Electrostatic Solitons Research Articles

Electrostatic wave instability and soliton formation with non-thermal electrons in O-H plasma of ionosphere

It is pointed out that the presence of non-thermal electrons and protons in oxygen plasma of the ionosphere plays a destructive role in the formation of electrostatic structures by nonlinear ion acoustic waves (IAWs). On the other hand, linear electrostatic perturbations at different IAW frequencies are excited by the field-aligned shear flow in oxygen-hydrogen plasma of the upper ionosphere, and non-thermal electrons cause an increase in the growth rate. The excitation of IAW and formation of solitary structures in the ionosphere are investigated at altitudes of 600 km and 1000 km in the auroral region.

On the role of separatrix instabilities in heating the reconnection outflow region

A study of the role microinstabilities at the reconnection separatrix can play in heating the electrons during the transition from inflow to outflow is being presented. We find that very strong flow shears at the separatrix layer lead to counterstreaming electron distributions in the region around the separatrix, which become unstable to a beam-type instability. Similar to what has been seen in earlier research, the ensuing instability leads to the formation of propagating electrostatic solitons. We show here that this region of strong electrostatic turbulence is the predominant electron heating site when transiting from inflow to outflow. The heating is the result of heating generated by electrostatic turbulence driven by overlapping beams, and its macroscopic effect is a quasi-viscous contribution to the overall electron energy balance. We suggest that instabilities at the separatrix can play a key role in the overall electron energy balance in magnetic reconnection.

Electrostatic solitons and Alfvén waves generated by streaming instability in electron-positron plasmas.

Electron-positron plasmas may be present in laboratory experiments and certain astrophysical environments. Due to the inertia symmetry there have been some debates about whether the nonlinear electrostatic solitons generated easily in electron-proton plasmas may develop in electron-positron plasmas. In this study we show the formation of electrostatic solitons and electromagnetic Alfvén waves in extensive magnetized electron-positron plasma system generated by streaming instabilities based on electromagnetic particle simulations along with fluid theory analyses. In particular, the four-component beam-plasma system may lead to the formation of interlacing electron and positron solitons in the early evolution stage (say, t<20ω_{p}^{-1}, where ω_{p}^{} is the plasma frequency) and large-amplitude Alfvén waves in the later phase (say, t>150ω_{p}^{-1}). The magnetic-field perturbations are generated by the beam and firehose-type instabilities associated with temperature anisotropy of T_{∥}>T_{⊥} resulting from the parallel plasma heating by the electrostatic instability. It is shown that the growth rates and the dominant wavelengths of both electrostatic and electromagnetic instabilities are consistent with the fluid theory. The coexistence of electrostatic solitons and electromagnetic Alfvén waves with significant magnetic field fluctuations in the same system is a unique feature of electron-positron plasmas and the unified theory behind the formation mechanisms is well addressed in the paper.

Vertical sizes of 1-D and 2-D electrostatic solitons with nonextensive and trapped electrons in the upper ionosphere

The vertical sizes of one-dimensional (1-D) and two dimensional (2-D) electrostatic solitons are estimated in the oxygen-hydrogen (O – H) and pure oxygen plasmas of the upper ionosphere taking into account the effects of non-extensive and trapped electrons. The field-aligned flow of oxygen ions is also considered. It is found that both electron trapping and non-extensivity play a constructive role in the formation of 1-D and 2-D solitary structures. The vertical size of the solitons is not known through observations, but here it is pointed out that the vertical size of these structures should be of the order of a few meters at the altitude of 800 km in the 1-D case. On the other hand, in the 2-D case, the vertical size is much larger than the horizontal size and it turns out to be of the order of a few kilometers, while the width is about a few hundred meters in agreement with the observations.

Solar wind interaction with dusty plasmas produces instabilities and solitary structures

It is pointed out that the solar wind interaction with dusty magnetospheres of the planets can give rise to purely growing instabilities as well as nonlinear electric field structures. Linear dispersion relation of the low frequency electrostatic ion-acoustic wave (IAW) is modified in the presence of stationary dust and its frequency becomes larger than its frequency in usual electron ion plasma even if ion temperature is equal to the electron temperature. This dust-ion-acoustic wave (DIAW) either becomes a purely growing electrostatic instability or turns out to be the modified dust-ion-acoustic wave (mDIAW) depending upon the magnitude of shear flow scale length and its direction. Growth rate of shear flow-driven electrostatic instability in a plasma having negatively charged stationary dust is larger than the usual D’Angelo instability of electron-ion plasma. It is shown that shear modified dust ion acoustic wave (mDIAW) produces electrostatic solitons in the nonlinear regime. The fluid theory predicts the existence of electrostatic solitons in the dusty plasmas in those regions where the inhomogeneous solar wind flow is parallel to the planetary or cometary magnetic field lines. The amplitude and width of the solitary structure depends upon dust density and magnitude of shear in the flow. This is a general theoretical model which is applied to dusty plasma of Saturn’s F-ring for illustration.

Nonlinear electrostatic periodic waves and solitons in an inhomogeneous magnetized dusty plasma

Low frequency nonlinear electrostatic cnoidal and solitary waves are investigated in an inhomogeneous magnetized dusty plasma in the presence of shear flow. The Sagdeev potential approach is used to find the nonlinear wave solution. It is found that nonlinear electrostatic potential rarefactive (dip) structures are formed for cnoidal waves and solitons in a magnetized inhomogeneous dusty plasma instead of compressive (hump) nonlinear electrostatic wave structures formed in an inhomogeneous magnetized electron-ion plasma. The amplitude of the nonlinear electrostatic potential structure is found to be increased in the case of decreasing shear flow parameter values in comparison with the case of increasing shear flow parameter values. The D'Angelo instability in an inhomogeneous magnetized dusty plasma in the presence of shear flow is also discussed. The numerical plots are also presented for illustrations which are applicable to space dusty plasma regions containing shear flows. The Hamiltonian function of such a dynamical planar system is also discussed for its phase portrait analysis.

Effect of non-Maxwellian electrons on shear flow modified ion acoustic solitons

Dynamics of shear flow modified ion acoustic wave is investigated assuming electrons to follow q-nonextensive and Cairns distribution functions. A modified linear dispersion relation and electrostatic KdV solitons are analyzed. Results are illustrated considering solar wind and F-region ionospheric plasmas. Effects of non-Maxwellian distribution of electrons on the amplitude and the width of solitons are pointed out in the presence of field-aligned inhomogeneous flow.

Linear and non-linear propagation of electrostatic positron-acoustic waves and envelope solitons in 4-component quantum plasma containing relativistically degenerate electrons and positrons

A hydrodynamic model is employed to investigate the linear and non-linear propagation of electrostatic positron acoustic waves (EPAWs) in a 4-component relativistic-degenerate electron-positron-ion plasma. The plasma constituents are cold positrons, hot relativistic-degenerate electrons and positrons, and cold static ions in the background. The hot electrons and positrons are treated as inertialess, and the cold positrons provide the inertia while the restoring force comes from the hot species. A dispersion relation for low-frequency EPAWs is derived. It is observed that an increase in the relative density of hot positrons to cold positrons and relativistic effects tend to reduce the speed of the EPAWs. Employing the standard Reductive Perturbation Technique, a Korteweg de Vries (KdV)-type equation is derived, and the existence of KdV solitons is demonstrated. In this case, an increase in the relative density of hot to cold positrons and relativistic effects decreases both the amplitude and width of the solitons. Furthermore, a Non-Linear Schrödinger (NLS) equation is also derived. The variation in the group velocity shows less change with the wavenumber for the higher concentration of positrons and also with the stronger relativistic effects. The interchange in the behaviour of group velocity with the positron concentration is observed for values k &amp;gt; 1. The growth rate of modulation instability is derived, and its dependence on the positron concentration and relativistic effects are discussed. The relativistic effects reduce the stability region while the growth rate is enhanced while moving from weak-relativistic to ultra-relativistic cases. The hot positron concentration makes the wave modulationally stable for an extended region of the wavenumber k. The solution of the NLS equation admits the existence of both bright and dark envelope solitons. The profiles of the envelope solitons show inverse dependence on the positron concentration and on the relativistic effects.

Electrostatic compressive and rarefactive dust ion-acoustic solitons in four component quantum plasma

Electrostatic compressive and rarefactive dust ion-acoustic solitons in four component quantum plasma

Arbitrary amplitude electrostatic wave propagation in a magnetized dense plasma containing helium ions and degenerate electrons

The obliquely propagating arbitrary amplitude electrostatic wave is studied in a dense magnetized plasma having singly and doubly charged helium ions with nonrelativistic and ultrarelativistic degenerate electrons pressures. The Fermi temperature for ultrarelativistic degenerate electrons described by N. M. Vernet [(Cambridge University Press, Cambridge, 2007), p. 57] is used to define ion acoustic speed in ultra-dense plasmas. The pseudo-potential approach is used to solve the fully nonlinear set of dynamic equations for obliquely propagating electrostatic waves in a dense magnetized plasma containing helium ions. The upper and lower Mach number ranges for the existence of electrostatic solitons are found which depends on the obliqueness of the wave propagation with respect to applied magnetic field and charge number of the helium ions. It is found that only compressive (hump) soliton structures are formed in all the cases and only subsonic solitons are formed for a singly charged helium ions plasma case with nonrelativistic degenerate electrons. Both subsonic and supersonic soliton hump structures are formed for doubly charged helium ions with nonrelativistic degenerate electrons and ultrarelativistic degenerate electrons plasma case containing singly as well as doubly charged helium ions. The effect of propagation direction on the soliton amplitude and width of the electrostatic waves is also presented. The numerical plots are also shown for illustration using dense plasma parameters of a compact star (white dwarf) from literature.

Atypical gravito-electrostatic fluctuations in the presence of active ion-inertial dynamics

The plasmas in space, cosmic and astrophysical environments are long known to consist of numerous massive ionic components contributing to various wave instability fluctuation phenomena. Indeed, the ion-inertial effects need to be incorporated into realistic analyses, rather than treating the gravitating ionic species traditionally as a Boltzmann distributed fluid. Herein, we present an atypical theoretical model setup to study gravito-electrostatic mode-fluctuations in self-gravitating inhomogeneous interstellar dust molecular clouds (DMCs) on the astrophysical fluid scales of space and time. The main goal is focused on investigating the influence of self-consistent dynamic ion-inertial effects on the stability. Methodological application of standard multiple scaling techniques reduces the basic plasma structure equations into a unique pair of decoupled Korteweg–de Vries (KdV) equations for the weak fluctuations. In contrast, the fully nonlinear counterparts are shown to evolve as a new gravito-electrostatically coupled pair of the Sagdeev energy-integral equations. In both the perturbation regimes, excitation of two distinct eigenmode classes – electrostatic compressive solitons and self-gravitational rarefactive solitons with unusual and unique parametric features – is demonstrated and portrayed. The graphical shape analysis reflects new plasma conditions for such eigenspectral patterns to coevolve in realistic interstellar parameter windows hitherto remaining unexplored. It is seen that the inertial ions play a destabilizing influential role leading to enhanced fluctuations toward establishing a reorganized gravito-electrostatic equilibrium structure. Finally, we discuss the consistency of our results in the framework of existing inertialess ion theories, experimental findings and multiple space satellite-based observations, together with new implications.

Obliquely propagating ion-acoustic solitons and supersolitons in four-component auroral plasmas

Arbitrary amplitude nonlinear low frequency electrostatic soliton and supersoliton structures are studied in magnetized four-component auroral plasmas composed of a cold singly charged oxygen-ion fluid, Boltzmann distribution of hot protons and two distinct group of electron species. Using the Sagdeev pseudo-potential technique, the characteristics of obliquely propagating nonlinear structures are investigated analytically and numerically. The model supports the evolution of soliton and supersoliton structures in the auroral acceleration region. Depending on the parametric region, the positive and negative potential solitons coexists at lower Mach numbers, but at higher Mach numbers only negative potential solitons and supersolitons can exist. The presence of hot protons restricted the Mach number of the nonlinear structures to exist only at the subsonic region. The present investigation concurs with the Swedish Viking satellite observations in the auroral region.

General formulation for electrostatic solitons in multicomponent nonthermal plasmas

A general formulation is proposed for electrostatic solitons in multicomponent plasmas consisting of one cold species described by the fluid model and multiple hot components described by the kinetic equation. For hot species two types of generalized velocity distributions are adopted: the kappa function and the highly nonthermal distribution with two free parameters which incorporate the widely used nonthermal distribution proposed by Cairns et al (1995 Geophys. Res. Lett. 22 2709) as a special limit. The general expressions for the KdV equations and the Sagdeev potential, as well as the conditions for electrostatic solitons with positive or negative polarity, are derived, which may give rise to various solutions for acoustic solitons in multicomponent plasmas with generalized nonthermal velocity distributions.

Two-dimensional electrostatic solitary structures in electron–positron plasmas

Due to the inertia symmetry the issue of whether electrostatic solitons may possibly form in pair plasmas has been addressed in a number of papers. Recently we have shown that pair solitons with interlacing electron and positron holes in electron–positron plasmas may form by means of streaming instability based on one-dimensional particle-in-cell simulations Jao and Hau (2012 Phys. Rev. E 86 056401). In this paper we present the first simulation results of two-dimensional electrostatic solitons in pair plasmas imbedded in a stationary background magnetic field. It is shown that the features of electrostatic solitary structures may depend on the ratio of to where and denote the electron cyclotron and plasma frequency, respectively. In particular, for weakly magnetized or unmagnetized plasmas with both parallel and transverse electric field with the same order of magnitude may first develop and be dissipated in the nonlinear stage such that electrostatic solitons are unable to form by the streaming instability, while for pair solitons resembling those occurring in one-dimensional simulations may possibly form. Comparisons between linear fluid theory and particle-in-cell simulations are made.

Auroral electrostatic solitons and supersolitons in a magnetized nonthermal plasma

Exploiting the spacecraft measurements in the auroral region, finite amplitude nonlinear low frequency electrostatic solitons and supersolitons in a magnetized plasma consisting of cold ions fluid, Boltzmann protons, and nonthermal hot electrons are studied by applying a pseudo-potential technique. The localized solution of the nonlinear structures is obtained through the charge neutrality condition. Further numerical investigation shows the existence of supersoliton solutions at supersonic Mach numbers regime. The amplitude of ion-acoustic structures decreased with an increase in nonthermal electrons and ion density ratio. For the plasma parameters relevant to the auroral zone of the Earth's magnetosphere, the electric field amplitude of supersolitons is found to be about 9 mV/m, which is in agreement with satellite observations.

Kadomtsev–Petviashvili solitons in a warm electronegative plasma with q-nonextensive electrons

The Kadomtsev–Petviashvili (KP) equation for electrostatic ion acoustic solitons in a warm electronegative plasma with q-nonextensive electrons is derived. It is pointed out with the help of some suitable parameters that the phase speed of two acoustic modes and two-dimensional KP solitons are significantly modified by variation of quantities such as q (nonextensive parameter), α (the ratio of the mass of negative to positive ion), μ (the electron to positive ion number density ratio) and (the ratio of positive ion to electron temperature).

Electrostatic Solitary Waves in Pair-ion Plasmas with Trapped Electrons

Electrostatic solitons in an unmagnetized pair-ion plasma comprising adiabatic fluid positive and negative ions and non-isothermal electrons are investigated using both arbitrary and small amplitude techniques. An energy integral equation involving the Sagdeev potential is derived, and the basic properties of large amplitude solitary structures are investigated. Various features of solitons differ in different existence domains. The effects of ion adiabaticity, particle concentration, and resonant electrons on the profiles of Sagdeev potential and corresponding solitary waves are investigated. The generalized Korteweg-de Vries equation with mixed-nonlinearity is derived by expanding the Sagdeev potential. Asymptotic solutions for different orders of nonlinearity are discussed for solitary waves. The present work is applicable to understanding the wave phenomena and associated nonlinear electrostatic perturbations in pair/bi-ion plasmas which may occur in space and laboratory plasmas.

Electrostatic solitary waves and hole structures generated by bump-on-tail instability in electron-positron plasmas.

Electrostatic solitary waves (ESWs) and solitons are widely present in the solar system plasma environment. Many theoretical and numerical studies have been carried out to address the formation and structure of ESWs and solitons in electron-ion plasmas. Due to the inertia symmetry, the issue of whether solitons can exist in pair plasmas has been raised and has been discussed in a number of papers. Recently, we have shown that interlacing electron and positron holes in phase space associated with periodic positive and negative potentials may be generated by current-free electron and positron beams streaming in stationary electron-positron background plasmas [Jao and Hau, Phys. Rev. E 86, 056401 (2012)]. The question remains of whether pure electron or positron holes with positive or negative polarity may exist in neutral electron-positron plasmas. In this paper, we show the formation of electron (positron) holes associated with ESWs of positive (negative) potential based on the particle-in-cell simulations of bump-on-tail streaming instability in pair plasmas. The fluid theory shows that the coexistence of two unstable modes with different wavelengths is the essential condition for the generation of electrostatic solitons and hole structures in an electron-positron plasma.

Ion-acoustic cnoidal waves in plasmas with warm ions and kappa distributed electrons and positrons

Electrostatic ion-acoustic periodic (cnoidal) waves and solitons in unmagnetized electron-positron-ion (EPI) plasmas with warm ions and kappa distributed electrons and positrons are investigated. Using the reductive perturbation method, the Korteweg-de Vries (KdV) equation is derived with appropriate boundary conditions for periodic waves. The corresponding analytical and various numerical solutions are presented with Sagdeev potential approach. Differences between the results caused by the kappa and Maxwell distributions are emphasized. It is revealed that only hump (compressive) structures of the cnoidal waves and solitons are formed. It is shown that amplitudes of the cnoidal waves and solitons are reduced in an EPI plasma case in comparison with the ordinary electron-ion plasmas. The effects caused by the temperature variations of the warm ions are also discussed. It is obtained that the amplitude of the cnoidal waves and solitons decreases for a kappa distributed (nonthermal) electrons and positrons plasma case in comparison with the Maxwellian distributed (thermal) electrons and positrons EPI plasmas. The existence of kappa distributed particles leads to decreasing of ion-acoustic frequency up to thermal ions frequency.

Nonlinear electrostatic excitations in magnetized dense plasmas with nonrelativistic and ultra-relativistic degenerate electrons

Linear and nonlinear electrostatic waves in magnetized dense electron-ion plasmas are studied with nonrelativistic and ultra-relativistic degenerate and singly, doubly charged helium (He+, He++) and hydrogen (H+) ions, respectively. The dispersion relation of electrostatic waves in magnetized dense plasmas is obtained under both the energy limits of degenerate electrons. Using reductive perturbation method, the Zakharov-Kuznetsov equation for nonlinear propagation of electrostatic solitons in magnetized dense plasmas is derived for both nonrelativistic and ultra-relativistic degenerate electrons. It is found that variations in plasma density, magnetic field intensity, different mass, and charge number of ions play significant role in the formation of electrostatic solitons in magnetized dense plasmas. The numerical plots are also presented for illustration using the parameters of dense astrophysical plasma situations such as white dwarfs and neutron stars exist in the literature. The present investigation is important for understanding the electrostatic waves propagation in the outer periphery of compact stars which mostly consists of hydrogen and helium ions with degenerate electrons in dense magnetized plasmas.