Electron-acoustic Shock Waves Research Articles

Interaction of Nonplanar Electron–Acoustic Shock Waves with Superthermal Hot Electrons

Interaction of Nonplanar Electron–Acoustic Shock Waves with Superthermal Hot Electrons

The Existence and Propagation of Electron Acoustic Shock Waves in Magnetized Plasma with Electron Beam

The Existence and Propagation of Electron Acoustic Shock Waves in Magnetized Plasma with Electron Beam

Theoretical analysis of electron acoustic shock waves in magnetized superthermal plasma with electron beam

AbstractWe have analysed the small‐amplitude non‐linear electron acoustic shock waves by taking into account the effects of electron beam in magnetized plasma. Satellite observations in different regions of the Earth's magnetosphere have shown that the electrostatic solitary waves are generally associated with electron or/and ion beams. The nonlinear Korteweg‐de‐Vries Burgers (KdVB) equation has been derived by considering the basic fluid equations and dissipation effects. The nonlinear coefficient of KdVB equation comes out to be negative. Only dip‐shaped potential structures are reported here. For the parameters discussed in this paper, we did not find positive polarity shocks. This could be due to the restrictions on the plasma parameters since we are using the fixed densities of the cold, hot, and beam electrons as observed by the Viking satellite in the auroral region. In this paper, the importance of the cold electron to hot electron temperature in conjunction with the beam speed is pointed out. Increase in beam density, kinematic viscosity, and magnetic field results in increase in the amplitude while the increase in hot electron concentration and superthermality leads to decrease in potential. The numerical analysis is presented for the parameters corresponding to the observation of burst b event by Viking satellite in the dayside auroral zone of the earth's magnetosphere.

Zakharov–Kuznetsov–Burgers equation in a magnetised non-extensive electron–positron–ion plasma

In this paper, we have studied the three-dimensional (3D) electron-acoustic waves (EAWs) in a three-component complex plasma containing q-non-extensive distributed hot electrons and positrons. The propagation characteristics of the 3D electron-acoustic (EA) shock waves under the influence of magnetic field have been studied. Our present plasma model supports the negative potential shocks. Combined action of dissipation $$(\eta )$$ , non-extensivity (q), concentration of positrons ( $$\beta $$ ), temperature ratio of cold electrons to positrons ( $$\sigma $$ ) and magnetic field ( $$\omega _c$$ ) on the EA shock waves has been studied in detail and the findings obtained here will be beneficial in future astrophysical investigations.

Effect of Anisotropic Pressure on Electron Acoustic Oscillatory and Monotonic Shocks in Superthermal Magnetoplasma

AbstractNonlinear oscillatory and monotonic electron acoustic shock waves in dissipative magnetorotating electron‐positron‐ion plasmas containing cold dynamical electrons, superthermal electrons, and positrons have been analyzed in the stationary background of massive positive ions. The Korteweg de‐Vries‐Burgers equation which describes the dynamics of the nonlinear shock structures is derived by using amplitude reductive perturbation technique. The quantitative analysis of impact of different physical parameters on the shock structures is presented here. The electron fluid viscosity plays a pivotal role for the transition of electron acoustic (EA) monotonic to oscillatory shocks and vice versa. It is remarkable that the shock structures are sensitive to the Coriolis force, obliqueness, electron temperature, and the positrons concentration. The present work may be employed to explore and to understand the formation of electron acoustic shock structures in the space and laboratory plasmas with superthermal electrons and positrons under magnetorotating effects, especially in auroral zone, Van Allen radiation belts, planetary magnetospheres, pulsars, black‐hole magnetospheres, etc.

Electron-Acoustic Shock Waves in Cylindrical and Spherical Geometry with Non-Extensive Electrons

We consider nonplanar electron acoustic shock waves composed of stationary ions, cold and non-extensive hot electrons under multiple temperature electrons model in unmagnetized plasma. In this model Modified Korteweg-de Vries–Burger (KdVB) equation is obtained in the cylindrical/spherical coordinates. On the basis of the solutions of KdVB equation, the variation of shock waves features (amplitude, velocity, and width) with different plasma parameters are analyzed. Dissipation effect is introduced in the model by means of kinematic viscosity term. KdVB equation always leads to monotonic solitons and no oscillatory part or peak may appear. It is observed that the combined effect of particle density $$(\alpha )$$, nonextensivity parameter q, electron temperature ratio $$(\theta )$$, and kinetic viscosity $$({{\eta }_{0}})$$ significantly changes the properties of shock waves in nonplanar geometry especially in spherical coordinates. Results could be helpful to analyze the soliton features in laboratory and in the space environments.

Effect of positron density and temperature on the electron acoustic waves in a magnetized dissipative plasma

AbstractZakharov–Kuznetsov–Burgers (ZKB) equation is derived for electron acoustic shock waves in magnetized e–p–i plasma. In the present model, magnetized plasma containing two electron population with kappa distributed positrons has been considered. The propagation characteristics of three dimensional electron acoustic (EA) shock waves have been studied under the influence of magnetic field. Our present plasma model supports the negative potential shocks. Combined action of dissipation (η), superthermality (κ), concentration of positrons (β), temperature ratio of cold electrons to positrons (σ), and magnetic field (ωc) significantly modify the properties of EA shock waves. The width and amplitude of the shock structures are modified by various physical parameters. It is found that shock wave width decreases with increase in β, η0, and ωc whereas it becomes wider for κ and σ. Further, potential of the shock wave decreases as one departs away from superthermal distribution.

Theoretical analysis of planar and non‐planar electron ‐ acoustic shock waves in electron‐positron‐ion plasma

The propagation properties of planar and non‐planar electron acoustic shock waves composed of stationary ions, cold electrons, and q‐non‐extensive hot electrons and positrons are studied in unmagnetized electron‐positron‐ion plasma. In this model, the Korteweg‐de Vries Burgers equation is obtained in the planar and non‐planar coordinates. We have investigated the combined action of the dissipation, non‐extensivity, density ratio of hot to cold electrons, concentration of positrons, and temperature difference of cold electrons, hot electrons, and positrons. It was found that the amplitude of shock wave in e‐p‐i plasma increases when the positron concentration and temperature increase. The same effect is observed in the case of kinematic viscosity η. Furthermore, it is noticed that spherical wave moves faster in comparison to the shock waves in cylindrical geometry. This difference arises due to the presence of the geometry term m/2τ. It should be noted that the contribution of the geometry factor comes through the continuity equation. Results of our work may be helpful to illustrate the different properties of shock wave features in different astrophysical and space environments like supernova, polar regions, and in the vicinity of black holes.

Study of obliquely propagating electron acoustic shock waves with non-extensive electron population

Obliquely propagating electron acoustic shock waves in magnetized plasma composed of stationary ions, cold and non-extensive hot electrons are investigated by deriving Korteweg–de Vries Burgers (KdVB) equation. The tangent hyperbolic method is used to solve the KdVB equation in dissipative medium. The dissipation effect is introduced in the model by means of kinematic viscosity term. The analytical calculations of the KdVB equation shows that the structures (amplitude, velocity and width) of the shock waves are modified significantly with kinematic viscosity (η0), obliqueness (kz) and magnetic field (ωc). Since plasmas are ubiquitously permeated with magnetic field, it is pertinent to explore the characteristics of KdVB equation in a magnetized plasmas.

Obliquely Propagating Electron Acoustic Shock Waves in Magnetized Plasma

Obliquely propagating electron acoustic shock waves in plasma with stationary ions, cold and superthermal hot electrons are investigated in magnetized plasma. Employing reductive perturbation method, Korteweg-de Vries-Burgers equation (KdVB) is derived in the small amplitude approximation limit. The analytical and numerical calculations of the KdVB equation show the variation of shock waves structure (amplitude, velocity, and width) with different plasma parameters. Particle density (α), superthermal parameter (κ), electron temperature ratio (𝜃), kinetic viscosity (η0), obliqueness (kz), and strength of magnetic field (ωc) significantly modify the properties of the shock waves structures. The present investigation is useful to understand dissipative structures observed in space or laboratory plasma where multielectrons population with superthermal electrons are prevalent.

Nonplanar Electron - Acoustic Shock Waves with Superthermal Hot Electrons

Nonplanar electron-acoustic shock waves having superthermal hot electrons are investigated with two temperature electrons model in unmagnetized plasma. Using reductive perturbation method, Korteweg-de Vries-Burgers (KdVB) equation is obtained in the cylindrical/spherical coordinates. Dissipation effect is introduced in the model by means of kinematic viscosity term. On the basis of the solutions of KdVB equation, variation of shock waves features (amplitude, velocity and width) with different plasma parameters are analysed. KdV-Burgers equation always leads to monotonic solitons and no oscillatory peak may appear. The combined effect of particle density (α), superthermal parameter (κ), electron temperature ratio (𝜃) and kinetic viscosity (η0) is numerically studied, and it is observed that these parameters significantly change the properties of the shock waves in nonplanar geometry especially in spherical coordinates. Results could be helpful to analyse the soliton features in laboratory as well as in the space environments.

On the Time Fractional Modulation for Electron Acoustic Shock Waves* *Supported by the Deanship of Scientific Research at Prince Sattam Bin Abdulaziz University under Grant No 2016/01/6239.

Nonlinear features of electron-acoustic shock waves are studied. The Burgers equation is derived and converted to the time fractional Burgers equation by Agrawal’s method. Using the Adomian decomposition method, the shock wave solutions of the time fractional Burgers equation are constructed. The effect of time fractional parameter on the shock wave properties in auroral plasma is investigated.

Nonlinear Electron Acoustic Waves in Dissipative Plasma with Superthermal Electrons

The nonlinear properties of small amplitude electron-acoustic ( EA) solitary and shock waves in a homogeneous system of unmagnetized collisionless plasma consisted of a cold electron fluid and superthermal hot electrons obeying superthermal distribution, and stationary ions have been investigated. A reductive perturbation method was employed to obtain the Kadomstev-Petviashvili-Burgers (KP-Brugers) equation. Some solutions of physical interest are obtained. These solutions are related to soliton, monotonic and oscillatory shock waves and their behaviour are shown graphically. The formation of these solutions depends crucially on the value of the Burgers term and the plasma parameters as well. By using the tangent hyperbolic (tanh) method, another interesting type of solution which is a combination between shock and soliton waves is obtained . The topology of phase portrait and potential diagram of the KP-Brugers equation is investigated.The advantage of using this method is that one can predict different classes of the travelling wave solutions according to different phase orbits. The obtained results may be helpful in better understanding of waves propagation in various space plasma environments as well as in inertial confinement fusion laboratory plasmas.

Propagation of Electron Acoustic Soliton, Periodic and Shock Waves in Dissipative Plasma with a q-Nonextensive Electron Velocity Distribution

The nonlinear properties of small amplitude electron-acoustic (EA) solitary and shock waves in a homogeneous system of unmagnetized collisionless plasma with nonextensive distribution for hot electrons have been investigated. A reductive perturbation method used to obtain the Kadomstev–Petviashvili-Burgers equation. Bifurcation analysis has been discussed for non-dissipative system in the absence of Burgers term and reveals different classes of the traveling wave solutions. The obtained solutions are related to periodic and soliton waves and their behavior are shown graphically. In the presence of the Burgers term, the EXP-function method is used to solve the Kadomstev–Petviashvili-Burgers equation and the obtained solution is related to shock wave. The obtained results may be helpful in better conception of waves propagation in various space plasma environments as well as in inertial confinement fusion laboratory plasmas.

Higher-order corrections to broadband electrostatic shock noise in auroral zone

Nonlinear shock wave structures in collisionless unmagnetized viscous plasma comprised of fluid of cold electron and nonisothermal hot electrons obeying superthermal electron distribution and ions in stationary state are examined. For nonlinear electron acoustic shock waves, a reductive perturbation method was applied to deduce the Burger equation in terms of first order potential. When the shock wave amplitude was enlarged, the steepness and the velocity of the wave sidetrack from Burger equation. We have to resume our calculations to obtain the Burger-type equation with higher order dissipation. The collective solution for the resulting equations has been given by the renormalization method. The effects of spectral index κ, the ratio of the initial equilibrium density of cold electron to hot electrons β, and the kinematic viscosity coefficient η on the broadband electrostatic shock noise in aurora are also argued.

Planar and Nonplanar Shock Waves in a Degenerate Quantum Plasma

AbstractThe 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)

Nonlinear propagation of Electron-acoustic waves in a nonextensive electron-positron-ion plasma

Electron-acoustic shock waves (EASWs) in an unmagnetized electron-positron-ion plasma system (consisting of a cold mobile viscous electron fluid, hot electrons and positrons following the q-nonextensive distribution, and immobile positive ions) are studied analytically. The Burgers equation is derived by using the well-known reductive perturbation method. The basic features (viz. polarity, amplitude, width, phase speed, etc.) of EASWs are briefly addressed. The basic features of EASWs are found to be significantly modified by the effects of nonextensivity of the hot electrons and positrons, the relative number density and temperature ratios, and the kinematic viscosity of the cold electrons. The present investigation can be useful in understanding the fundamental characteristics of EASWs in various space plasmas.

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 electrons and positrons following the q-nonextensive 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 examined 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.

Rarefactive electron-scale shock excitations in a degenerate quantum plasma

The nonlinear propagation of the electron-acoustic shock waves (EASWs) in an unmagnetized, collisionless degenerate quantum plasma system has been investigated theoretically. The plasma system is assumed to contain two distinct groups of electrons (one inertial non-relativistic cold electrons and other inertialess ultra-relativistic hot electrons) and positively charged static ions. The Burgers equation has been derived by employing the reductive perturbation method and numerically examined to identify the basic features (speed, amplitude, width, etc.) of EASWs. It is shown that only rarefactive shock waves can propagate in such a quantum plasma system. It is found that the effect of degenerate pressure and number density of hot and cold electron fluids, and positively charged static ions significantly modify the basic features of EASWs. It is also noted that the inertial cold electron fluid is the source of dissipation for EA waves and is responsible for the formation of shock structures. The implications of this investigation in astrophysical compact objects (viz. non-rotating white dwarfs, neutron stars, etc.) are briefly mentioned.

Theoretical study on the interaction of electron-acoustic shock waves in a generalized Lorentzian plasma

The nonlinear interaction between electron-acoustic shock waves in a dissipative, non-Maxwellian plasma composed of cold fluid electrons, stationary background ions, and inertialess superthermal electrons has been studied. The effects of plasma parameters on the trajectory changes (i.e., phase shifts) of shock waves after their head-on collision is our main concern. The results indicate that the interactions between shocks are different from those of solitons. Also, it is found that the occurrence and variation of trajectory shifts may be due to the combined role played by the dispersion and dissipation of the colliding nonlinear structure.