Exact electrostatic solitons in a magnetoplasma with degenerate electrons

Fully nonlinear planar ion-acoustic solitary waves (IASWs) moving obliquely to an external magnetic field are studied in a collisionless magnetoplasma with degenerate electrons. The features of the nonlinear IASWs are investigated through the derivation of an energy balance-like equation involving the Sagdeev-type potential as well as the nonlinear dispersion relation.     

Ion-acoustic solitary waves in a dense pair-ion plasma containing degenerate electrons and positrons

Fully nonlinear propagation of ion-acoustic solitary waves in a collisionless dense/quantum electron–positron–ion plasma is investigated. The electrons and positrons are assumed to follow the Thomas–Fermi density distribution and the ions are described by the hydrodynamic equations. An energy balance-like equation involving a Sagdeev-type pseudo-potential is derived. Finite amplitude solutions are obtained numerically and their characteristics are discussed. The small-but finite-amplitude limit is also considered and an exact analytical solution is obtained. The present studies might be helpful to understand the excitation of nonlinear ion-acoustic solitary waves in a degenerate plasma such as in superdense white dwarfs.     

Head-on collision of ion-acoustic solitary waves in a Thomas-Fermi plasma containing degenerate electrons and positrons

Head-on collision between two ion acoustic solitary waves in a Thomas-Fermi plasma containing degenerate electrons and positrons is investigated using the extended Poincaré-Lighthill-Kuo (PLK) method. The results show that the phase shifts due to the collision are strongly dependent on the positron-to-electron number density ratio, the electron-to-positron Fermi temperature ratio and the ion-to-electron Fermi temperature ratio. The present study might be helpful to understand the excitation of nonlinear ion-acoustic solitary waves in a degenerate plasma such as in superdense white dwarfs.     

Explosive and solitary excitations in a very dense magnetoplasma

A two-component dense magnetoplasma consisting of ions and degenerate electrons is considered. The basic set of hydrodynamic and Poisson equations are reduced to the Zakharov-Kuznetsov (ZK) equation by using the reductive perturbation technique. The basic features of the electrostatic excitations are investigated by applying a new direct method to the ZK equation. It is found that the latter has new solutions, which admit the propagation of either solitary or explosive pulses. The relevance of the new direct method to other nonlinear partial differential equations is also discussed.     

Dust acoustic wave in a dusty plasmas with streaming ions and nonadiabatic dust charge variation

The effects of nonadiabatic dust charge fluctuation on the nonlinear propagation of the dust acoustic (DA) solitary wave in collisionless dusty plasma with streaming ions have been investigated. By using the reductive perturbation technique, a modified Korteweg-de Vries (mKdV) equation governing the nonlinear waves was derived and the solitary solution of the mKdV equation was also obtained. It was shown that the damping rate of the slow mode DA solitary wave was strongly affected by the ion streaming velocity.     

Parallel velocity shear driven electrostatic waves in a very dense nonuniform magnetoplasma

It is shown that the parallel (magnetic field-aligned) velocity shear can drive the low-frequency (in comparison with the ion gyrofrequency) electrostatic (LF-ES) waves in an ultracold super-dense nonuniform magnetoplasma. By using an electron density response arising from the balance between the electrostatic and quantum Bohm forces, as well as the ion density response deduced from the continuity and momentum equations, a wave equation for the LF-ES waves is derived. In the local approximation, a new dispersion relation is obtained by Fourier transforming the wave equation. The dispersion relation reveals an oscillatory instability of dispersive drift-like modes in super-dense quantum magnetoplasmas.     

Effect of Thermionic Emission on Dust-Acoustic Solitons in a Dust-Electron Plasma

The effects of thermionic emission on dust-acoustic solitons with a very small but finite amplitude in a dustelectron plasma are studied using the reductive perturbation technique. The self-consistent variation of dust charge is taken into account. It is shown that the thermionic emission could significantly increase the dust positive charge. The dependences of the phase velocity, amplitude, and width of such solitons on the dust temperature and the dust work function of dust material are plotted and discussed.     

On the interaction of two beating electrostatic waves with plasma electrons

This paper is devoted to the study of the interaction of particles with two beating plasma waves. We follow the instructional article by Ott and Dum. According to them, the sum of wave actions during the interaction is constant, supposing the effect of trapped particles on the beat can be neglected. In the present paper, this problem is solved more generally, just for the case of trapped and also untrapped particles in the wave. Our study shows that the sum of wave actions is constant also in the case when the influence of the trapped particles on the amplitudes of two waves was considered. On the contrary this conclusion is not valid if it is supposed that two original waves are amplitude modulated e.g. by the influence of the interaction of the beat with particles. The author is deeply indebted to Dr. Ladislav Krlín for guidance and encouragement throughout the course of this work.     

Quantum ion acoustic solitary waves in electron-ion plasmas: A Sagdeev potential approach

Linear and nonlinear ion acoustic waves are studied in unmagnetized electron-ion quantum plasmas. Sagdeev potential approach is employed to describe the nonlinear quantum ion acoustic waves. It is found that density dips structures are formed in the subsonic region in a electron-ion quantum plasma case. The amplitude of the nonlinear structures remains constant and the width is broadened with the increase in the quantization of the system. However, the nonlinear wave amplitude is reduced with the increase in the wave Mach number. The numerical results are also presented.     

Nonlinear-Ion-Acoustic-Wave Instability, Threshold, Half Width of Trapped Region and Transition Region

Nonlinear Landau damping of ion acoustic wave (IAW) is one of the most important phenomena in the ionosphere and in space and laboratory plasma as well. The instability growth rate of the IAW with electron drift, the amplitude threshold for exciting the nonlinear effects, the half widths of the trapped region with the trapped electrons are studied experimentally. Under the experimental conditions, it is shown that there is a frequency range of 140--160 kHz, within which the growth rate has the largest value of about 6×10⁴--1.5×10⁵ s^-1. We obtain the transitional region width caused by collisions theoretically and experimentally, for the first time to our knowledge. The experimental results are in good agreement with the theoretical prediction.     

Coexistence of positive and negative solitary potential structures in dusty plasma

A dusty plasma system consisting of electrons, ions, and negative as well as positive dust particles has been considered. The basic properties of arbitrary amplitude solitary potential structures that may exist in such a multi-component dusty plasma have been theoretically investigated by the pseudo-potential approach. It has been found that the presence of additional positive dust component does not only significantly modify the basic properties of solitary potential structures, but also causes the coexistence of positive and negative solitary potential structures, which is a completely new feature shown in a dusty plasma with dust of opposite polarity.     

Electrostatic solitons in unmagnetized hot electron-positron-ion plasmas

Linear and nonlinear electrostatic waves in unmagnetized electron-positron-ion (e-p-i) plasmas are studied. The electrons and positrons are assumed to be isothermal and dynamic while ions are considered to be stationary to neutralize the plasma background only. It is found that both upper (fast) and lower (slow) Langmuir waves can propagates in such a type of pair (e-p) plasma in the presence of ions. The small amplitude electrostatic Korteweg-de Vries (KdV) solitons are also obtained using reductive perturbation method. The electrostatic potential hump structures are found to exist when the temperature of the electrons is larger than the positrons, while the electrostatic potential dips are obtained in the reverse temperature conditions for electrons and positrons in e-p-i plasmas. The numerical results are also shown for illustration. The effects of different ion concentration and temperature ratios of electrons and positrons, on the formation of nonlinear electrostatic potential structures in e-p-i plasmas are also discussed.     

Effects of adiabaticity of electrons and ions on dust-ion-acoustic solitary waves

The nonlinear propagation of dust-ion-acoustic (DIA) waves in an adiabatic dusty plasma (containing adiabatic inertial-less electrons, adiabatic inertial ions, and negatively charged static dust) is investigated by the pseudo-potential approach. The combined effects of adiabatic electrons and negatively charged static dust on the basic properties (critical Mach number, amplitude, and width) of small as well as arbitrary amplitude DIA solitary waves are explicitly examined. It is found that the combined effects of adiabatic electrons and negatively charged static dust significantly modify the basic properties (critical Mach number, amplitude, and width) of the DIA solitary waves. It is also found that due to the effect of adiabaticity of electrons, negative DIA solitary waves [which are found to exist in a dusty plasma (containing isothermal electrons, cold ions, and negatively charged static dust) for α=zdnd0/ni0>2/3, where zd is the number of electrons residing onto a dust grain surface, nd0 is the constant (static) dust number density and ni0 is the equilibrium ion number density] disappears, i.e. due to the effect of adiabatic electrons, one cannot have negative DIA solitary waves for any possible set of dusty plasma parameters [0?α<1 and 0?σ=Ti0/Te0?1, where Ti0 (Te0) is electron (ion) temperature at equilibrium].     

Small amplitude variable charge dust Bernstein-Greene-Kruskal double layers

A first theoretical attempt is made to investigate small amplitude, variable charge dust Bernstein-Greene-Kruskal (BGK) double layers (DLs). The nature of the dust BGK-DLs (compressive or rarefactive), their strength and thickness depend sensitively on the net negative charge residing on the grain surface, the dust grain dynamics and, more interestingly, on the ion-to-electron temperatures ratio.     

Nonlinear localized dust acoustic waves in a charge varying dusty plasma with trapped ions

The problem of nonlinear variable charge dust acoustic waves in a dusty plasma with trapped ions is revisited. The correct non-isothermal ion charging current is presented for the first time based on the orbit motion limited (OML) approach. The variable dust charge is then expressed in terms of the Lambert function and we take advantage of this new transcendental function to investigate nonlinear localized dust acoustic waves in a charge varying dusty plasma with trapped ions more rigorously.     

Dispersion properties of low-frequency electrostatic oscillations in metallic carbon nanotubes

Dispersion properties of low-frequency electrostatic waves in metallic carbon nanotubes (CNTs) are investigated. We assume that metallic CNTs are charged due to the field emission, and hence the metallic nanotubes can be regarded as charged dust rods surrounded by degenerate electrons and ions. We deduce the perturbed electron and ion number densities by using the quantum hydrodynamic model, while the dust rod density perturbation follows the classical expression. The Poisson equation, in turn, gives the dispersion relation for the low-frequency electrostatic oscillations in our three-species bounded plasma system composed of metallic CNTs. The oscillation frequency of CNTs can be used for diagnostic purposes, e.g. for the determination of charge on nanotubes.     

Rarefactive ion-acoustic electrostatic solitary structures in nonthermal plasmas

An investigation has been made of ion-acoustic solitary waves in an unmagnetized nonthermal plasma whose constituents are an inertial ion fluid and nonthermally distributed electrons. The properties of stationary solitary structures are briefly studied by the pseudo-potential approach, which is valid for arbitrary amplitude waves, and by the reductive perturbation method which is valid for small but finite amplitude limit. The time evolution of both compressive and rarefactive solitary waves, which are found to coexist in this nonthermal plasma model, is also examined by solving numerically the full set of fluid equations. The temporal behaviour of positive (compressive) solitary waves is found to be typical, i.e., the positive initial disturbance breaks up into a series of solitary waves with the largest in front. However, the behaviour of negative (rarefactive) solitary waves is quite different. These waves appear to be unstable and produce positive solitary waves at a later time. The relevancy of this investigation to observations in the magnetosphere of density depressions is briefly pointed out. Received 12 October 1999     

Reply to: “Comment on: ‘Spherical Kadomtsev–Petviashvili equation and nebulons for dust ion-acoustic waves with symbolic computation’ ” [Phys. Lett. A 361 (2007) 520]

Dusty plasmas exist almost everywhere in the Universe and relevant nonlinear studies are encouragingly going to non-planar geometry. On our recent construction of a spherical Kadomtsev–Petviashvili model for the dust-ion-acoustic waves in a cosmic dusty plasma [B. Tian, Y.-T. Gao, Phys. Lett. A 340 (2005) 243], Hong [W.P. Hong, Phys. Lett. A (2006), doi:10.1016/j.physleta.2006.11.021, in press] comments that certain interesting coordinate transformations exist, with presentation of a transformed equation (TE) and nebulon solutions. In this Reply, we point out that the TE is valuable to the studies on both cosmic plasmas and applied mathematics. We obtain an auto-Bäcklund transformation on the TE and more general nebulons. With series of pictures, we discuss nebulon structures out of the TE, and address that there are cosmic plasma systems for which the TE is valid. We remove a constraint set in that Comment so that the TE can be useful for the Saturn-F-ring-typed dusty plasmas as well.     

Comment on: “Spherical Kadomtsev–Petviashvili equation and nebulons for dust ion-acoustic waves with symbolic computation” [Phys. Lett. A 340 (2005) 243]

Tian and Gao [B. Tian, Y.T. Gao, Phys. Lett. A 340 (2005) 243] have recently constructed a spherical Kadomtsev–Petviashvili equation for the dust-ion-acoustic waves with zenith-angle perturbation in a cosmic dusty plasma, and symbolically obtained and discussed spherical structures of the expanding dark, shrinking dark, expanding bright and shrinking bright nebulons. In this Comment, we point out that certain simple coordinate transformations exist, which make the analytic nebulon solutions more easily accessible. We also show that the transformed solutions can result in a couple of nebulon solutions in addition to the second-order nebulons found by Tian and Gao.     

Symbolic computation on cylindrical-modified dust-ion-acoustic nebulons in dusty plasmas

In this Letter, for the dust-ion-acoustic waves with azimuthal perturbation in a dusty plasma, a cylindrical modified Kadomtsev–Petviashvili (CMKP) model is constructed by virtue of symbolic computation, with three families of exact analytic solutions obtained as well. Dark and bright CMKP nebulons are investigated with pictures and related to such dusty-plasma environments as the supernova shells and Saturn's F-ring. Difference of the CMKP nebulons from other known nebulons is also analyzed, and possibly-observable CMKP-nebulonic effects for the future plasma experiments are proposed, especially those on the possible notch/slot and dark-bright bi-existence.