and dissipative coefficients, is derived employing the well known reductive perturbation method. The integration of this equation is carried out by the $\mathit{tanh}$ method taking the stable shock formation condition into account. The effects of nonthermal electrons and positrons, nonthermal electrons with isothermal positrons, isothermal electrons with nonthermal positrons, and isothermal electrons and positrons on oblique propagation of IA shock waves in weakly relativistic regime are described. Furthermore, the effects of plasma parameters on oblique propagation of IA shock waves in highly relativistic regime are discussed and compared with weakly relativistic case. It is seen that the plasma parameters within certain limits significantly modify the structures of the IA shock waves in both cases. The results may be useful for better understanding of the interactions of charged particles with extra-galactic jets as well as astrophysical compact objects.

Korteweg–deVries–Burgers (KdVB) equation in a five component cometary plasma with kappa described electrons and ions

We investigate the existence of ion-acoustic shock waves in a five component cometary plasma consisting of positively and negatively charged oxygen ions, kappa described hydrogen ions, hot solar electrons, and slightly colder cometary electrons. The KdVB equation has been derived for the system, and its solution plotted for different kappa values, oxygen ion densities, as well as the temperature ratios for the ions. It is found that the amplitude of the shock wave decreases with increasing kappa values. The strength of the shock profile decreases with increasing temperatures of the positively charged oxygen ions and densities of negatively charged oxygen ions.

Effect of ion viscosity on dust ion-acoustic shock waves in a nonextensive magnetoplasma

The nonlinear features of dust ion-acoustic shock waves (DIASWs) in a magnetoplasma containing cold positive ions, nonextensive electrons, and immobile negatively charged dust grains taking into account the cold ion kinematic viscosity are investigated. The reductive perturbation technique is used to derive a Zakharov-Kuznetsov-Burgers (ZK-Burgers). It is found that the fundamental properties of the DIASWs are significantly modified by the different system parameters such as the nonextensive parameter, the ion gyrofrequency, the dust concentration, the viscosity parameter, and the direction cosines. Also, the polarities (positive and negative shocks) of the potential are found to exist in the plasma under consideration. The implications of our results may be used in understanding the acoustic shock waves propagation in laboratory and space plasmas.

Variational principle, conservation laws and exact solutions for dust ion acoustic shock waves modeling modified Burger equation

The nonlinear dust ion acoustic (DIA) shock waves have been investigated in one-dimensional, collisionless and unmagnetized dusty plasma consisting of mobile ion, vortex-like electron and charge fluctuating static dust particles. The basic set of fluid equations is reduced to the modified Burger equation by using the reductive perturbation method. The effects of dust grain charge fluctuation and vortex-like (trapped) electron are found to modify the properties of the DIA shock waves significantly. By the semi-inverse method, a variational principle, and conservation laws for the modified Burger equation are obtained. It is shown that the modified Burger equation is non-integrable using Painlevé analysis. A set of new exact solutions are obtained by the auto-Bäcklund transformations. Finally, we will study the physical meanings of solutions.

Effect of dust size distribution and dust charge fluctuation on dust ion-acoustic shock waves in a multi-ion dusty plasma

The effects of dust size distribution and dust charge fluctuation of dust grains on the small but finite amplitude nonlinear dust ion-acoustic shock waves, in an unmagnetized multi-ion dusty plasma which contains negative ions, positive ions and electrons, are studied in this paper. A Burgers equation and its stationary solutions are obtained by using the reductive perturbation method. The analytical and numerical results show that the height with polynomial dust size distribution is larger than that of the monosized dusty plasmas with the same dust grains, but the thickness in the case of different dust grains is smaller than that of the monosized dusty plasmas. Furthermore, the moving speed of the shock waves also depend on different dust size distributions.

Time fractional effect on ion acoustic shock waves in ion-pair plasma

The nonlinear properties of ion acoustic shock waves are studied. The Burgers equation is derived and converted into the time fractional Burgers equation by Agrawal’s method. Using the Adomian decomposition method, shock wave solutions of the time fractional Burgers equation are constructed. The effect of the time fractional parameter on the shock wave properties in ion-pair plasma is investigated. The results obtained may be important in investigating the broadband electrostatic shock noise in D- and F-regions of Earth’s ionosphere.

Rogue waves in electronegative space plasmas: The link between the family of the KdV equations and the nonlinear Schrödinger equation

We examine the likelihood of the ion-acoustic rogue waves propagation in a non-Maxwellian electronegative plasma in the framework of the family of the Korteweg–de Vries (KdV) equations (KdV/modified KdV/Extended KdV equation). For this purpose, we use the reductive perturbation technique to carry out this study. It is known that the family of the KdV equations have solutions of distinct structures such as solitons, shocks, kinks, cnoidal waves, etc. However, the dynamics of the nonlinear rogue waves is governed by the nonlinear Schrodinger equation (NLSE). Thus, the family of the KdV equations is transformed to their corresponding NLSE developing a weakly nonlinear wave packets. We show the possible region for the existence of the rogue waves and define it precisely for typical parameters of space plasmas. We investigate numerically the effects of relevant physical parameters, namely, the negative ion relative concentration, the nonthermal parameter, and the mass ratio on the propagation of the rogue waves profile. The present study should be helpful in understanding the salient features of the nonlinear structures such as, ion-acoustic solitary waves, shock waves, and rogue waves in space and in laboratory plasma where two distinct groups of ions, i.e. positive and negative ions, and non-Maxwellian (nonthermal) electrons are present.

Influence of Compressive and Rarefactive Ion-Acoustic Shock Waves in a Multi-Component Degenerate Dense Plasma

Influence of Compressive and Rarefactive Ion-Acoustic Shock Waves in a Multi-Component Degenerate Dense Plasma

The effect of trapped electrons on the three-dimensional ion-acoustic shock wave in magnetized ionic-pair plasma

The effect of trapped electrons featuring vortex-like distribution on the nonlinear behavior of a three-dimensional ion-acoustic shock wave is investigated in a magnetized ionic-pair plasma. In the long-wave approximation, the dynamics of the shock wave is governed by the -dimensional Schamel-Zakharov-Kuznetsov-Burgers' equation due to the presence of trapped electrons and ion kinematic viscosity. By using the homogeneous balance principle and tanh function method, we obtain a novel exact shock wave solution of the equation. It is found for the first time that the trapped electrons can support a shock wave with only positive polarity.

Shock waves and double layers in a quantum electron-positron-ion plasma

The ion-acoustic (IA) shock waves and double layers (DLs) in an unmagnetized, dissipative, quantum electron-positron-ion (EPI) plasma (composed of a viscous heavy ion fluid, Fermi electrons and positrons) have been theoretically investigated. The higher-order Burgers and Gardner equations are derived by employing the reductive perturbation method. The basic features of the IA shock waves and the DLs are identified by analyzing the solutions of both the higher-order Burgers and Gardner equations. The ratio of the Fermi temperature of the positron to that of the electron, the Fermi pressure of electrons and positrons, the viscous force, the plasma particle number densities, etc. are found to change remarkably the basic features (viz. amplitude, width, phase speed, etc.) of the IA waves. The results of our investigation may be helpful in understanding the nonlinear features of localized IA waves propagating in quantum EPI plasmas which are ubiquitous in astrophysical, as well as laboratory, environments.