Electrostatic Solitons Research Articles

Nonlinear Structures of Dispersive Electrostatic Solitary Waves in a Multi‐Ion Partially Ionized Plasma

ABSTRACTThe nonlinear structure and dynamics of dispersive solitons and breather waves described by Korteweg‐de Vries and nonlinear Schrödinger equations are studied. The theoretical and numerical study of the generalized hydrodynamic equations, accounting for wave dissipation and particle production‐loss mechanism, are considered. The reductive expansion method has been used in the context of the instability problem of multi‐fluid dynamics, applied to the study of electrostatic solitons and ion‐acoustic waves. A nonlocal model of interacting solitary‐breather waves has been presented. Applications of the theory, concerning the ion streaming instability in the framework of plasma physics, are presented.

Ion acoustic solitons collision in spin-polarized relativistic quantum plasma

The dynamics of electrostatic ion acoustic solitons collision in relativistic magnetized spin-polarized plasma is studied using a Magnetized Relativistic Quantum Hydrodynamics model. The plasmas components are relativistic degenerate electron with spin-up (n e↑) and spin-down (n e↓) concentrations, and relativistic inertial classical ions. In two-dimensional plasma geometry, a homogeneous external magnetic field is provided along the z-direction, i.e. . The extended Poincare Lighthill Kuo (PLK) approach is used to calculate the Kortewegde Vries equations for oppositely moving ion-acoustic solitons. Before and after collision, their trajectories and associated phase shifts are computed. Only negative polarity pulses of ion acoustic solitons are observed in our stated relativistic magnetized plasma. The spin density popularization ratio κ is shown to have a significant impact on the phase shifts of colliding solitons. It is found that when κ increases, one soliton's phase shift increases while the other soliton's phase shift decreases. The relativistic effects are also analyzed numerically and found that the phase shift of colliding ions acoustic solitons grows as the relativistic component rises from weakly to ultra-relativistic. It is observed that the phase shift of both solitons is to be dependent on their phase velocity with each other. Our research is noteworthy in that it focuses on, the astrophysical systems such as white dwarf, neutron star and pulsar.

Dynamical energy effects in subsonic collapsing electrostatic Langmuir soliton

The nonlinear characteristic of subsonic Langmuir collapsing waves and energy has been explored using a mathematical system for plasma fluids. New electrostatic Langmuir structures such as supersolitary, breather dissipative, and supersoliton structures have been obtained via a mathematical robust solver. The obtained structures become important in constrained relation between the nonlinearity, dispersion, and dissipative effects in the model. It was discovered that the type of Langmuir structures controlled the collapsing energy for density turbulence. Breather shock forms in time are used to characterize the collapsing Langmuir dissipative waves. This structure mainly affects the electric field and related densities in the subsonic case. Finally, the results explored here may be applicable to the observation of energy collapsing Langmuir solar wind waves.

Effects of ion to electron temperatures on electrostatic solitons with applications to space plasma environments

Electrostatic solitary waves (ESW) and solitons are widely observed nonlinear plasma phenomena in various space environments, which may be generated by the electron streaming instability as shown in many particle simulations. The predicted electron holes associated with the ESW, however, are not observed by the recent high resolution spacecraft. This raises a possibility for the ion acoustic solitons being the potential candidate, which are described by the Sagdeev potential theory with hot electrons and cold ions being treated by the kinetic equilibrium and fluid models, respectively. The assumption of Ti/Te=0 adopted in the theoretical models for ion acoustic solitons, however, imposes a great constraint for the space applications considering that Ti/Te may vary in a wide range of 0.1–10 in the Earth's space environments. This paper examines the effect of Ti/Te on ion acoustic solitons by including a finite temperature in the fluid equations for the ions, which, however, can no longer be solved based on the standard Sagdeev potential method. It is shown based on the nonlinear theory that larger Ti/Te may result in larger propagation speeds and the critical flow velocity for the existence of steady solitons increases with increasing Ti/Te values. The nonlinear solutions for various Ti/Te values may be characterized by an effective Mach number. For Ti/Te ≫ 1 the hot ions and cold electrons shall be described by the kinetic and fluid models, respectively, which may result in negative electric potentials opposite to the standard ion acoustic solitons. Comparisons between the model calculations and observations are made.

Effect of Ion Temperature Anisotropy on Modulated Electrostatic Waves and Envelope Solitons in a Magnetized Plasma

The modulational instability (MI) of electrostatic waves, i.e., slow and fast electrostatic modes, is investigated in a magnetized plasma in the presence ion pressure anisotropy. The anisotropic ion pressure is defined using the double adiabatic Chew–Goldberger–Low (CGL) theory. The nonlinear Schrödinger equation (NLSE) is derived to study the amplitude modulation of obliquely propagating electrostatic waves in a magnetized plasma using the Krylov-Bogoliubov–Mitropolsky (KBM) method. The dispersive and nonlinear coefficients, i.e., <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$P$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> , respectively, of NLSE are obtained which depends on system parameters such as plasma density, the magnetic field intensity, wave propagation angle <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\theta $ </tex-math></inline-formula> , and ion parallel and perpendicular temperatures (anisotropy effects), respectively. The modulationally unstable regions ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$PQ&gt;0$ </tex-math></inline-formula> ) of modulated slow [or ion-acoustic wave (IAW)] and fast [or ion-cyclotron wave (ICW)] electrostatic modes are investigated numerically in a magnetized plasma with ion temperature anisotropy, and the contour plots of product <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$PQ&gt;0$ </tex-math></inline-formula> with wave propagation angle <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\theta $ </tex-math></inline-formula> and critical wave numbers are also presented. It is found that the unstable regions for modulated IAW and ICW are extended to large wave propagation angle <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\theta $ </tex-math></inline-formula> and its corresponding critical wave numbers in the presence of ion temperature anisotropy in comparison to cold ions’ case. The existence of magnetized plasma with ion pressure anisotropy in different space plasma regions and in the laboratory experiments is also pointed out.

Formation and interaction of multi-dimensional electrostatic ion-acoustic solitons in two-electron temperature plasmas

Ion-acoustic waves are investigated in an unmagnetized collisionless plasma comprising dynamical ions and inertialess cold and hot (C–H) electrons expressed by Maxwellian, kappa, and (r, q) distributions. The reductive perturbation theory is applied for deriving a modified Kadomtsev–Petviashvili (mKP) equation to examine the characteristics of ion-acoustic structures (solitary waves, IASWs). The Hirota bilinear formalism is used to investigate the propagation of a single soliton and the interaction of two solitons with special reference to space plasmas. It is found that ratio of number density of cold to hot electrons and non-Maxwellian nature of cold electrons not only affect the propagation characteristics of single mKP solitons but also alter the interaction time of the IASWs. It is found that the swiftness of the interaction of solitons for flat-topped distribution surpasses both kappa and Maxwellian distributions. It is also found that the bipolar and tripolar structures depend on the ratio of the propagation vectors. The ranges of electric field amplitude for the IASWs are calculated for C–H electron distributions corresponding to Saturn's B-ring and the region just beyond terrestrial magnetopause, and are shown to agree with Cassini wideband receiver observational data and wideband plasma wave instrument's waveform data.

Homotopy Study of Spherical Ion-Acoustic Waves in Relativistic Degenerate Galactic Plasma

In this work, we start with the ion-acoustic waves in galactic plasma with the degenerate matter. We use the reductive perturbation technique to derive the spherical Kadomtsev–Petviashvili (SKP) equation. We next employ homotopy-aided symbolic simulation (HASS) to study the evolution of the spherical solitary wavefront. We compare the results obtained by HPM and RPT. To understand how the system behaves, we transform the evolutionary equations into a dynamical system. The phase portraits and the superperiodic waves reflect on the intricate processes within the plasma and determine the stability criteria and possible situations of chaos. The work will find applications in many astrophysical observations, such as electrostatic wave modes, gamma-ray bursts, and double-layer solitons. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PACS</i> —95.30.Qd, 52.65.-y, 52.35.-g, 52.35.Tc.

Dynamics of dust-ion acoustic cnoidal and solitary pulses in a magnetized collisional complex plasma

ABSTRACT The diagnostic of magnetized radio frequency complex plasma via probing techniques and spectroscopy is challenging. However, a self-excited dust ion acoustic waves (DIAWs) have been observed employing laser scattering. Inspired by the current high enthusiasm for the theoretical description of complex plasma, we study the propagation of DIAWs in a three-dimensional collisional and magnetized dusty plasma medium. We consider the fluid model for dust and ion particles, while we neglect the inertia of electrons considering the Boltzmann distribution. A linear dispersion relation is obtained and a nonlinear modified Zakharov–Kuznetsov equation is derived utilizing the reductive perturbation technique. The effects of ion-neutral and dust-neutral collisions on the dynamics of the nonlinear DIAWs are considered. The phase portrait analysis and numerical illustration of a rarefactive DIA cnoidal waves and solitons are also presented. Our findings agree with experimental observations by Choudhary M, Bergert R, Mitic S, and Thomas MH. [Influence of external magnetic field on dust acoustic waves in a capacitive rf discharge. Contrib Plasma Phys. 2020;60:e201900115] as the growth of nonlinear periodic waves is recorded when the magnetic field is roughly 0.05 T and vanishes when the magnetic field is close to 0.1 T. Moreover, the model reveals that the electrostatic cnoidal and soliton waves propagate with low frequencies up to 140 Hz.

Radio Emission by Soliton Formation in Relativistically Hot Streaming Pulsar Pair Plasmas

Abstract A number of possible pulsar radio emission mechanisms are based on streaming instabilities in relativistically hot electron–positron pair plasmas. At saturation, the unstable waves can, in principle, form stable solitary waves, which could emit the observed intense radio signals. We searched for the proper plasma parameters that would lead to the formation of solitons, and investigated their properties and dynamics as well as the resulting oscillations of electrons and positrons that possibly lead to radio wave emission. We utilized a one-dimensional version of the relativistic particle-in-cell code ACRONYM initialized with an appropriately parameterized one-dimensional Maxwell–Jüttner particle distribution in velocity space to study the evolution of the resulting streaming instability in a pulsar pair plasma. We found that strong electrostatic superluminal L-mode solitons are formed for plasmas with normalized inverse temperatures ρ ≥ 1.66 or relative beam drift speeds with Lorentz factors γ &gt; 40. The parameters of the solitons fulfill the conditions for wave emission. For appropriate pulsar parameters the resulting energy densities of superluminal solitons can reach 1.1 × 105 erg cm−3, while those of subluminal solitons reach only 1.2 × 104 erg cm−3. Estimated energy densities of up to 7 × 1012 erg cm−3 suffice to explain pulsar nanoshots.

Solar wind interaction with dusty plasma produces electrostatic instabilities and solitons

It is shown that the solar wind interaction with dusty plasma in planetary magnetospheres gives rise to electrostatic instabilities and solitary structures. Non-Maxwellian electrons increase the growth rate of shear flow instability and reduce the amplitude of solitary pulses formed by the modified dust ion acoustic wave (mDIAW) in nonlinear regime. Dust number density plays the similar role. The kappa ( $\kappa $ ) and Cairns distribution functions are used to take into account the role of non-Maxwellian electrons in the presence of stationary dust and flowing ions along the external magnetic field with inhomogeneous velocity. This theoretical model is general and it can be applied to various dusty plasma environments such as interstellar medium, cometary tails and planetary magnetospheres. Here it has been applied to the Saturn’s $F$ -ring plasma.

Evolution of ion-acoustic soliton waves in Venus’s ionosphere permeated by the solar wind

Abstract Wave observations are as yet an important technique to resolve fine structures in the plasma that cannot be identified by different instruments. In this way, we proposed the generation of electrostatic solitary waves during the interaction between the solar wind particles and Venus’s atmosphere at high altitude. The plasma system is treated as a multicomponent unmagnetized plasma consists of background electrons, positive ions (H+ and O+), and streaming solar wind electrons and protons. The dispersion relation is derived for linear waves and the stability/instability of electrostatic wavepackets is investigated. The dependence of the instability growth rate on the ion beam speed has been analyzed. Stability analysis reveals the occurrence of an imaginary frequency part in three regions. Using the reductive perturbation theory, the set of fluid equations is reduced to the Korteweg-de Vries (KdV) equation to describe the evolution of small but finite amplitude soliton waves. The model predicts the propagation of electrostatic soliton waves with an electric field of 1.2 mV/m and a time duration of 0.4 ms. The output of the fast Fourier transform of the electric field pulse is a broadband in the frequency range of ~ 3.2 to 199.5 kHz. It is proposed that the model can be a decent possibility for clarifying the observation of a wide variety of plasma oscillations by Galileo flyby of Venus.

Electrostatic dust‐acoustic envelope solitons in an electron‐depleted plasma

AbstractA standard nonlinear Schrödinger equation has been established by using the reductive perturbation method to investigate the propagation of electrostatic dust‐acoustic waves, and their modulational instability as well as the formation of localized electrostatic envelope solitons in an electron‐depleted unmagnetized dusty plasma system comprising opposite polarity dust grains and super‐thermal positive ions. The relevant physical plasma parameters (viz., charge, mass, number density of positive and negative dust grains, and super‐thermality of the positive ions, etc.) have rigorous impact to recognize the stability conditions of dust‐acoustic waves. The present study is useful for understanding the mechanism of the formation of dust‐acoustic envelope solitons associated with dust‐acoustic waves in the laboratory and space environments.

Proliferation of soliton, explosive, shocklike, and periodic ion-acoustic waves in Titan's ionosphere

We report on many electrostatic nonlinear structures, namely, soliton, explosive, shocklike, and periodic waves, which may exist due to the dynamics of different ion species in Titan's ionosphere. Using the latest available observations of Titan at an altitude of ≈ 1300 km, the main ion components are HCNH+, C2H5+, and C3H5+. The dynamics of these waves are described by the Korteweg–de Vries (KdV) equation. Using the G′/G–expansion method, we obtain a class of solutions that elucidate these nonlinear structures. As the wave amplitude increases, both the width and velocity of the wave deviate from the prediction of the KdV equation. To describe the waves of larger amplitude, the higher-order dispersion has to be taken into account. The G′/G–expansion method is used, for the first time, to solve the KdV equation with higher-order dispersion. We compare between both KdV and higher-order dispersive KdV solutions, i.e., soliton, explosive, shocklike, and periodic waves.

Precursor magneto-sonic solitons in a plasma from a moving charge bunch

The nature of fore-wake excitations created by a charge bunch moving in a magnetized plasma is investigated using particle-in-cell simulations. Our studies establish for the first time the existence of precursor magneto-sonic solitons traveling ahead of a moving charge bunch. The nature of these excitations and the conditions governing their existence are delineated. We also confirm earlier molecular dynamic and fluid simulation results related to electrostatic precursor solitons obtained in the absence of a magnetic field. The electromagnetic precursors could have interesting practical applications such as in the interpretation of observed nonlinear structures during the interaction of the solar wind with the Earth and the Moon and may also serve as useful tracking signatures of charged space debris traveling in the ionosphere.

Nonlinear cnoidal waves and solitary structures in unmagnetized plasmas with generalized (r, q) distributed electrons

Theoretical investigation of electrostatic ion acoustic periodic (cnoidal) waves and solitons with warm ions is presented with electrons that are assumed to follow the double spectral index distribution function. The double spectral index distribution imitates effectively the distributions that have often been seen in space plasmas. Using the standard reductive perturbation technique, the Korteweg–de Vries (KdV) equation is derived which describes the nonlinear periodic waves with appropriate boundary conditions. By using planar dynamical system to this KdV equation, the existence of solitary wave solutions and periodic wave solutions are found. It is shown that changing the electron population in regions of low and high phase space density regions alter the propagation characteristics of nonlinear ion acoustic periodic and solitary structures. Comparison of non-Maxwellian distribution functions with Maxwellian distribution is also made. The importance of the present work with regard to space plasmas is also pointed out.

Electrostatic flat-top solitons near double layers and triple root structures in multispecies plasmas: How realistic are they?

Electrostatic flat-top solitons are a new acoustic-type nonlinear mode and found to be a generic feature accompanying the occurrence of double layers and/or triple root structures, in multispecies plasmas admitting the latter. Their existence domains can be parameterized by the difference between their velocities and the double layer or triple root velocities, but these velocity differences turn out to be extremely small, of the order 10−5 or less. The onset of their flat top character in the electrostatic potential is clearly seen in the corresponding electric field or charge density profiles. However, even at the limit of the numerical accuracy for vanishing velocity differences, their profiles are still soliton-like, very unlike those of double layers or triple root structures. So although the Sagdeev potential varies continuously as the structure velocity approaches that of the double layer or triple root structure, the character of the nonlinear modes changes in a discontinuous manner. For sufficiently wide flat-top solitons, the electric field signature looks very much like two unipolar signals with opposite polarities, where unipolar electric fields typically characterize double layers or triple root structures. We are not aware of flat-top solitons having been reported to date, and their extremely limited existence range raises the question of whether they may be observable at all, unless helped by a fortunate stroke of serendipity. This topic requires suitable numerical simulations to ascertain their stability and interaction properties.

Electrostatic solitary pulses in magnetized relativistic spin-polarized quantum plasma

A Magnetized Relativistic Quantum Hydrodynamics model is used to study the behavior of low fRequency electrostatic solitons in relativistic magnetized spin-polarized quantum plasma. The constituents of the plasma are inertia-less relativistic quantum electrons having concentration of both spin-up and spin-down species, and relativistic classical ions. We have used two-dimensional geometry in which a uniform ambient magnetic field is applied in the z-direction i.e. . The linear analysis shows the presence of two types of modes; slow (acoustic) mode and a fast Langmuir-like mode. A nonlinear Zakharov–Kuznetsov (ZK) type equation is derived for the electrostatic potential by using reductive perturbation technique. The dependence of the spin density polarization ratio κ on the properties of solitary wave profile is being investigated. It has been demonstrated that amplitude as well as width of the soliton depend significantly on the spin density polarization ratio, obliqueness and relativistic effects. We have also observed that the soliton solution of the ZK equation is unstable to the oblique perturbations. The instability growth rate varies appreciably with the density polarization and relativistic effects.

Periodic and localized structures in a degenerate Thomas-Fermi plasma

The propagation of electrostatic ion-acoustic cnoidal waves (IACWs) and solitons in a degenerated electron-positron-ion plasma with cold inertial ions and Thomas-Fermi distributed electrons and positrons is investigated. Adopting a reductive perturbation technique (RPT), the Korteweg-de Vries (KdV) equation is obtained and its cnoidal waves (CWs) solution is analyzed. The plasma configuration parameters (namely, the positron concentration and the Fermi temperature ratio of electron-to-positron) are shown to affect remarkably the dynamical characteristics of IACWs and solitons. The relevance of the present work to superdense white dwarfs is pointed out.

Investigations of energy and an exchange of energies between electrostatic solitons: higher-order corrections and efficiency improvement of semiconductor plasmas

ABSTRACT Investigations of the nonlinear excitation and collisions of electrostatic solitons in a dense semiconductor plasma composed of electrons and holes are improved by using the higher-order corrections. Applying the extended Poincaré-Lighthill-Kuo (EPLK) method to obtain the Korteweg–de Vries (KdV) equations, which govern the nonlinear excitation of electrostatic solitons. Furthermore, the phase shift equations due to the collisions between electrostatic solitons are obtained. A theoretical analysis is improved by employing the KdV equations with the effects of the fifth – order dispersion terms. The numerical illustrations demonstrate that the higher-order soliton energy depends significantly on the quantum semiconductor plasma number density. On the other hand, the density of the semiconductor plasma has a weak effect on the lowest-order soliton energy. Therefore, one has to be careful about the choosing semiconductor plasma parameters to avoid any deficiency of the modern semiconductor devices.

Effect of Pressure Anisotropy on Nonlinear Periodic Waves in a Magnetized Superthermal Electron-Positron-Ion Plasma

The propagation properties of electrostatic cnoidal waves (periodic waves) and solitons are studied in a magnetized electron-positron-ion (EPI) plasma bearing ion pressure anisotropy and superthermality. In a two-dimensional geometry, we considered the ions to be warm having pressure anisotropy due to magnetic field. The anisotropic ions are modeled via double adiabatic Chew-Golberger-Low (CGL) theory and the lighter species (electron and positron) are following kappa distributions. A Korteweg-de Vries (KdV)-type equation is derived by employing reductive perturbation technique, and obtained the nonlinear periodic waves solutions with appropriate boundary conditions. The anisotropy in the ion thermal pressure relative to the external magnetic field (different values in parallel and perpendicular directions) have significant effects on the characteristics of cnoidal waves. It is observed that by increasing the ion parallel and perpendicular pressure (keeping the relative anisotropy) tends to reduce the wavelength of the cnoidal wave structure, while the amplitude tends to increase. The influence of superthermality of electron and positron, the positron content and strength of the external magnetic field on the cnoidal waves are studied in detail. Furthermore, phase portrait analysis is carried out and traced out the equilibrium points around which nonlinear periodic waves can be formed. The saddle points which correspond to the homoclinic orbits are also shown. The investigation can be useful in exploring the nonlinear wave dynamics in both laboratory and space plasma where ion pressure anisotropy and superthermality exist.