Nonlinear Electron-acoustic Waves Research Articles

Influences of densities and thermal temperatures of electron and beam fluids on the characteristics of the electron acoustic electrostatic fields and fluid energies

A model of nonlinear electron acoustic electrostatic plasma waves having electron beams has been investigated. The structure of Korteweg–de Vries soliton energy and the corresponding electrostatic field have been discussed. The parametric regimes for wave existence of compressive and rarefactive structures have been examined via auroral zone data. The effects of densities and thermal temperature of electrons and beams on the nature of the electrostatic field and fluid energies have been taken into account.

Bifurcation analysis of electron-acoustic waves in electron beam-plasma with suprathermal electrons

It has investigated the properties of nonlinear electron-acoustic waves propagating in a four-component collisionless, unmagnetized plasma. The system consists of cool inertial background electrons of temperature T c , the cool inertial electron beam of temperature T b , hot inertialess suprathermal electrons modeled by a κ-distribution of temperature T h , and ions. The nonlinear modified Korteweg-de Vries-Burgers (mKdV-Burgers) equation that characterizes the electron acoustic waves in such a plasma model is derived. The wave solutions of the resultant mKdV-Burgers equation are investigated using planar dynamical system bifurcation theory. The unperturbed hot, cool, and beam electron densities and the superthermal electron parameter are revealed to have a considerable influence on the nonlinear electron-acoustic traveling waves and the associated electric fields. The system evolves also monotonic shock waves when the dissipation term dominates over the dispersion term. The current model might be useful for understanding the generation of nonlinear electron-acoustic waves in a variety of astrophysical plasma settings, including the Earth's magnetosphere.

Nonlinear electron-acoustic waves in non-Maxwellian plasma: application in terrestrial magnetosphere

Nonlinear electron-acoustic waves in non-Maxwellian plasma: application in terrestrial magnetosphere

Overtaking interaction of electron-acoustic solitons in Saturn’s magnetosphere

The progression of nonlinear electron-acoustic waves (EAWs) in a magnetized and collision-free plasma made up of cold inertial electrons, inertialess superthermal electrons, and stationary background ions with special reference to Saturn’s magnetosphere (SMS) is explored. The method of reductive perturbation (MRP) is employed to obtain the evolution equation (i.e., Zakharov– Kuznetsov equation (ZKE)) that governs the propagation of electron acoustic solitons (EASs). Using the elegant and efficient Hirota bilinear method (HBM), multi-soliton solutions (MSSs) of the ZKE are determined. The impact of the effects of hot-to-cold electron density ratio, magnetic field (MF) strength, and superthermality on single as well as the interaction of EASs is examined. Estimates of the values of the electric field at several radii of SMS (i.e., 12 R s − 17.8 R s, where R s is the radius of Saturn) are presented, which are found in μV/ m to mV/ m range and are in perfect agreement with the data from Cassini radio and plasma wave science wideband receiver. Moreover, the influence of the relevant plasma parameters on the interaction time and spatial extent of the interacting EASs is also explored.

On weakly nonlinear electron-acoustic waves in the fluid ions, bifurcation analysis, generalized symmetries and series solution propagated via Biswas–Milovic equation

On weakly nonlinear electron-acoustic waves in the fluid ions, bifurcation analysis, generalized symmetries and series solution propagated via Biswas–Milovic equation

Interaction of electron acoustic solitons in auroral region for an electron beam plasma system

The propagation of linear and nonlinear electron acoustic waves (EAWs) in an unmagnetized plasma, comprising dynamical inertial electrons, hot (r, q) distributed electrons, warm electron beam, and immobile ions is studied. The linear dispersion relation is investigated for varying beam velocity. The Korteweg-de Vries (KdV) equation for EAWs is derived in the small amplitude limit. Depending on the beam density, temperature and velocity, we get a critical condition for which the quadratic nonlinearity vanishes from the plasma system. For such a condition, the modified Korteweg de Vries (mKdV) equation, with cubic nonlinearity, is derived, which admits both negative and positive potential solitary structures. It is noted that the spectral indices r and q of the generalized (r, q) distribution, the concentration of the cold, hot and the beam electrons, and the temperature ratios, significantly affect the fundamental properties of the propagation and interaction of electron acoustic solitary waves (EASWs). The types of possible overtaking interaction of two mKdV solitons are investigated. The spatial regime for the two soliton interaction is found to vary in accordance with the variation of single soliton for various plasma parameters. The results of present study may be beneficial to comprehend the interaction between two EASWs in laboratory, space and astrophysical plasmas.

Shocks and solitons in collisional dense laser produced plasmas

The characteristics of nonlinear electron-acoustic waves such as shocks and solitons, are investigated in a three component, dense laser produced plasma consisting of ions and two distinct groups of electrons, using the quantum hydrodynamic model and the standard reductive perturbation method. The modified Korteweg-deVries (mKdV) and Korteweg-deVries-Burgers (KdVB) equations have been derived for the electron-acoustic waves in the plasma. The dependence of both shocks and solitons on various parameters has been extensively studied. It is observed that whenever the density crosses the limit from the classical to the quantum range, the effective potential remains invariant for the solitary profiles; but shows a slight variation for the shock profiles. The collisional effect plays a significant role in the dissipation of solitary waves and the dissipation is larger for higher values of collision frequencies. The results obtained could prove helpful for understanding the parametric dependence of nonlinear waves in highly intense laser plasma interactions.

Weakly nonlinear electron-acoustic waves in the fluid ions propagated via a (3+1)-dimensional generalized Korteweg–de-Vries–Zakharov–Kuznetsov equation in plasma physics

In present work, we discussed the (3+1)-dimensional generalized Korteweg–de-Vries–Zakharov–Kuznetsov equation (gKdV-ZKe) which describes the effect of magnetic field on weak nonlinear ion-acoustic waves studied in the field of plasma comprised of cool and hot electrons. The solutions of gKdV-ZKe are acquired by new modified extended direct algebraic method (MEDAM) and are observed in the form of solitary, shock, singular, shock-singular, solitary-shock and double singular soliton solutions. Moreover, the families of rational solutions are also emerged during the derivation. The results we derive, in this article, are useful to study and verify the analytical solutions with numerical and experimental solutions in plasma physics. The obtained solutions are also illustrated graphically.

Analysis of electron acoustic waves interaction in the presence of homogeneous unmagnetized collision-free plasma

In this research, the transmission and interaction of nonlinear electron acoustic waves (EAWs) in such an unmagnetized, homogeneous, collision-free plasma composed of hot and cold electrons together with stationary ions throughout in the background have been analyzed. For the small-amplitude limit, the Korteweg–de Vries (KdV) equation for (EAWs) have been extracted. For electron acoustic solitary waves (EASWs), using the new extended direct algebraic approach, soliton solutions have also documented. The parametric analysis demonstrated that the hot to cold electron ratio and hot electron superthermal play a key role in changing the (EASWs) amplitude. The family of semi-bright solitons, dark singular solitons, Type 1 as well as 2 single solitons, trigonometric, intermingled hyperbolic and rational solitons was constructed and tested with the assistance of the innovative package software of numerical computations. The results show that the method is clear and efficient, produces analytical results in a generalized form, and these findings can also help resolve the difficulties and predicaments in the relevant disciplines of plasma physics and may be useful for studying the relationship between two (EASWs) in astrophysical and laboratory plasma. The solutions presented in this prototype are the latest in a literature review. For physical interpretation, some randomly selected solutions are shown graphically. Conclusions are held at the end.

Determination of maximum electric field amplitude sustained by electron acoustic solitary waves in an unmagnetized plasma with kappa-distributed electrons

This manuscript investigates the maximum electric field amplitude sustained by nonlinear electron acoustic waves, without losing their initial structure, and propagating in an unmagnetized homogeneous plasma comprising cold inertial electrons, hot kappa-distributed electrons, and stationary ions. Using nonlinear fluid Maxwell’s equations in one dimension, traveling wave solutions have been derived in the wave frame, and negative potential solitary structures have been observed. Furthermore, a pseudo-potential method has been employed to determine the maximum electric field amplitude as a function of the dimensionless Mach number (M), initial density ratio of hot to cold electron species (Rn=nh0nc0), and spectral index (κ) of the hot electron species velocity distribution function. We find that at this maximum electric amplitude, the density of the cold electron fluid becomes singular and thus can be called the wave breaking limit [J. M. Dawson, Phys. Rev. 113, 383 (1959)]. Density singularity is an artifact of the cold fluid plasma model and actually diminishes if one introduces a nonzero temperature to the cold inertial electrons. In that case, we find that the maximum electric field amplitude gets modified and follows the same scaling as the ratio of cold to hot electron species temperature (σ=TecTeh), as obtained by Coffey [Phys. Fluids 14, 1402 (1971)], with electron thermal velocity derived for the wave breaking limit of electron plasma waves in a warm plasma.

Nonlinear coherent structures of electron acoustic waves in unmagnetized plasmas

The propagation dynamics of nonlinear electron acoustic waves (EAW) are explored analytically and numerically in collisionless unmagnetized plasmas. The dynamics of the nonlinear wave is shown to be governed by a Boussinesq equation. In the supersonic range, the wave becomes unstable in the short wave limit. In the nonlinear stage, this unstable mode reaches a maximum values and after that it damps. Different limiting cases of the general solutions are discussed. Analytical and computational results predict that the nonlinear EAW possesses breather structures apart from the usual solitary wave solutions. The results are discussed in the context of astrophysical plasmas.

Arbitrary amplitude electron-acoustic solitons and double layers with Cairns–Tsallis-distributed hot electrons

In the present research paper, propagation attributes of nonlinear electron-acoustic (EA) waves have been investigated in an unmagnetised plasma system consisting of cool fluid electrons and hot electrons observing the hybrid Cairns–Tsallis distribution. Sagdeev pseudopotential method has been used to explore the occurrence of large-amplitude solitons and double layers, focussing on how their characteristics depend upon different parameters. The analysis is further extended to examine the dynamics of large- and small-amplitude double layers. It is revealed that the present plasma system supports the existence of negative potential solitons and double layers in certain region of parameter space. The numerical results show that the Cairns–Tsallis-distributed hot electrons may affect the spatial profiles of EA waves and double layers. The present investigation may be relevant to the observation from Viking satellite in the dayside auroral zone.

Electron acoustic solitary structures and shocks in dense inner magnetosphere finite temperature plasma

In this paper, a theoretical investigation of nonlinear electron acoustic waves in plasmas containing degenerate electrons at finite temperature, non-degenerate cold electrons and stationary ions has been carried out. We have considered various effects and by employing the standard reductive perturbation technique (RPT), the KdV-Burger equation describing the shock fronts has been studied. The absence of viscous term results in the transformation of KDV-B to KdV equation. The shock fronts have been studied with variations in different plasma parameters. Analytical derivation and numerical simulations have been carried out. The results are important in explaining many phenomena in the inner magnetosphere.

Interaction of electron acoustic waves in the presence of superthermal electrons in terrestrial magnetosphere

We have investigated the propagation and interaction of nonlinear electron acoustic waves (EAWs) in a plasma comprising hot (superthermal) and cold electrons and immobile ions. We have derived the Korteweg-de Vries equation for EAWs in the small amplitude limit. Employing the Hirota's Direct method, we have investigated the multisoliton solutions for electron acoustic solitary waves (EASWs). It has been found that the system under consideration admits only rarefactive electrostatic solitary structures. As the observable data are available in terms of electric field rather than electric potential, therefore, we have discussed our results in terms of bipolar electric field structures. The numerical analysis has revealed that the ratio of hot to cold electrons and superthermality of hot electrons play a crucial role in changing the amplitude of EASWs. The interaction of the two solitons and its dependence on the choice of propagation vectors, superthermality, and density ratio have also been elaborated. The results of the present study may be beneficial to comprehend the interaction between two EASWs in astrophysical and laboratory plasmas.

Effects of electron trapping on nonlinear electron-acoustic waves excited by an electron beam via particle-in-cell simulations

By performing one-dimensional particle-in-cell simulations, the nonlinear effects of electron-acoustic (EA) waves are investigated in a multispecies plasma, whose constituents are hot electrons, cold electrons, and beam electrons with immobile neutralized positive ions. Numerical analyses have identified that EA waves with a sufficiently large amplitude tend to trap cold electrons. Because EA waves are dispersive, where the wave modes with different wavenumbers have different phase velocities, the trapping may lead to the mixing of cold electrons. The cold electrons finally get thermalized or heated. The investigation also shows that the excited EA waves give rise to a broad range of wave frequencies, which may be helpful for understanding the broadband-electrostatic-noise spectrum in the Earth’s auroral region.

Electron acoustic waves in a 2-electron, dissipative, quantum magneto plasma

A theoretical study is presented for the oblique propagation of linear and nonlinear electron acoustic waves (EAWs) in a two-electron population, dissipative, quantum magnetoplasma. The linear dispersion relation yields a complex plasma wave frequency $\omega$ , denoting a decaying wave, with the amount of damping directly related to the strength of the dissipative force. The small amplitude analysis for the nonlinear structures using the reductive perturbation technique, gives the Korteweg-de Vries-Burgers equation. The numerical solutions depict a soliton for negligible dissipation and a monotonic shock for relatively large dissipation. For intermediate values, the solutions are damped oscillations. The dispersion of the EAWs gets enhanced with increase in strength of the magnetic field and a higher value of the ratio of hot to cold electron density. The stability analysis is also carried out, and the corresponding phase portraits are plotted to observe the trajectories. Of the two critical points, one is a saddle point, hence always unstable, while the other is a stable focus or a stable node, depending on the relative strengths of the plasma parameters.

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.

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.

A note on the cylindrical solitary waves in an electron-acoustic plasma with vortex electron distribution

In the present work, we consider the propagation of nonlinear electron-acoustic non-planar waves in a plasma composed of a cold electron fluid, hot electrons obeying a trapped/vortex-like distribution, and stationary ions. The basic nonlinear equations of the above described plasma are re-examined in the cylindrical coordinates through the use reductive perturbation method in the long-wave approximation. The modified cylindrical Korteweg–de Vries equation with fractional power nonlinearity is obtained as the evolution equation. Due to the nature of nonlinearity, which is fractional, this evolution equation cannot be reduced to the conventional Korteweg–de Vries equation. An analytical solution to the evolution equation, by use of the method developed by Demiray [Appl. Math. Comput. 132, 643 (2002); Comput. Math. Appl. 60, 1747 (2010)] and a numerical solution by employing a spectral scheme are presented and the results are depicted in a figure. The numerical results reveal that both solutions are in good agreement.

Interactions of nonlinear electron-acoustic solitary waves with vortex electron distribution

In the present work, based on a one dimensional model, we consider the head-on-collision of nonlinear electron-acoustic waves in a plasma composed of a cold electron fluid, hot electrons obeying a trapped/vortex-like distribution, and stationary ions. The analysis is based on the use of extended Poincare, Lighthill-Kuo method [C. H. Su and R. M. Mirie, J. Fluid Mech. 98, 509 (1980); R. M. Mirie and C. H. Su, J. Fluid Mech. 115, 475 (1982)]. It is shown that, for the first order approximation, the waves propagating in opposite directions are characterized by modified Korteweg-de Vries equations. In contrary to the results of previous investigations on this subject, we showed that the phase shifts are functions of both amplitudes of the colliding waves. The numerical results indicate that the waves with larger amplitude experience smaller phase shifts. Such a result seems to be plausible from physical considerations.