Low-frequency Ion-acoustic Waves Research Articles

Dimensionless Zakharov equation; high-frequency Langmuir waves and low-frequency ion-acoustic waves’ interaction

This study investigates the physical significance of the dimensionless Zakharov equation ZE, which theoretically describes the interaction between high-frequency Langmuir waves and low-frequency ion-acoustic waves. Coastal engineering, fluid dynamics, nonlinear optics, and plasma wave physics are all fields of study that explore this relationship. We use the modified Khater method, the auxiliary equation approach, and the Khater II method, all cutting-edge ways to compute, to come up with a wide range of new and different solutions. Other physical aspects of this interaction are briefly explained below. To figure out the originality of our solutions, we have to compare our results to those of other published studies.

Beam-driven whistler mode nonlinear saturation and turbulence in the magnetopause

This work presents a model to understand the generation of whistler turbulence in the magnetic reconnection region of magnetopause by the energetic electron beams (generated by magnetic reconnection process) as observed by magnetospheric multiscale mission [Zhao et al., J. Geophys. Res.: Space Phys. 126, e2020JA028525 (2021)]. In this model, the magnetic reconnection process has been replaced by the energetic electron beam source. Hence, the beam-driven whistler-mode dynamical equation has been set up by anticipating that it will grow from noise level due to beam energy and then will attain large amplitude such that nonlinear effects due to ponderomotive force will lead to the localization of whistler waves, and finally, this will lead to the turbulent state. For this, a non-linear two-dimensional fluid model is developed in which nonlinear interaction between high-frequency whistler wave and low-frequency ion acoustic wave (IAW) is pertinent to the magnetopause region. Due to large-amplitude whistler waves, ponderomotive force components emerge, which are included in IAW's nonlinear dynamics. The system of the dimensionless equations consists of the dynamics of whistler wave and IAW, and this has been solved by the numerical method. The results of the simulation show that the whistler's temporal evolution results in localized structures that eventually lead to turbulence. The relevance of the present investigation to the recent observations has also been pointed out.

Nonlinear evolution of Kinetic Alfvén Wave and the associated turbulence spectra in laser produced plasmas and laboratory simulation of astrophysical phenomena

This investigation presents the nonlinear interplay between pump wave (Kinetic Alfvén Wave (KAW)) and low-frequency ion acoustic wave (IAW) in the magnetized plasma. The model is developed by taking into account the ponderomotive nonlinearity associated due to the pump KAW. The coupled dimensionless equations (pump and IAW) are solved by adopting numerical simulation technique. The deduced results give the localization and filamentary structures of KAW, which eventually become chaotic with the evolution of time. The fundamental physics governing the dynamics of these two waves is influenced by the plasma beta () parameter; thereby affecting the nature of nonlinearity, dispersive properties and magnetic field amplification. The saturated spectra are analogous to that observed for many astrophysical scenarios for low (Chatterjee et al 2017 Nat. Commun. 8 15970) and high beta (White et al 2019 Nat. Commun. 10 1758; Tzeferacos et al 2017 Phys. Plasmas 24 041404) plasma. This theoretical model outlining the nonlinear interaction can be imperative in understanding the dynamics of magnetic field amplification in various astrophysical scenarios.

Numerical simulations of Zakharov’s (ZK) non-dimensional equation arising in Langmuir and ion-acoustic waves

The trigonometric quintic B-spline scheme is used in this research paper to research Zakharov’s (ZK) nonlinear dimensional equation’s numerical solution. The ZK model’s solutions explain the relationship between the high-frequency Langmuir and the low-frequency ion-acoustic waves with many applications in optical fiber, coastal engineering, and fluid mechanics of electromagnetic waves, plasma physics, and signal processing. Three recent computational schemes (the expanded [Formula: see text]-expansion method, generalized Kudryashov method, and modified Khater method) have recently been used to investigate this model’s moving wave solution. Many innovative solutions have been established in this paper to determine the original and boundary conditions that allow numerous numerical schemes to be implemented. Here, the trigonometric quintic B-spline method is used to analyze the precision of the collected analytical solutions. To illustrate the precision of the numerical and computational solutions, distinct drawings are depicted.

Free space Thomson scattering to study high energy density shocks

A free space collective Thomson scattering system has been developed to study pulsed power produced plasmas. While most Thomson scattering diagnostics on pulsed power machines use a bundle of fibers to couple scattered light from the plasma to the spectrometer, this system used free space coupling of the light, which enabled a spatially continuous image of the plasma. Initial experiments with this diagnostic were performed on an inverse wire array generated by a 200 kA, 1100ns rise time pulse power generator. The capabilities of this diagnostic were demonstrated by using the low frequency ion acoustic wave feature of the Thomson scattering spectra to measure the plasma flow velocity. The diagnostic was demonstrated to measure velocities between 20 and 40 km/s with an error of 4.7 km/s when fitting with a 600 μm spatial resolution or 8.9 km/s when fitting with a 150 μm spatial resolution. In some experiments, the diagnostic observed a bow shock in the plasma flow as the scattering intensity increased and flow velocity decreased.

Electron exchange-correlation effects on dispersion properties of electrostatic waves in degenerate quantum plasmas

Based on the quantum Magnetohydrodynamic (QMHD) model, the obliquely propagation of electrostatic waves in degenerate magnetized quantum plasmas with electron exchange-correlation effects are theoretically investigated. The modified linear dispersion relations of electrostatic waves are obtained and discussed in some specific cases. The analytical results clearly show that the dispersion properties of the high frequency electron waves (including the Langmuir wave and upper-hybrid wave) and the low frequency ion acoustic wave are modified by the quantum effects together with the electron exchange-correlation effects. The numerical results depict that the Langmuir wave and upper-hybrid wave can be unstable in the presence of the electron exchange-correlation effects, and it is also evidently indicated that the electron exchange-correlation effects can reduce the phase velocity of the waves, especially in the high wave number region. The corresponding results should be of relevance for identifying electrostatic fluctuations which transport in an inhomogeneous and magnetized quantum plasmas.

Dissipative ion-acoustic solitons in electron-positron-ion plasma with non-thermal electrons and iso-thermal positrons

Abstract Dispersive properties and damping rates of low-frequency ion-acoustic waves are studied in a three-component collisional plasma consisting of non-thermal electrons and iso-thermal positrons and inertial ions. We have shown that the positron to electron ratio p, non-thermality parameter β e and collision rate ν have a significant effect on the dispersion and nonlinear structures. The effective charge screening length and effective ion-acoustic speed in the plasma are analyzed. Dissipative Korteweg de-Vries (KdV) equation derived via the Reductive Perturbation Technique (RPT) expressed exact solutions in the form of dissipative solitary waves. The dynamics are analyzed analytically and numerically. Our observations would be useful in understanding the behavior of astrophysical objects, magnetosphere, the lower ionosphere of the earth surface, and laboratory studies in which ion-neutral collisions are of concern.

The structure of ion-acoustic waves in a low-frequency three-component electron–ion space plasma with two-electron populations

Low-frequency ion-acoustic waves are analysed on the ion time-scale, in a three-component electron–ion space plasma. The solitary waves propagate in the positive x direction relative to an ambient magnetic field $$\vec {B}_0$$ which forms static background for a configuration consisting of cool fluid ions and both warm and hot Boltzmann-distributed electrons with temperatures $$T_{ic},$$ $$T_{ew}$$ and $$T_{eh},$$ respectively. We derive linear dispersion relation for the waves by introducing first-order density, pressure and velocity perturbations into the ion fluid equations. Additionally, the variation in the nonlinear structure of the waves are investigated by carrying out a full parametric analysis utilising our numerical code. Our results reveal that ion-acoustic waves exhibit well-defined nonlinear spikes at speeds of $$M\ge 2.25$$ and an electric field amplitude of $$E_0=0.85.$$ It is also shown that low wave speeds $$(M\le 2),$$ higher densities of the hot electrons, antiparallel drifting of the cool fluid ions, and increased ion temperatures all lead to significant dispersive effects. The ion-acoustic plasma waves featured in this paper have forms that are consistent with those classified as the type-A and type-B broadband electrostatic noise (BEN) observed in the data obtained from earlier satellite missions.

Existence and blowup of solutions for the modified Klein-Gordon-Zakharov equations for plasmas with a quantum correction

This paper studies the existence and blowup of solutions for the modified Klein-Gordon-Zakharov equations for plasmas with a quantum correction, which describe the interaction between high frequency Langmuir waves and low frequency ion-acoustic waves in a plasma considering the quantum effects. Firstly the existence and uniqueness of the local smooth solutions are obtained by the a priori estimates and the Galerkin method. Secondly, and what is more, by introducing some auxiliary functionals and invariant manifolds, the authors study and derive a sharp threshold for the global existence and blowup of solutions by applying potential well argument and the concavity method. Furthermore, two more specific conditions of how small the initial data are for the solutions to exist globally are concluded by the dilation transformation.

Nonlinear interaction of kinetic Alfvén waves and ion acoustic waves in coronal loops

Over the years, coronal heating has been the most fascinating question among the scientific community. In the present article, a heating mechanism has been proposed based on the wave–wave interaction. Under this wave–wave interaction, the high frequency kinetic Alfvén wave interacts with the low frequency ion acoustic wave. These waves are three dimensionally propagating and nonlinearly coupled through ponderomotive nonlinearity. A numerical code based on pseudo-spectral technique has been developed for solving these normalized dynamical equations. Localization of kinetic Alfvén wave field has been examined, and magnetic power spectrum has also been analyzed which shows the cascading of energy to higher wavenumbers, and this cascading has been found to have Kolmogorov scaling, i.e., k−5/3. A breakpoint appears after Kolmogorov scaling and next to this spectral break; a steeper scaling has been obtained. The presented nonlinear interaction for coronal loops plasmas is suggested to generate turbulent spectrum having Kolmogorov scaling in the inertial range and steepened scaling in the dissipation range. Since Kolmogorov turbulence is considered as the main source for coronal heating; therefore, the suggested mechanism will be a useful tool to understand the mystery of coronal loop heating through Kolmogorov turbulence and dissipation.

Localization and implication of oblique whistler wave in the magnetopause region

Nonlinear interaction between highly oblique whistler wave and ion acoustic wave pertinent to magnetopause has been investigated. The density perturbation in whistler wave is supposed to be originated due to the presence of ion acoustic wave in the background. The ponderomotive force components arising due to the high amplitude pump wave, viz., whistler wave are constituted in the nonlinear dynamics of low frequency ion acoustic wave. The coupled nonlinear dynamical equations are then modelled in the form of modified nonlinear Schrödinger equation by considering adiabatic response of low frequency ion acoustic wave. The numerical simulation of this coupled nonlinear equation is performed to study the temporal evolution of nonlinear whistler wave. The obtained simulation results show that the temporal evolution also leads to the cascade of broadband turbulence spectrum at smaller wavelengths. The relevance of the obtained results with the observations of THEMIS spacecraft in the magnetopause region has been pointed out.

Soliton solutions and chaotic motions of the Zakharov equations for the Langmuir wave in the plasma

For the interaction between the high-frequency Langmuir waves and low-frequency ion-acoustic waves in the plasma, the Zakharov equations are studied in this paper. Via the Hirota method, we obtain the soliton solutions, based on which the soliton propagation is presented. It is found that with λ increasing, the amplitude of u decreases, whereas that of v remains unchanged, where λ is the ion-acoustic speed, u is the slowly-varying envelope of the Langmuir wave, and v is the fluctuation of the equilibrium ion density. Both the head-on and bound-state interactions between the two solitons are displayed. We observe that with λ decreasing, the interaction period of u decreases, while that of v keeps unchanged. It is found that the Zakharov equations cannot admit any chaotic motions. With the external perturbations taken into consideration, the perturbed Zakharov equations are studied for us to see the associated chaotic motions. Both the weak and developed chaotic motions are investigated, and the difference between them roots in the relative magnitude of the nonlinearities and perturbations. The chaotic motions are weakened with λ increasing, or else, strengthened. Periodic motion appears when the nonlinear terms and external perturbations are balanced. With such a balance kept, one period increases with λ increasing.

Exchange interaction effects on waves in magnetized quantum plasmas

We have applied the many-particle quantum hydrodynamics that includes the Coulomb exchange interaction to magnetized quantum plasmas. We considered a number of wave phenomena that are affected by the Coulomb exchange interaction. Since the Coulomb exchange interaction affects the longitudinal and transverse-longitudinal waves, we focused our attention on the Langmuir waves, the Trivelpiece-Gould waves, the ion-acoustic waves in non-isothermal magnetized plasmas, the dispersion of the longitudinal low-frequency ion-acoustic waves, and low-frequency electromagnetic waves at Te ≫ Ti. We have studied the dispersion of these waves and present the numeric simulation of their dispersion properties.

Small amplitude ion acoustic solitons in a weakly magnetized plasma with anisotropic ion pressure and kappa distributed electrons

The Zakharov–Kuznetzov (ZK) equation is derived for nonlinear electrostatic waves in a weakly magnetized plasma in the presence of anisotropic ion pressure and superthermal electrons. The anisotropic ion pressure is defined using Chew–Goldberger–Low (CGL) while a generalized Lorentzian (kappa) distribution is assumed for the non-thermal electrons. The standard reductive perturbation method (RPM) is employed to derive the two dimensional ZK equation for the dynamics of obliquely propagating low frequency ion acoustic wave. The influence of spectral index (kappa) of non-thermal electron on the soliton is discussed in the presence of anisotropic ion pressure in plasmas. It is found that ion pressure anisotropy and superthermality of electrons affect both the width and amplitude of the solitary waves. On the other hand the magnetic field is found to alter the dispersive property of the plasma only, and hence the width of the solitons is affected while the amplitude of the solitary waves is independent of external magnetic field. The numerical results are also presented for illustrations.

Nonlinear Interaction of 3D Kinetic Alfvén Waves and Ion Acoustic Waves in Solar Wind Plasmas

We have investigated the nonlinear interaction between a 3D kinetic Alfven wave (KAW) and an ion acoustic wave (IAW) in solar wind plasmas. A set of dimensionless equations was developed that describes the pump KAW perturbed by a low-frequency ion acoustic wave. The dependence of the growth rate of the modulational instability on the perturbation wave number was studied. We simulated numerically the dynamical equation of KAW with a pseudo-spectral method, taking ponderomotive nonlinearity into account. The 3D KAW itself propagates in the form of a vortex beam in a magnetised plasma, which manifests the presence of orbital angular momentum of the wave eigenmodes. We discuss the evolution of these vortex structures. Our results reveal that the Kolmogorov scaling is followed by a steeper scaling of power spectra, which is consistent with the solar wind observations by the Cluster spacecraft. We discuss the relevance of our investigation for solar wind plasmas.

Electrostatic solitons in rotating dusty plasmas with anisotropic ion pressure

The Zakharov-Kuznetsov (ZK) equation is derived for electrostatic wave in a rotating magnetoplasma with anisotropic ion pressure and in the presence of stationary charged dust particles. The anisotropic ion pressure is defined using double adiabatic Chew-Golberger-Low (CGL) theory. The reductive perturbation method is employed to study the dynamics of obliquely propagating low frequency ion acoustic wave with adiabatic ions. It is found that the ion pressure anisotropy, polarity, density of the dust particles and rotational frequency have significant effects on the formation nonlinear structures in rotating magnetized dusty plasmas. The numerical results are also presented for illustration.

Electrostatic Waves in Weakly Magnetized Quantum Plasmas

By using the quantum magnetohydrodynamic model, the electrostatic waves in weakly magnetized quantum plasmas are investigated. The electrons are treated as a quantum and magnetized species, while the ions are classical unmagnetized ones. The general dispersion relations are derived. It is shown that, both the high frequency electron waves (Langmuire wave and upper-hybrid wave) and the low frequency ion acoustic wave can propagate when the plasmas are cold.

Kinetic dispersion of Langmuir waves. I. The Langmuir decay instability

We derive a fully kinetic, three-dimensional dispersion relation for Langmuir waves with a focus on the Langmuir decay instability (LDI). The kinetic dispersion is compared to the standard fluid dispersion found with an equation of state (EOS) closure. The EOS closure fails to capture the intricacies of the nonlinear pressure when high frequency electron plasma waves (EPWs) couple to low frequency ion acoustic waves (IAWs). In particular, we find discrepancies in the kλd scaling of the LDI growth rate, where k is the wavenumber of the incident EPW and λd is the Debye length. As a result, the kinetic dispersion relation for LDI results in instability thresholds that can be in excess of twice those predicted by the fluid theory. Both the fluid and kinetic dispersion relations predict a nonlinear frequency shift due to the beating of the pump and scattered EPWs, but again the kλd scaling of these frequency shifts differ. In addition, the kinetic dispersion predicts a nonlinear reduction in the IAW damping from the three-wave interaction.

Ion acoustic waves in pair-ion plasma: Linear and nonlinear analyses

Linear and nonlinear properties of low frequency ion acoustic wave (IAW) in pair-ion plasma in the presence of electrons are investigated. The dispersion relation and Kadomtsev–Petviashvili equation for linear/nonlinear IAW are derived from sets of hydrodynamic equations where the ion pairs are inertial while electrons are Boltzmannian. The dispersion curves for various concentrations of electrons are discussed and compared with experimental results. The predicted linear IAW propagates at the same frequencies as those of the experimentally observed IAW if ne0∼104 cm−3. It is found that nonlinear profile of the ion acoustic solitary waves is significantly affected by the percentage ratio of electron number density and temperature. It is also determined that rarefactive solitary waves can propagate in this system. It is hoped that the results presented in this study would be helpful in understanding the salient features of the finite amplitude localized ion acoustic solitary pulses in a laboratory fullerene plasma.

Pulsar eclipsing mechanisms: the effect of photon-beam-induced acoustic turbulence

Pulsar eclipse due to induced three-wave interactions involving low-frequency acoustic turbulence is discussed. We consider both the case of electron acoustic waves when the ion temperature Ti is higher than the electron temperature Te and that of ion acoustic waves whenTe >Ti. In each case the corresponding growth rate for low-frequency acoustic waves induced by a high-frequency photon beam is evaluated. For Ti > Te, the maximum growth rate for electron acoustic waves depends strongly on Ti/Te and may be comparable to that of a Langmuir counterpart for sufficiently large temperature ratio Ti/Te. It is shown that induced scattering off electron acoustic waves can be important and can cause pulsar eclipse. We show also that for Te > Tiand in the small-angle approximation, growth of low-frequency ion acoustic waves due to the photon beam is always slower than Langmuir waves and the corresponding induced scattering is less effective than induced Raman scattering. Thus, induced Brillouin scattering involving low-frequency ion acoustic waves cannot be the main cause for pulsar eclipses.