Ion Acoustic Shock Waves Research Articles

Ion acoustic shock and solitary waves in highly relativistic plasmas with nonextensive electrons and positrons

The Korteweg-de Vries Burgers (KdVB)-like equation is derived to study the characteristics of nonlinear propagation of ion acoustic solitions in a highly relativistic plasma containing relativistic ions and nonextensive distribution of electrons and positrons using the well known reductive perturbation technique. The KdVB-like equation is solved employing the Bernoulli's equation method taking unperturbed positron to electron concentration ratio, electron to positron temperature ratio, strength of nonextensivity, ion kinematic viscosity, and highly relativistic streaming factor. It is found that these parameters significantly modify the structures of the solitonic excitation. The ion acoustic shock profiles are observed due to the influence of ion kinematic viscosity. In the absence of dissipative term to the KdVB equation, compressive and rarefactive solitons are observed in case of superthermality, but only compressive solitons are found for the case of subthermality.

Oblique shock waves in a two electron temperature superthermally magnetized plasma

A study is presented for the oblique propagation of low-frequency ion acoustic (IA) shock waves in a magnetized plasma consisting of cold ions and two temperature superthermally distributed electrons. A nonlinear Korteweg de-Vries-Burger (KdV-Burger) equation is obtained by using the reductive perturbation method (RPM) which governs the dynamics of the IA shock wave. Using the solution of KdV-Burger equation, the characteristics of the IA shock wave have been studied for various plasma parameters. The combined effects of the cold to hot electron temperature ratio ( $\sigma$ ), the density ratio of hot electrons to ions ( $f$ ), the superthermality of cold and hot electrons ( $\kappa_{c}, \kappa_{h}$ ), the strength of the magnetic field ( $\omega_{ci}$ ), and the obliqueness ( $\theta$ ), significantly influence the profile of the shock wave. The findings in the present study could be important for the electrostatic wave structures in the Saturn’s magnetosphere, where two temperature electrons exist with a kappa distribution.

Ion acoustic shock wave in collisional equal mass plasma

The effect of ion-ion collision on the dynamics of nonlinear ion acoustic wave in an unmagnetized pair-ion plasma has been investigated. The two-fluid model has been used to describe the dynamics of both positive and negative ions with equal masses. It is well known that in the dynamics of the weakly nonlinear wave, the viscosity mediates wave dissipation in presence of weak nonlinearity and dispersion. This dissipation is responsible for the shock structures in pair-ion plasma. Here, it has been shown that the ion-ion collision in presence of collective phenomena mediated by the plasma current is the source of dissipation that causes the Burgers' term which is responsible for the shock structures in equal mass pair-ion plasma. The dynamics of the weakly nonlinear wave is governed by the Korteweg-de Vries Burgers equation. The analytical and numerical investigations revealed that the ion acoustic wave exhibits both oscillatory and monotonic shock structures depending on the frequency of ion-ion collision parameter. The results have been discussed in the context of the fullerene pair-ion plasma experiments.

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 ion-acoustic shock waves in a multi-ion plasma with nonextensive electrons and positrons

The basic features of ion-acoustic shock waves (IASHWs) in a multi-ion nonextensive plasma (containing positive light ions, negative heavy ions, as well as nonextensive electrons and positrons) have been rigorously investigated in a nonplanar geometry. The standard reductive perturbation method has been employed to derive the Modified Burgers (MB) equation. The combined effects of the electron and positron nonextensivity, and the ion kinematic viscosity significantly have been found to modify the basic properties of these electrostatic shock structures. The properties of the cylindrical and the spherical IASHWs are observed to differ significantly from those of onedimensional planar waves. The findings obtained from this theoretical investigation may be useful in understanding the characteristics of IASHWs both in space and laboratory plasmas.

Modeling of modified ion-acoustic shock waves in a relativistic electron degenerate multi-ion plasma for higher order nonlinearity

A nonlinear propagation of modified ion-acoustic (mIA) shock waves in a relativistic degenerate plasma (containing inertial viscous positive and negative ion fluids, relativistic electron fluids, and negatively charged immobile heavy ions) has been investigated theoretically. The modified Burgers (mB) and further modified Burgers (FmB) equations have been derived by adopting reductive perturbation technique. The solutions of both mB and FmB equations have been numerically analyzed to characterize the basic features of mIA shock waves. The basic properties (speed, amplitude, width, etc.) of these electrostatic shock waves are found to be significantly modified by the effects of negatively charged static heavy ions and the plasma particle number densities. It is found that the properties of these shock waves obtained from this analysis are significantly different from those obtained from the analysis of standard Burgers equation. The implications of our results in space and interstellar compact objects like non-rotating white dwarfs, neutron stars, etc. are briefly discussed.

Cylindrical and Spherical Ion-Acoustic Shock Waves in Nonextensive Electron-Positron–Ion Plasma

The properties of cylindrical and spherical ion-acoustic shock waves in an unmagnetized plasma system consisting of inertial ions, nonextensive electrons, and nonextensive positrons are investigated. A modified Burgers equation is derived using the reductive perturbation technique and its numerical solution is obtained. It is found that the properties of the cylindrical and spherical ion-acoustic shock waves significantly differ from those of 1-D planar shock waves. The findings of this investigation may be used in understanding the wave propagation in laboratory and space plasmas.

Ion-Acoustic Shock Waves in Nonextensive Electron-Positron-Ion Plasma

A rigorous theoretical investigation is made of ion-acoustic shock structures in an unmagnetized three-component plasma whose constituents are nonextensive electrons, nonextensive positrons, and inertial ions. The Burgers equation is derived by employing the reductive perturbation method. The effects of electron and positron nonextensivity and ion kinematic viscosity on the properties of these ion-acoustic shock waves are briefly discussed. It is found that shock waves with positive and negative potentials are obtained to depend on the plasma parameters. The entailment of our results may be useful to understand some astrophysical and cosmological scenarios including stellar polytropes, hadronic matter and quark-gluon plasma, protoneutron stars, dark-matter halos, etc., where effects of nonextensivity can play significant roles.

Study of the higher-order shock excitations in a degenerate quantum plasma

We propose a comprehensive theory for one dimensional ion-acoustic shock waves (IASWs) in an unmagnetized degenerate quantum plasma that is assumed to contain inertial ions and relativistic degenerate electrons. The modified Burgers (mB) and the Gardner equations have been derived by employing the reductive perturbation method and have been analyzed in order to identify the basic features (amplitude, width, speed, etc.) of the IASWs. The basic features of these shocks obtained from this analysis are observed to be significantly different from those obtained from the standard Burgers equation. The implications of our results in space and interstellar compact objects (viz. white dwarfs, non-rotating neutron stars, active galactic nuclei, cometary tails, etc.) are briefly mentioned.

Nonlinear features of ion acoustic shock waves in dissipative magnetized dusty plasma

The nonlinear propagation of small as well as arbitrary amplitude shocks is investigated in a magnetized dusty plasma consisting of inertia-less Boltzmann distributed electrons, inertial viscous cold ions, and stationary dust grains without dust-charge fluctuations. The effects of dissipation due to viscosity of ions and external magnetic field, on the properties of ion acoustic shock structure, are investigated. It is found that for small amplitude waves, the Korteweg-de Vries-Burgers (KdVB) equation, derived using Reductive Perturbation Method, gives a qualitative behaviour of the transition from oscillatory wave to shock structure. The exact numerical solution for arbitrary amplitude wave differs somehow in the details from the results obtained from KdVB equation. However, the qualitative nature of the two solutions is similar in the sense that a gradual transition from KdV oscillation to shock structure is observed with the increase of the dissipative parameter.

Roles of arbitrarily charged heavy ions and degenerate plasma pressure in cylindrical and spherical IA shock waves

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 dense plasma system containing degenerate electron and ion fluids, and arbitrarily charged static heavy ions. This investigation is valid for both the non-relativistic limit and the ultra-relativistic limit. The reductive perturbation technique has been employed to derive the standard Burgers equation. The solution of this equation has been analyzed both for planar geometry and for nonplanar geometry. The basic features (speed, amplitude, width, and so on) 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. It has also been found that the properties of IA shock waves in nonplanar (cylindrical or spherical) geometry significantly differ from those in planar (one-dimensional) geometry. The implications of our results for space and interstellar compact objects such as white dwarfs, neutron stars, black holes, and so on have been briefly discussed.

Nonplanar ion-acoustic shock waves in degenerate plasmas with positively charged heavy ions

The theoretical and numerical study on the nonlinear propagation of heavy-ion-acoustic (HIA) shock waves has been carried out in an unmagnetized, collisionless dense plasma system (containing degenerate electron and inertial light ion fluids, and positively charged static heavy ions). The normal mode analyse is used to investigate the linear wave properties. Reductive perturbation technique is used to derive the Burgers equation which admits a localized wave solution for the shock profile. It is seen that the shock wave characteristics have been influenced significantly for the non-relativistic as well as for the ultra-relativistic limits. It has also been found that the effect of degenerate pressure and number density of electron and inertial light ion fluids, and positively charged static heavy ions significantly modify the basic features (speed, amplitude, width, etc.) of HIA shock waves. The relevance of our results in astrophysical objects (like white dwarfs and neutron stars), which are of scientific interest, is briefly discussed.

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.

Numerical study of ion acoustic shock waves in dense quantum plasma

Two fluid quantum hydrodynamic equations are solved numerically to investigate the propagation characteristics of ion acoustic shock waves in an unmagnetized dense quantum plasma, whose constituents are the electrons and ions. For this purpose, we employ the standard finite difference Lax Wendroff and relaxation methods, to examine the quantum effects on the profiles of shock potential, the electron/ion number densities, and velocity even for quantum parameter at H = 2. The effects of the latter vanish in a weakly non-linear limit while obeying the KdV theory. It is shown that the evolution of the wave depends sensitively on the plasma density and the quantum parameter. Numerical results reveal that the kinks or oscillations are pronounced for large values of quantum parameter, especially at H = 2. Our results should be important to understand the shock wave excitations in dense quantum plasmas, white dwarfs, neutron stars, etc.

Oblique shock dynamics in nonextensive magnetized plasma

A study is presented for the oblique propagation of low-frequency ion-acoustic (IA) shock waves in a magnetized plasma having cold viscous ion fluid and nonextensively distributed electrons. A weakly nonlinear analysis is carried out to derive a Korteweg de-Vries-Burger like equation. Dependence of the shock wave characteristics (height, width and nature) on plasma parameters is then traced and studied in details. We hope that our results will aid to explain and interpret the nonlinear oscillations occurring in magnetized space plasmas.

Shock waves and double layers in electron degenerate dense plasma with viscous ion fluids

The properties of ion-acoustic shock waves and double layers propagating in a viscous degenerate dense plasma (containing inertial viscous ion fluid, non-relativistic and ultra-relativistic degenerate electron fluid, and negatively charged stationary heavy element) is investigated. A new nonlinear equation (viz. Gardner equation with additional dissipative term) is derived by the reductive perturbation method. The properties of the ion-acoustic shock waves and double layers are examined by the analysis of the shock and double layer solutions of this new equation (we would like to call it “M-Z equation”). It is found that the properties of these shock and double layer structures obtained from this analysis are significantly different from those obtained from the analysis of standard Gardner or Burgers’ equation. The implications of our results to dense plasmas in astrophysical objects (e.g., non-rotating white dwarf stars) are briefly discussed.

Nonlinear electrostatic coherent structures: solitary and shock waves in a dissipative, nonplanar multi-component quantum plasma

The nonlinear propagation of ion-acoustic solitary and shock waves in a dissipative, nonplanar quantum plasma comprised of electrons, positrons, and ions are studied. A modified Korteweg-de Vries Burgers equation is derived in the limit of low frequency and long wavelength by taking into account the kinematic viscosity among the plasma constituents. It is shown that this plasma system supports the propagation of both compressive and rarefactive nonlinear waves. The effects of variation of various plasma parameters on the time evolution of nonplanar solitary waves, the profile of shock waves, and the nonlinear structure induced by the collision of solitary waves are discussed. It is found that these parameters have significant effects on the properties of nonlinear waves in cylindrical and spherical geometries, and these effects for compressive and rarefactive nonlinear waves are obviously different.

Characteristic of ion acoustic shock waves in a dissipative quantum pair plasma with dust particulates

The behavior of quantum dust ion-acoustic (QDIA) shocks in a plasma including inertialess quantum electrons and positrons, classical cold ions and stationary negative dust grains are studied, using a quantum hydrodynamic model (QHD). The effect of dissipation due to the viscosity of ions is taken into account. The propagation of small but finite amplitude QDIA shocks is governed by the Kortoweg-de Vries-Burgers (KdVB) equation. The existence regions of oscillatory and monotonic shocks will depend on the quantum diffraction parameter (H) and dust density (d) as well as dissipation parameter (η0). The effect of plasma parameters (d,H,η0), on these structures is investigated. Results indicate that the thickness and height of monotonic shocks; oscillation amplitude of the oscillatory shock wave and it’s wavelength effectively are affected by these parameters. Additionally, the possibility of propagation of both compressive and rarefactive shocks is investigated. It is found that depending on some critical value of dust density (dc), which is a function of H, compressive and rarefactive shock waves can’t propagate in model plasma. The present theory is applicable to analyze the formation of nonlinear structures at quantum scales in dense astrophysical objects.

Dissipative ion-acoustic solitary and shock waves in a plasma with superthermal electrons

The excitation of a nonlinear ion-acoustic (IA) wave packet in a viscous plasma consisting of superthermal electrons and cold ions is investigated. It is assumed that the superthermal components obey the Kappa distribution. The standard reductive perturbation technique is employed to obtain a cubic complex Ginzburg–Landau type equation, which governs the dynamics of the amplitude of IA wave packets in a viscous plasma. In a weakly dissipative regime, by means of a perturbation method adopted from non-integrable dynamical systems theory, explicit soliton solutions are obtained of the dissipative dynamical system, determined as fixed points of a two-dimensional system of evolution equations describing the soliton amplitude and velocity. The stability of bright solitons is addressed using adiabatic perturbation theory in a weakly dissipative case. In a general dissipation regime, a novel type of travelling solitary (dissipative solitons) and shock-type solutions are derived for an envelope equation. Moreover, the dependence of the solitary and shock wave characteristics on relevant physical parameters of the problem is studied. It is shown that dissipative solitons do exist, sustained by a mutual balance between loss and gain terms, in addition to the interplay between dispersion and nonlinearity. The dependence of solitary and shock wave velocities on the parameters of the system are investigated. To feature distinctive characteristics of a dissipative soliton, it is compared with the bright soliton solution of the nonlinear Schrödinger equation.

Propagation of ion acoustic shock waves in negative ion plasmas with nonextensive electrons

Nonlinear ion acoustic shocks (monotonic as well as oscillatory) waves in negative ion plasmas are investigated. The inertialess electron species are assumed to be nonthermal and follow Tsallis distribution. The dissipation in the plasma is considered via kinematic viscosities of both positive and negative ion species. The Korteweg-de Vries Burgers (KdVB) equation is derived using small amplitude reductive perturbation technique and its analytical solution is presented. The effects of variation of density and temperature of negative ions and nonthermal parameter q of electrons on the strength of the shock structures are plotted for illustration. The numerical solutions of KdVB equation using Runge Kutta method are obtained, and transition from oscillatory to monotonic shock structures is also discussed in detail for negative ions nonthermal plasmas.