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.
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References
N. N. Rao, P. K. Shukla, and M. Yu, Planet. Space Sci. 38, 543 (1990).
M. Horànyi and D. A. Mendis, J. Geophys. Res. 91, 355 (1986).
D. A. Mendis and M. Rosenberg, Annu. Rev. Astron. Astrophys. 32, 418 (1994).
P. K. Shukla and A. A. Mamun, Introduction to Dusty Plasma Physics (IOP, Bristol, 2002).
J. H. Chu and J. B. Du, J. Phys. D 27, 296 (1994).
J. H. Chu and J. B. Du, Phys. Rev. Lett. 72, 4009 (1994).
P. K. Shukla and V. P. Silin, Phys. Scr. 45, 508 (1992).
F. Melandso, Phys. Plasmas 3, 3890 (1996).
P. K. Kaw and A. Sen, Phys. Plasmas 5, 3552 (1998).
N. N. Rao, Phys. Plasmas 6, 4414 (1999).
W. F. El-Taibany and M. Wadati, Phys. Plasmas 14, 103703 (2007).
Y. N. Nejoh, Phys. Plasmas 4, 2813 (1997).
B. S. Xie, K. F. He, and Z. Q. Huang, Phys. Lett. A 247, 403 (1998).
A. V. Ivlev and G. Morfill, Phy. Rev. E 63, 026412 (2001).
S. I. Kopnin, I. N. Kosarev, S. I. Popel, and M. Y. Yu, Plasma Phys. Rep. 31, 198 (2005).
P. K. Sakanaka, Phys. Fluids 15, 1323 (1972).
J. E. Borovsky and G. Joyce, J. Plasma Phys. 29, 45 (1983).
K. Saeki, P. Michelsen, H. P. Pecseli, and J. J. Rasmussen, Phys. Rev. Lett. 42, 501 (1979).
H. Schamel, Phys. Rep. 140, 161 (1986).
H. Schamel, Plasma Phys. 14, 905 (1972).
Y. A. Shchekinov, Phys. Lett. A 225, 117 (1997).
S. K. El-Labany and W. F. El-Taibany, Phys. Plasmas 12, 4685 (2003).
O. Rahman, A. A. Mamun, and K. S. Ashrafi, Astrophys. Space Sci. 335, 425 (2011).
H. Alinejad, Astrophys. Space Sci. 337, 223 (2012).
S. K. El-Labany, W. F. El-Taibany, A. A. Mamun, and W. M. Moslem, Phys. Plasmas 11, 926 (2004).
A. A. Mamun, B. Eliasson, and P. K. Shukla, Phys Lett. A 332, 412 (2004).
H. Alinejad, Phys Lett. A 374, 1855 (2010).
S. Younsi and M. Tribeche, Phys. Lett. A 372, 5181 (2008).
S. V. Vladimirov, V. N. Tsytovich, S. I. Popel, and F. Kh. Khakimov, Modulational Interactions in Plasmas (Kluwer Academic, Dordrecht, 1995).
A. K. Gailitis, Ph.D. Thesis (Lebedev Physical Institute, USSR Acad. Sci., Moscow, 1964).
A. A. Vedenov and L. I. Rudakov, Sov. Phys. Doklady 9, 1073 (1965).
Y. Nejoh, IEEE Trans. Plasma Sci. 2, 80 (1992).
S. V. Vladimirov and S. I. Popel, Aust. J. Phys. 47, 375 (1994).
S. I. Popel, V. N. Tsytovich, and S. V. Vladimirov, Phys. Plasmas 1, 2176 (1994).
S. I. Popel, Plasma Phys. Rep. 24, 1022 (1998).
G. C. Das, J. Sarma, and M. Talukdar, Phys. Plasmas 5, 63 (1998).
G. C. Das and J. Sarma, Phys. Plasmas 5, 3918 (1998).
S. Hamaguchi and R. T. Farouki, Phys. Rev. E 49, 4430 (1994).
S. A. Khrapak, A. V. IvIev, V. V. Yaroshenko, and G. E. Morfill, Phys. Rev. Lett. 102, 245004 (2009).
S. K. El-Labany, W. F. El-Taibany, E. F. El-Shamy, A. El-Depsy, and N. A. Zedan, Phys. Plasmas 19, 103708 (2012).
S. K. El-Labany, E. F. El-Shamy, W. F. El-Taibany, and N. A. Zedan, Chin. Phys. B 24, 035201 (2015).
H. Schamel, J. Plasma Phys. 9, 377 (1973).
E. C. Whipple, Rep. Prog. Phys. 44, 1198 (1981).
M. S. Barnes, J. H. Keller, J. C. Forster, J. A. O’Neill, and D. K. Coultas, Phys. Rev. Lett. 68, 313 (1992).
W. F. El-Taibany, I. Kourakis, and M. Wadati, Plasma Phys. Controlled Fusion 50, 074003 (2008).
S. I. Popel, Plasma Phys. Rep. 27, 448 (2001).
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El-Labany, S.K., El-Taibany, W.F., El-Bedwehy, N.A. et al. Stability of dust acoustic wavepackets suffering from polarization force due to the presence of trapped ions. Plasma Phys. Rep. 43, 756–763 (2017). https://doi.org/10.1134/S1063780X17070042
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DOI: https://doi.org/10.1134/S1063780X17070042