S. K. El-Labany

Ion Acoustic Solitary Waves in Degenerate Electron-Ion Plasmas

Employing the reductive perturbation method, a rigorous study of ion acoustic solitary waves (IASWs) in dense electron-ion plasmas is carried out leading to two evolution equations. Both the nonrelativistic and ultrarelativistic degenerate electron cases are considered. It is found that the relativistic parameter R0 affects the IASW phase velocity. Stationary solutions of the derived evolution equations are estimated. The higher order contributions of the nonlinear and dispersion terms are calculated. It has been shown that it is more important to be included in the case of nonrelativistic electrons. These findings are devoted to explaining the observed solitary waves propagating in the outer periphery of compact dense stars, which mostly consists of hydrogen and helium ions with degenerate electrons.

Stability of dust acoustic wavepackets suffering from polarization force due to the presence of trapped ions

The combined effects of the polarization force, free and trapped ions, and dust charge variation are incorporated in a rigorous study of the nonlinear dust acoustic waves (DAWs) propagating in an unmagnetized dusty plasma. Owing to the departure from the Boltzmann ion distribution, it is found that the nonlinear DAWs are governed by a modified Korteweg−de Vries (mKdV) equation. The association between the mKdV solitary wave and the DAW envelope in the system under consideration is discussed. A modified nonlinear Schrödinger equation appropriate for describing the modulated DAWs is derived. The modulation instability (MI) and the dependence of the system physical parameters on the polarization force, trapped ions, and dust charge variation have been analyzed. It is found that the critical curve separating the stable/unstable regions is strongly influenced by both of the polarization and the ion trapping parameters. Moreover, increasing the polarization leads to an increase of the critical wave number, while increasing the trapping parameter yields the opposite effect. The MI maximum growth rate decreases (increases) as the polarization (trapped ion) increases. The obtained results may be helpful in better understanding of space observations of the solar energetic particle flows in interplanetary space and the energetic particle events in the Earth’s magnetosphere.

Development of Cnoidal Waves in Positively Charged Dusty Plasmas

The dust-acoustic nonlinear periodic (cnoidal) waves are investigated in a positively charged dusty plasma that interacts with streaming electrons and ions. Different nonlinear evolution equations are derived using the reductive perturbation method, and their cnoidal wave solutions are obtained. The dependence of the dust-acoustic speed and the streaming densities of the ions and electrons on the cnoidal wave profiles are examined. The present model may be of interest to recognize the nonlinear waves in the magnetosphere of Jupiter.

Dust acoustic cnoidal waves in a polytropic complex plasma

The nonlinear characteristics of dust acoustic (DA) waves in an unmagnetized collisionless complex plasma containing adiabatic electrons and ions and negatively charged dust grains (including the effects of modified polarization force) are investigated. Employing the reductive perturbation technique, a Korteweg–de Vries–Burgers (KdVB) equation is derived. The analytical solution for the KdVB equation is discussed. Also, the bifurcation and phase portrait analyses are presented to recognize different types of possible solutions. The dependence of the properties of nonlinear DA waves on the system parameters is investigated. It has been shown that an increase in the value of the modified polarization parameter leads to a fast decay and diminishes the oscillation amplitude of the DA damped cnoidal wave. The relevance of our findings and their possible applications to laboratory and space plasma situations is discussed.

Ion-acoustic Gardner solitons in multi-ion degenerate plasma with the effect of polarization and trapping in the presence of a quantizing magnetic field

A theoretical investigation is presented for ion-acoustic Gardner solitons (GSs) and double layers (DLs) in a multi-ion plasma system. The plasma consists of inertial positively and negatively charged ions and negatively charged immobile heavy ions and electrons which are in trapping distribution, all existing in a quantizing magnetic field. The reductive perturbation method is used to derive Korteweg-de Vries (KdV), modified KdV (mKdV), and Gardner equations. It is found that the KdV solitons and Gardner solitons (GSs) are either compressive or rarefactive depending on the plasma parameters, whereas only compressive solitons are obtained in the mKdV case, wherever Gardner positive DLs exist. These solitons are significantly modified due to the introduction of the trapping parameter and polarization coefficient. The presented results are considered to be beneficial in understanding the solitary structures in dense quantum plasmas such as those existing in white dwarfs.