W. F. El-Taibany

Dust acoustic solitary waves and double layers in a dusty plasma with two-temperature trapped ions

The combined effects of trapped ion distribution, two-ion-temperature, dust charge fluctuation, and dust fluid temperature are incorporated in the study of nonlinear dust acoustic waves in an unmagnetized dusty plasma. It is found that, owing to the departure from the Boltzmann ion distribution to the trapped ion distribution, the dynamics of small but finite amplitude dust acoustic waves is governed by a modified Korteweg–de Vries equation. The latter admits a stationary dust acoustic solitary wave solution, which has stronger nonlinearity, smaller amplitude, wider width, and higher propagation velocity than that involving adiabatic ions. The effect of two-ion-temperature is found to provide the possibility for the coexistence of rarefactive and compressive dust acoustic solitary structures and double layers. Although the dust fluid temperature increases the amplitude of the small but finite amplitude solitary waves, the dust charge fluctuation does the opposite effect. The present investigation should help us to understand the salient features of the nonlinear dust acoustic waves that have been observed in a recent numerical simulation study.

Dust-acoustic solitary waves and double layers in a magnetized dusty plasma with nonthermal ions and dust charge variation

The effect of nonthermal ions and variable dust charge on small-amplitude nonlinear dust-acoustic (DA) waves is investigated. It is found that both compressive and rarefactive solitons exist and depend on the nonthermal parameter a. Using a reductive perturbation theory, a Zakharov–Kuznetsov (ZK) equation is derived. At critical value of a, ac, a modified ZK equation with third- and fourth-order nonlinearities, is obtained. Depending on a, the solution of the evolution equation reveals whether there is coexistence of both compressive and rarefactive solitary waves or double layers (DLs) with the possibility of their two kinds. In addition, for certain plasma parameters, the solitary wave disappears and a DL is expected. The variation of dust charge number, wave velocity, and soliton amplitude and its width against system parameters is investigated for the DA solitary waves. It is shown that the incorporation of both the adiabatic dust-charge variation and the nonthermal distributed ions modifies significa...

Effect of two-temperature trapped electrons to nonlinear dust-ion-acoustic solitons

Propagation of three-dimensional dust-ion-acoustic solitons is investigated in a dusty plasma consisting of positive ions, negatively variable-charged dust particles, and two-temperature trapped electrons. We use the reductive perturbation theory to reduce the basic set of fluid equations to one evolution equation called damped modified Kadontsev-Petviashivili equation. Exact solution of this equation is not possible, so we obtain the time evolution solitary wave form approximate solution. It is found that only compressive soliton can propagate in this system. We develop a theoretical estimate condition under which the solitons can propagate. It is found that this condition is satisfied for Saturn’s F ring. It is found also that low electron temperature has a role on the behavior of the soliton width, i.e., for lower (higher) range of low electron temperature the soliton width decreases (increases). However, high electron temperature decreases the width. The trapped electrons have no effect on the soliton...

Three-dimensional stability of dust-ion acoustic solitary waves in a magnetized multicomponent dusty plasma with negative ions

Using the small-k expansion perturbation method, the three-dimensional stability of dust-ion acoustic solitary waves (DIASWs) in a magnetized multicomponent dusty plasma containing negative heavy ions and stationary variable-charge dust particles is analyzed. A nonlinear Zakharov–Kuznetsov equation adequate for describing these solitary structures is derived. Moreover, the basic features of the DIASWs are studied. The determination of the stability region leads to two different cases depending on the oblique propagation angle. In addition, the growth rate of the produced waves is estimated. The increase of either the negative ion number density or their temperatures or even the number density of the dust grains results in reducing the wave growth rate. Finally, the present results should elucidate the properties of DIASWs in a multicomponent plasma with negative ions, particularly in laboratory experiment and plasma process.

Dust-ion-acoustic solitons with transverse perturbation

The ionization source model is considered, for the first time, to study the combined effects of trapped electrons, transverse perturbation, ion streaming velocity, and dust charge fluctuations on the propagation of dust-ion-acoustic solitons in dusty plasmas. The solitary waves are investigated through the derivation of the damped modified Kadomtsev–Petviashivili equation using the reductive perturbation method. Conditions for the formation of solitons as well as their properties are clearly explained. The relevance of our investigation to supernovae shells is also discussed.

Higher-order nonlinearity of electron-acoustic solitary waves with vortex-like electron distribution and electron beam

The nonlinear wave structure of small-amplitude electron-acoustic solitary waves (EASWs) is investigated in a four-component plasma consisting of cold electron fluid, hot electrons obeying vortex-like distribution traversed by a warm electron beam and stationary ions. The streaming velocity of the beam, uo, plays the dominant role in determining the roots of the linear dispersion relation associated with the system. Using the reductive perturbation theory, the basic set of equations is reduced to a modified Korteweg–de Vries (mKdV) equation. With the inclusion of higher-order nonlinearity, a linear inhomogeneous mKdV type equation with fifth-order dispersion term is derived and the higher-order solution is obtained using a renormalization method. However, both mKdV and mKdV-type solutions present a positive potential, which corresponds to a hole (hump) in the cold (hot) electron number density. The mKdV-type solution has a smaller energy amplitude and a wider width than that of mKdV solution. The dependen...

Propagation of three-dimensional ion-acoustic solitary waves in magnetized negative ion plasmas with nonthermal electrons

Properties of small amplitude nonlinear ion-acoustic solitary waves in a warm magneto plasma with positive-negative ions and nonthermal electrons are investigated. For this purpose, the hydrodynamic equations for the positive-negative ions, nonthermal electron density distribution, and the Poisson equation are used to derive the corresponding nonlinear evolution equation; Zkharov–Kuznetsov (ZK) equation, in the small amplitude regime. The ZK equation is analyzed to examine the existence regions of the solitary pulses. It is found that compressive and rarefactive ion-acoustic solitary waves strongly depend on the mass and density ratios of the positive and negative ions as well as the nonthermal electron parameter. Also, it is found that there are two critical values for the density ratio of the negative-to-positive ions (υ), the ratio between unperturbed electron-to-positive ion density (μ), and the nonthermal electron parameter (β), which decide the existence of positive and negative ion-acoustic solitar...

Higher-order contribution to obliquely nonlinear electron-acoustic waves with electron beam in a magnetized plasma

Propagation of electron-acoustic waves in a strongly magnetized four-component plasma consisting of cold and hot electrons, a warm electron beam, and stationary ions is investigated. The present model considered weakly dispersive and strongly magnetized plasma in the limit of long wavelengths. The introduction of an electron beam allows the existence of electron-acoustic solitons with velocity related to the beam velocity. With increasing the beam velocity and the beam temperature, both the soliton amplitude and the width increase. Applying a reductive perturbation theory, a nonlinear Zakharov-Kuznetsov (ZK) equation for the first-order perturbed potential and a linear inhomogeneous Zakharov-Kuznetsov (ZK-type) equation for the second-order perturbed potential are derived. Stationary solutions of these coupled equations are obtained using a renormalization method. These solutions admit either compressive or rarefactive soliton type depending on the electron-beam parameters. Moreover, the dependence of the...

On the higher-order solution of the dust-acoustic solitary waves in a warm magnetized dusty plasma with dust charge variation

The higher-order contribution in reductive perturbation theory is studied for small-butfinite-amplitude dust-acoustic solitary waves in warm magnetized three-component dusty plasmas comprised of variational charged dust grains, isothermal ions, and electrons. The basic set of fluid equations is reduced to the Zakharov–Kuznetsov equation for the first-order perturbed potential and a linear inhomogeneous Zakharov–Kuznetsov-type equation for the second-order perturbed potential. Stationary solutions of both equations are obtained using a renormalization method. The effects of the higher-order contribution, external magnetic field, dust charge variation, dust grain temperature, ratios of temperature and density of positive ions to electrons, and directional cosine of the wave vector k along the x axis on the nature of the solitary waves are investigated.

Finite amplitude solitary excitations in rotating magnetized nonthermal complex "dusty… plasmas

The nonlinear dynamics of finite amplitude dust acoustic solitary waves in rotating magnetized nonthermal plasma are investigated. For this purpose, the hydrodynamic equations for the dust grains, nonthermal ion density, and Boltzmann electron distributions together with the Poisson equation are used to derive the energy integral equation with a new Sagdeev potential. It is found that the solitary excitations strongly depend on the nonthermal ion parameters, rotational frequency, as well as dust gyrofrequency. The present investigations may be applicable to the dusty plasma situation near to the moon.