W. M. Moslem

Nonlinear excitations in electron-positron-ion plasmas in accretion disks of active galactic nuclei

The propagation of acoustic nonlinear excitations in an electron-positron-ion (e-p-i) plasma composed of warm electrons and positrons, as well as hot ions, has been investigated by adopting a two-dimensional cylindrical geometry. The electrons and positrons are modeled by hydrodynamic fluid equations, while the ions are assumed to follow a temperature-parametrized Boltzmann distribution (the fixed ion model is recovered in the appropriate limit). This situation applies in the accretion disk near a black hole in active galactic nuclei, where the ion temperature may be as high as 3 to 300 times that of the electrons. Using a reductive perturbation technique, a cylindrical Kadomtsev-Petviashvili equation is derived and its exact soliton solutions are presented. Furthermore, real situations in which the strength of the nonlinearity may be weak are considered, so that higher-order nonlinearity plays an important role. Accordingly, an extended cylindrical Kadomtsev-Petviashvili equation is derived, which admits both soliton and double-layer solutions. The characteristics of the nonlinear excitations obtained are investigated in detail.

Nonlinear Dynamics of Rotating Multi-Component Pair Plasmas and e-p-i Plasmas ∗)

The propagation of small amplitude stationary profile nonlinear electrostatic excitations in a pair plasma is investigated, mainly drawing inspiration from experiments on fullerene pair-ion plasmas. Two distinct pair ion species are considered of opposite polarity and same mass, in addition to a massive charged background species, which is assumed to be stationary, given the frequency scale of interest. In the pair-ion context, the third species is thought of as a background defect (e.g. charged dust) component. On the other hand, the model also applies formally to electron-positron-ion (e-p-i) plasmas, if one neglects electron-positron annihilation. A two-fluid plasma model is employed, incorporating both Lorentz and Coriolis forces, thus taking into account the interplay between the gyroscopic (Larmor) frequency ωc and the (intrinsic) plasma rotation frequency Ω0. By employing a multi-dimensional reductive perturbation technique, a Zakharov-Kuznetsov (ZK) type equation is derived for the evolution of the electric potential perturbation. Assuming an arbitrary direction of propagation, with respect to the magnetic field, we derive the exact form of nonlinear solutions, and study their characteristics. A parametric analysis is carried out, as regards the effect of the dusty plasma composition (background number density), species temperature(s) and the relative strength of rotation to Larmor frequencies. It is shown that the Larmor and mechanical rotation affect the pulse dynamics via a parallel-to-transverse mode coupling diffusion term, which in fact diverges at ωc →± 2Ω0. Pulses collapse at this limit, as nonlinearity fails to balance dispersion. The analysis is complemented by investigating critical plasma compositions, in fact near-symmetric (T− ≈ T+) “pure” (n− ≈ n+) pair plasmas, i.e. when the concentration of the 3rd background species is negligible, case in which the (quadratic) nonlinearity vanishes, so one needs to resort to higher order nonlinear theory. A modified ZK equation is derived and analyzed. Our results are of relevance in pair-ion (fullerene) experiments and also potentially in astrophysical environments, e.g. in pulsars.

Effects of two-temperature ions, magnetic field, and higher-order nonlinearity on the existence and stability of dust-acoustic solitary waves in Saturn’s F ring

Nonlinear propagation of dust-acoustic solitary waves (DASWs) in a strong magnetized dusty plasma comprising warm adiabatic variable-charged dust particles, isothermal electrons, and two-temperature ions is investigated. Applying a reductive perturbation theory, a nonlinear Zakharov-Kuznetsov (ZK) equation for the first-order perturbed potential and a linear inhomogeneous ZK-type equation for the second-order perturbed potential are derived. However, at a certain value of high-temperature ion density, the coefficient of the nonlinear terms of both ZK and ZK-type equations vanishes. Therefore, a new set of expansion physical parameters and stretched coordinates are then used to derive a modified Zakharov-Kuznetsov (mZK) equation for the first-order perturbed potential and a mZK-type equation for the second-order perturbed potential. Stationary solutions of these equations are obtained using a renormalization method. A condition for two-temperature ions assumption is examined for various cosmic dust-laden p...

Effects of trapped electron temperature, dust charge variations, and grain radius on the existence of the dust-ion-acoustic waves

The ionization source model is considered to study the effects of trapped electron temperature, dust charge variations, and grain radius on the nonlinear dust ion acoustic waves (DIAWs) in dusty plasmas having trapped electrons. It has been shown that the nonlinear DIAWs damp waves and these waves are governed by a damped modified Korteweg–de Vries equation. It is found that only compressive dust ion acoustic solitons can propagate in dusty plasmas with trapped electrons. The amplitude and the width of the solitons depend mainly on the trapped electron temperature, dust charge variations and grain radius. The existence of the solitons is independent of the trapped electron temperature. The findings of this investigation may be useful in understanding laboratory plasma phenomena and astrophysical situations.

Solitary and blow-up electrostatic excitations in rotating magnetized electron–positron–ion plasmas

The nonlinear dynamics of a rotating magnetoplasma consisting of electrons, positrons and stationary positive ions is considered. The basic set of hydrodynamic and Poisson equations are reduced to a Zakharov-Kuznetsov (ZK) equation for the electric potential. The ZK equation is solved by applying an improved modified extended tanh-function method (2008 Phys. Lett. A 372 5691) and its characteristics are investigated. A set of new solutions are derived, including localized solitary waves, periodic nonlinear waveforms and divergent (explosive) pulses. The characteristics of these nonlinear excitations are investigated in detail.

Freak waves in white dwarfs and magnetars

We report properties of ion acoustic freak waves that propagate in a plasma composed of warm ions and ultrarelativistic electrons and positrons. The dynamics of the nonlinear freak waves is governed by the nonlinear Schrodinger equation. The possible region for the freak waves to exist is defined precisely for typical parameters of white dwarfs and magnetars corona. It is found that for low wave number, the nonlinear ion-acoustic wave packets are structurally stable in magnetars corona than in white dwarfs. However, for large wave numbers the situation is opposite. The critical wave number threshold (kc), which indicates where the modulational instability sets in, is defined for both applications. It is seen that near to kc the freak wave amplitude becomes high, but it decreases whenever we stepped away from kc. For the wave numbers close to kc, the increase of the unperturbed density ratio of positrons-to-electrons (β) would lead to increase the freak wave amplitude, but for larger wave numbers the ampli...

Finite amplitude envelope solitons in a pair-ion plasma

The nonlinear coupling between finite amplitude ion thermal waves (ITWs) and quasistationary density perturbations in a pair-ion plasma is considered. A generalized nonlinear Schrodinger equation is derived for the ITW electric field envelope, accounting for large amplitude quasistationary plasma slow motion describing the ITW ponderomotive force. The present theory accounts for the trapping of ITWs in a large amplitude ion density hole. The small amplitude limit is considered and exact analytical solutions are obtained. Finite amplitude solutions are obtained numerically and their characteristics are discussed.

Linear and nonlinear properties of dust-acoustic waves in collisional, magnetized dusty plasmas

Effects of dust-neutral collision and densities of positive ions and electrons have been investigated for the propagation of dust-acoustic waves (DAWs) in magnetized dusty plasmas. It is found that, due to collisions, the DAWs damp waves and the damping rate of the waves depends mainly on the collision frequency (i.e., if there are no collisions the waves do not damp waves). The collisions are found to significantly change the basic properties (viz., the amplitude and the width) of the DAWs. The densities of positive ions and electrons have important roles in the behavior of the DAWs. The present analysis shows that only rarefactive solitary waves exist in the system. This investigation can be relevant to the DAWs in various space plasma environments, such as Jupiter’s ring, the F ring of Saturn, and interstellar dusty clouds.

Three dimensional cylindrical Kadomtsev–Petviashvili equation in a very dense electron-positron-ion plasma

By using the hydrodynamic equations of ions, Thomas–Fermi electron/positron density distribution, and Poisson equation, a three-dimensional cylindrical Kadomtsev–Petviashvili (CKP) equation is derived for small but finite amplitude ion-acoustic waves. The generalized expansion method is used to analytically solve the CKP equation. New class of solutions admits a train of well-separated bell-shaped periodic pulses is obtained. At certain condition, the latter degenerates to solitary wave solution. The effects of physical parameters on the solitary pulse structures are examined. Furthermore, the energy integral equation is used to study the existence regions of the localized pulses. The present study might be helpful to understand the excitation of nonlinear ion-acoustic waves in a very dense astrophysical objects such as white dwarfs.

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.