Hostname: page-component-848d4c4894-cjp7w Total loading time: 0 Render date: 2024-07-05T18:43:02.789Z Has data issue: false hasContentIssue false
  • English
  • Français

Nonlinear dust acoustic travelling waves in dusty plasmas due to dust charge fluctuations

Published online by Cambridge University Press:  13 July 2015

Asit Saha ,
Prasanta Chatterjee  and
Nikhil Pal
Asit Saha*
Affiliation:
Department of Mathematics, Sikkim Manipal Institute of Technology, Majitar, Rangpo, East-Sikkim 737 136, India Department of Mathematics, Siksha Bhavana, Visva Bharati University, Santiniketan 731 235, India
Prasanta Chatterjee
Affiliation:
Department of Mathematics, Siksha Bhavana, Visva Bharati University, Santiniketan 731 235, India
Nikhil Pal
Affiliation:
Department of Mathematics, Siksha Bhavana, Visva Bharati University, Santiniketan 731 235, India
*
†Email address for correspondence: asit_saha123@rediffmail.com
Get access Rights & Permissions [Opens in a new window]

Abstract

Dust acoustic solitary waves, blow-up solitary waves and periodic waves have been investigated in unmagnetized dusty plasmas with Maxwell-distributed electrons and ions, considering dust charge fluctuations using the bifurcation theory of planar dynamical systems. The basic equations are transformed to an ordinary differential equation involving the electrostatic potential. Applying the bifurcation theory of planar dynamical systems, we have established the existence of solitary, blow-up solitary and periodic waves. Four exact solutions of the solitary, blow-up solitary and periodic waves are derived depending on the physical parameters. Regarding the solitary, blow-up solitary and periodic waves, we have presented the combined effects of the density ratio of electrons and ions (${\it\alpha}$), the temperature ratio of electrons and ions $({\it\beta})$ and the speed of the travelling wave ($v$) on the characteristics of dust acoustic solitary, blow-up solitary and periodic waves.

Type
Research Article
Information
Journal of Plasma Physics , Volume 81 , Issue 5 , October 2015 , 905810509
Copyright
© Cambridge University Press 2015 

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

Asgari, H., Muniandy, S. V. & Wong, C. S. 2011 The role of dust charging frequency in the linear and nonlinear propagation of dust acoustic waves. Wave Motion 48, 268–274.CrossRefGoogle Scholar
Barkan, A., Merlino, R. L. & D’Angelo, N. 1995 Laboratory observation of the dust-acoustic wave mode. Phys. Plasmas 2, 3563.Google Scholar
Barkan, A., Merlino, R. L. & D’Angelo, N. 1996 Experiments on ion-acoustic waves in dusty plasmas. Planet. Space Sci. 44, 239–242.Google Scholar
Chatterjee, P. 2004 Speed and shape of solitary waves in two-electron plasmas with relativistic warm ions. Z. Naturforsch. A 59, 353.Google Scholar
Chatterjee, P. & Das, B. 2004a Speed and shape of solitary waves in non-isothermal plasma with warm ions. Indian J. Phys. 78B, 223.Google Scholar
Chatterjee, P. & Das, B. 2004b Effect of electron inertia on the speed and shape of ion-acoustic solitary waves in plasma. Phys. Plasmas 11, 3616.Google Scholar
Chatterjee, P. & Roychoudhury, R. 1994 Effect of ion temperature on large-amplitude ion-acoustic solitary waves in relativistic plasma. Phys. Plasmas 1, 2148.CrossRefGoogle Scholar
D’Angelo, N. 1990 Low-frequency electrostatic waves in dusty plasmas. Planet. Space Sci. 38, 1143–1146.Google Scholar
D’Angelo, N. 1995 Coulomb solids and low-frequency fluctuations in RF dusty plasmas. J. Phys. D 28, 1009.Google Scholar
Duan, W. S., Lu, K. P. & Zhao, J. B. 2001 Hot dust acoustic solitary waves in dust plasma with variable dust charge. Chin. Phys. Lett. 18, 1088.Google Scholar
El-Labany, S. K. & El-Taibany, W. F. 2004 Effect of dust-charge variation on dust acoustic solitary waves in a dusty plasma with trapped electrons. J. Plasma Phys. 70, 69–87.Google Scholar
El-Labany, S. K., El-Taibany, W. F., El-Bedwehy, N. A. & El-Fayoumy, M. M. 2011 Arbitrary amplitude dust acoustic solitary waves in a dusty plasma with an ion beam. Eur. Phys. J. D 64, 375.Google Scholar
Goertz, C. K. 1989 Dusty plasmas in the solar system. Rev. Geophys. 27, 271–292.Google Scholar
Guckenheimer, J. & Holmes, P. J. 1983 Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields. Springer.Google Scholar
Johnston, C. R. & Epstein, M. 2000 On the exact amplitude, speed and shape of ion-acoustic waves. Phys. Plasmas 7, 906.CrossRefGoogle Scholar
Kourakis, I. & Shukla, P. K. 2004 Lagrangian description of nonlinear dust-ion acoustic waves in dusty plasmas. Eur. Phys. J. D 30, 97–103.Google Scholar
Maitra, S. & Roychoudhury, R. 2003 Speed and shape of dust acoustic solitary waves. Phys. Plasmas 10, 2230.CrossRefGoogle Scholar
Malfliet, W. & Wieers, E. 1996 The theory of nonlinear ion-acoustic waves revisited. J. Plasma Phys. 56, 441–450.Google Scholar
Melandso, F. 1996 Lattice waves in dust plasma crystals. Phys. Plasmas 3, 3890.Google Scholar
Mendis, D. A. 2002 Progress in the study of dusty plasmas. Plasma Sources Sci. Technol. 11, A219.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
Nakamura, Y., Bailung, H. & Shukla, P. K. 1999 Observation of ion-acoustic shocks in a dusty plasma. Phys. Rev. Lett. 83, 1602.Google Scholar
Rao, N. N. & Shukla, P. K. 1994 Nonlinear dust-acoustic waves with dust charge fluctuations. Planet. Space Sci. 42 (3), 221–225.Google Scholar
Rao, N. N., Shukla, P. K. & Yu, M. Y. 1990 Dust-acoustic waves in dusty plasmas. Planet. Space Sci. 38, 543–546.Google Scholar
Saha, A. 2012 Bifurcation of travelling wave solutions for the generalized KP-MEW equations. Commun. Nonlinear Sci. Numer. Simul. 17, 3539–3551.CrossRefGoogle Scholar
Saha, A. & Chatterjee, P. 2014a Bifurcations of electron acoustic traveling waves in an unmagnetized quantum plasma with cold and hot electrons. Astrophys. Space Sci. 349, 239–244.Google Scholar
Saha, A. & Chatterjee, P. 2014b Bifurcations of ion acoustic solitary waves and periodic waves in an unmagnetized plasma with kappa distributed multi-temperature electrons. Astrophys. Space Sci. 350, 631–636.Google Scholar
Saha, A. & Chatterjee, P. 2014c Bifurcations of ion acoustic solitary and periodic waves in an electron–positron–ion plasma through non-perturbative approach. J. Plasma Phys. 80, 553–563.Google Scholar
Saha, A. & Chatterjee, P. 2014d Bifurcations of dust acoustic solitary waves and periodic waves in an unmagnetized plasma with nonextensive ions. Astrophys. Space Sci. 351, 533–537.Google Scholar
Saha, A. & Chatterjee, P. 2014e New analytical solutions for dust acoustic solitary and periodic waves in an unmagnetized dusty plasma with kappa distributed electrons and ions. Phys. Plasmas 21, 022111.Google Scholar
Samanta, U. K., Saha, A. & Chatterjee, P. 2013a Bifurcations of nonlinear ion acoustic travelling waves in the frame of a Zakharov–Kuznetsov equation in magnetized plasma with a kappa distributed electron. Phys. Plasmas 20, 052111.Google Scholar
Samanta, U. K., Saha, A. & Chatterjee, P. 2013b Bifurcations of dust ion acoustic travelling waves in a magnetized dusty plasma with a $q$ -nonextensive electron velocity distribution. Phys. Plasmas 20, 022111.Google Scholar
Samanta, U. K., Saha, A. & Chatterjee, P. 2013c Bifurcations of dust ion acoustic travelling waves in a magnetized quantum dusty plasma. Astrophys. Space Sci. 347, 293–298.CrossRefGoogle Scholar
Selwyn, G. S. 1993 A phenomenlogical study of particulates in plasma tools and processes. Japan. J. Appl. Phys. 32, 3068.Google Scholar
Shukla, P. K. & Silin, V. P. 1992 Dust ion-acoustic wave. Phys. Scr. 45, 508.Google Scholar
Shukla, P. K. & Varma, R. K. 1993 Convective cells in nonuniform dusty plasmas. Phys. Fluids B 5, 236.Google Scholar
Shukla, P. K., Yu, M. Y. & Bharuthram, R. 1991 Linear and nonlinear dust drift waves. J. Geophys. Res. 96, 21343–21346.CrossRefGoogle Scholar
Thomas, H., Morfill, G. E. & Dammel, V. 1994 Plasma crystal: Coulomb crystallization in a dusty plasma. Phys Rev. Lett. 73, 652.Google Scholar
Tribeche, M. & Bacha, M. 2010 Nonlinear dust acoustic waves in a charge varying dusty plasma with suprathermal electrons. Phys. Plasmas 17, 073701.Google Scholar
Tribeche, M. & Zerguini, T. H. 2004 Small amplitude Bernstein–Greene–Kruskal solitary waves in a thermal charge-varying dusty plasma. Phys. Plasmas 11, 4115.Google Scholar
Verheest, F. 2000 Waves in Dusty Space Plasmas. Kluwer.Google Scholar
Verheest, F., Hellberg, M. A. & Kourakis, I. 2008 Acoustic solitary waves in dusty and/or multi-ion plasmas with cold, adiabatic, and hot constituents. Phys. Plasmas 15, 112309.Google Scholar
Watanabe, S. & Jiang, B. 1993 Higher-order solution of an ion-acoustic solitary wave in a plasma. Phys. Fluids B 5, 409.Google Scholar
Xie, B., He, K. & Huang, Z. 1999 Dust-acoustic solitary waves and double layers in dusty plasma with variable dust charge and two-temperature ions. Phys. Plasmas 6, 3808.Google Scholar
Xue, J. K. 2003 A spherical KP equation for dust acoustic waves. Phys. Lett. A 314, 479–483.Google Scholar