Hostname: page-component-76fb5796d-dfsvx Total loading time: 0 Render date: 2024-04-26T12:21:29.649Z Has data issue: false hasContentIssue false
  • English
  • Français

The stability of the dust acoustic waves under transverse perturbations in a magnetized and collisionless dusty plasma

Published online by Cambridge University Press:  13 December 2013

Dong-Ning Gao ,
Xin Qi ,
Xue-Ren Hong ,
Xue Yang ,
Wen-Shan Duan  and
Lei Yang
Dong-Ning Gao
Affiliation:
College of Physics and Electronic Engineering and Joint Laboratory of Atomic and Molecular Physics of NWNU & IMP CAS, Northwest Normal University, Lanzhou, 730070 and Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China
Xin Qi
Affiliation:
College of Physics and Electronic Engineering and Joint Laboratory of Atomic and Molecular Physics of NWNU & IMP CAS, Northwest Normal University, Lanzhou, 730070 and Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China
Xue-Ren Hong
Affiliation:
College of Physics and Electronic Engineering and Joint Laboratory of Atomic and Molecular Physics of NWNU & IMP CAS, Northwest Normal University, Lanzhou, 730070 and Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China
Xue Yang
Affiliation:
College of Physics and Electronic Engineering and Joint Laboratory of Atomic and Molecular Physics of NWNU & IMP CAS, Northwest Normal University, Lanzhou, 730070 and Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China
Wen-Shan Duan*
Affiliation:
College of Physics and Electronic Engineering and Joint Laboratory of Atomic and Molecular Physics of NWNU & IMP CAS, Northwest Normal University, Lanzhou, 730070 and Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China
Lei Yang*
Affiliation:
College of Physics and Electronic Engineering and Joint Laboratory of Atomic and Molecular Physics of NWNU & IMP CAS, Northwest Normal University, Lanzhou, 730070 and Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China Department of Physics, Lanzhou University, Lanzhou 730000, China
*
†Email address for correspondence: (duanws@nwnu.edu.cn and lyang@impcas.ac.cn).
†Email address for correspondence: (duanws@nwnu.edu.cn and lyang@impcas.ac.cn).
Get access Rights & Permissions [Opens in a new window]

Abstract

Numerical and theoretical investigations are carried out for the stability of the dust acoustic waves (DAWs) under the transverse perturbation in a two-ion temperature magnetized and collisionless dusty plasma. The Zakharov-Kuznetsov (ZK) equation, modified ZK equation, and Extended ZK (EZK) equation of the DAWs are given by using the reductive perturbation technique. The cut-off frequency is obtained by applying higher-order transverse perturbations to the soliton solution of the EZK equation. The propagation velocity of solitary waves, the real cut-off frequency, as well as the growth rate of the higher-order perturbation to the solitary wave are obtained.

Type
Papers
Information
Journal of Plasma Physics , Volume 80 , Issue 3 , June 2014 , pp. 425 - 436
Copyright
Copyright © Cambridge University Press 2013 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Ahmad, Z., Mushtaq, A. and Mamun, A. A. 2013 Effects of plasma particle trapping on dust-acoustic solitary waves in an opposite polarity dust-plasma medium. Phys. Plasmas 20, 032302.Google Scholar
Akhter, T., Hossain, M. M. and Mamun, A. A. 2012 Multi-dimensional instability of dust-acoustic solitary waves in a magnetized plasma with opposite polarity dust. Phys. Plasmas 19, 093707.Google Scholar
Amin, M. R., Morfill, G. E. and Shukla, P. K. 1998 Modulational instability of dust-acoustic and dust-ion-acoustic waves. Phys. Rev. E 58, 6517.Google Scholar
Amin, M. R., Paul, S. K., Mandal, G. and Mamun, A. A. 2012 Effects of vortex-like (trapped) electron distribution on non-linear dust-acoustic waves with positive dust charge fluctuation. J. Plasma Phys. 76, 477.Google Scholar
Anowar, M. G. M. and Mamun, M. M. 2008 Multidimensional instability of electron-acoustic solitary waves in a magnetized plasma with vortexlike electron distribution. Phys. Plasmas 15, 102111.CrossRefGoogle Scholar
Asgari, H., Muniandy, S. V. and Wong, C. S. 2011 The role of dust charging frequency in the linear and nonlinear propagation of dust acoustic waves. Wave Motion 48, 268.CrossRefGoogle Scholar
Barkan, A., Merlino, R. L. and D'Angelo, N. 1995 Laboratory observation of the dust-acoustic wave mode. Phys. Plasmas 2, 3563.CrossRefGoogle Scholar
Benzekka, M. and Tribeche, M. 2013 Dust acoustic solitons in a charge varying dusty plasma in the presence of ion nonthermality and background nonextensivity. Phys. Plasmas 20, 083702.Google Scholar
Bharuthram, K. and Pather, T. 2009 The kinetic dust-acoustic instability in a magnetized dusty plasma. Planet. Space Sci. 44, 137.Google Scholar
D'Angelo, N. and Merlino, R. L. 1996 Current-driven dust-acoustic instability in a collisional plasma. Planet. Space Sci. 44, 1593.Google Scholar
Das, A. and Bandyopadhyay, A. 2009 Dust acoustic solitary waves in non-thermal plasmas consisting of negatively charged dust grains and isothermal electrons J. Plasma Phys. 75, 455.Google Scholar
Duan, W. S. 2004a Effect of adiabatic variation of dust charges on dust acoustic solitary waves in magnetized dusty plasmas. Chin. Phys. Soc. 13, 0598.Google Scholar
Duan, W. S. 2004b Nonlinear waves propagating in the electrical transmission line. Europhys. Lett. 66, 192–197.Google Scholar
El-Labany, S. K. and El-Taibany, W. F. 2003 Dust acoustic solitary waves and double layers in a dusty plasma with an arbitrary streaming ion beam. Phys. Plasmas 10, 989.CrossRefGoogle Scholar
El-Taibany, W. F. and Kourakis, I. 2006 Modulational instability of dust acoustic waves in dusty plasmas: modulation obliqueness, background ion nonthermality, and dust charging effects. Phys. Plasmas 13, 062302.Google Scholar
El-Taibany, W. F. and Sabry, R. 2005 Dust-acoustic solitary waves and double layers in a magnetized dusty plasma with nonthermal ions and dust charge variation. Phys. Plasmas 12, 082302.Google Scholar
Gao, D. N., Wang, C. L., Yang, X., Duan, W. S. and Yang, L. 2012 The stability and the growth rate of the electron acoustic traveling wave under transverse perturbations in a magnetized quantum plasma. Phys. Plasmas 19, 122112.Google Scholar
Gill, T. S., Bains, A. S. and Bedi, C. 2010 Modulational instability of dust acoustic solitons in multicomponent plasma with kappa-distributed electrons and ions. Phys. Plasmas 17, 013701.Google Scholar
Kalejahi, A. E., Ghazi, M. A., Noori, K. and Irani, S. 2012 Large amplitude dust-acoustic solitary waves in electron-positron-ion plasma with dust grains. Phys. Plasmas 19, 082308.Google Scholar
Lee, M. J. and Jung, Y. D. 2006 Rotation effects of elongated dust grains on a surface dust-acoustic wave in a semi-bounded dusty plasma. J. Plasma Phys. 72, 241.CrossRefGoogle Scholar
Lin, M. M. and Duan, W. S. 2005 The Kadomtsev-Petviashvili (KP), MKP, and coupled KP equations for two-ion temperature dusty plasmas. Chaos Solitons Fractals 23, 929.Google Scholar
Lou, S. Y. and Chen, L. L. 1994 Solitary wave solutions and cnoidal wave solutions to the combined KdV and mKdV equation. Math. Methods Appl. Sci. 17, 339.Google Scholar
Ma, J. X. and Liu, J. Y. 1997 Dust-acoustic soliton in a dusty plasma. Phys. Plasmas 4, 253.CrossRefGoogle Scholar
Maitra, S. and Roychoudhury, R. 2003 Speed and shape of dust acoustic solitary waves. Phys. Plasmas 10, 2230.Google Scholar
Mamun, A. A., Cairns, A. R. and Shukla, P. K. 1996 Effects of vortex-like and non-thermal ion distributions on non-linear dust-acoustic waves. Phys. Plasmas 3, 2610.Google Scholar
Meuris, P., Verheest, F. and Lakhina, G. S. 1997 Influence of dust mass distributions on generalized Jeans-Buneman instabilities in dusty plasmas. Planet. Space Sci. 45, 449.CrossRefGoogle Scholar
Misra, A. P. and Samanta, S. 2008 Quantum electron-acoustic double layers in a magnetoplasma. Phys. Plasmas 15, 122307.Google Scholar
Mushtap, A. and Shah, H. A. 2005 Nonlinear Zakharov-Kuznetsov equation for obliquely propagating two-dimensional ion-acoustic solitary waves in a relativistic, rotating magnetized electron-positron-ion plasma. Phys. Plasmas 12, 072306.Google Scholar
Nejoh, Y. N. 1997 The dust charging effect on electrostatic ion waves in a dusty plasma with trapped electrons. Phys. Plasmas 4, 2813.Google Scholar
Rao, N. N. 1998 Linear and nonlinear dust-acoustic waves in non-ideal dusty plasmas. J. Plasma Phys. 59, 561.Google Scholar
Rao, N. N., Shukla, P. K. and Yu, M. Y. 1990 Dust-acoustic waves in dusty plasmas. Planet. Space Sci. 38, 543.Google Scholar
Rosenberg, M., Merlino, R. L. and Shukla, P. K. 2011 On the possibility of refraction of dust acoustic waves. J. Plasma Phys. 77, 231.Google Scholar
Sadiq, M., Ali, S. and Sabry, R. 2009 Propagation of the three-dimensional dust acoustic solitons in magnetized quantum plasmas with dust polarity effect. Phys. Plasmas 16, 013706.Google Scholar
Shahmansouri, M. and Alinejad, H. 2013 Dust acoustic solitary waves in a magnetized electron depleted superthermal dusty plasma. Phys. Plasmas 20, 033704.Google Scholar
Shukla, P. K. 2000 Instability of a dusty plasma in the presence of a dc electric field and an equilibrium dust charge gradient. Phys. Lett. A 268, 100.CrossRefGoogle Scholar
Shukla, P. K. and Morfill, G. 1996 Ionization instability of dust-acoustic waves in weakly ionized colloidal plasmas. Phys. Lett. A 216, 153.Google Scholar
Singh, S. V. and Rao, N. N. 1998 Adiabatic dust-acoustic waves with dust-charge fluctuations. J. Plasma Phys. 60, 541.Google Scholar
Thompson, C., Barkan, A., D'Angelo, N. and Merlino, R. L. 1997 Dust acoustic waves in a direct current glow discharge. Phys. Plasmas 4, 2331.CrossRefGoogle Scholar
Varma, R. K., Shukla, P. K. and Krishan, V. 1993 Electrostatic oscillations in the presence of grain-charge perturbations in dusty plasmas. Phys. Rev. E 47, 3612.Google Scholar
Verheest, F., Shukla, P. K., Rao, N. N. and Meuris, P. 1997 Dust-acoustic waves in self-gravitating dusty plasmas with fluctuating dust charges. J. Plasma Phys. 58, 163.CrossRefGoogle Scholar
Wadati, M. 1975 Wave propagation in nonlinear lattice. I. J. Phys. Soc. Jpn. 38, 673.Google Scholar
Wang, Z. X., Liu, Y., Liu, J. Y. and Wang, X. G. 2005 Dust-acoustic soliton in dust-electron plasmas induced by ultraviolet irradiation. Phys. Plasmas 12, 014505.Google Scholar
Wang, Z. X., Wang, X. G., Ren, L. W., Liu, J. Y. and Liu, Y. 2005 Dust-acoustic soliton in electronegative complex plasmas with streaming positive ions. Phys. Plasmas 12, 082104.CrossRefGoogle Scholar
Wang, Y. L., Zhou, Z. X., Jiang, X. Q., Ni, X. D., Shen, J. and Qian, P. 2009 Modulational instability of dust acoustic waves in dusty plasmas with ultraviolet irradiation and nonadiabatic dust charge variation. Phys. Plasmas 16, 033706.Google Scholar
Xie, B. S., He, K. F. and Huang, Z. Q. 1998 Effect of adiabatic variation of dust charges on dust-acoustic solitary waves. Phys. Lett. A 247, 403.Google Scholar
Yadav, L. L., Singh, S. V. and Bharuthram, R. 2009 Dust-acoustic nonlinear periodic waves in a dusty plasma with charge fluctuation. J. Plasma Phys. 75, 697.Google Scholar