Stability of dust acoustic wavepackets suffering from polarization force due to the presence of trapped ions
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DUSTY PLASMA
Stability of Dust Acoustic Wavepackets Suffering from Polarization Force Due to the Presence of Trapped Ions1 S. K. El-Labanya,*, W. F. El-Taibanya, N. A. El-Bedwehyb, and N. A. Zedana a
Department of Physics, Faculty of Science, Damietta University, New Damietta, Egypt of Mathematics, Faculty of Science, Damietta University, New Damietta, Egypt *e-mail: [email protected]
b Department
Received August 12, 2016; in final form, November 17, 2016
Abstract—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. DOI: 10.1134/S1063780X17070042
solitons with varying dust charge and they showed that only rarefactive solitary waves exist when the Mach number lies within an appropriate regime, depending on the system parameters. Ivlev and Morfill [14] have considered two limiting cases of ion distribution (Boltzmann and highly energetic cold ions) in studying dust acoustic solitons with variable charged dust grains. It is found that the charge variation is crucial if the particle number density is sufficiently high. Taken noctilucent clouds and polar mesosphere summer echoes as proper applications containing vast amounts of charged dust or aerosols, Kopnin et al. [15] have studied the effect of the dust charge sign on the properties of dust acoustic solitons propagating in this dusty ionosphere. It is shown that when the dust charge is negative, dust acoustic solitons correspond to a well in the electron density and a hill in the ion density. When the dust is charged positively, the situation is opposite. If streaming particles are injected into plasmas, we often find that they evolve toward a coherent trapped particle state, instead of developing into a turbulent one. This has been confirmed by compu
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