Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-26T00:21:54.877Z Has data issue: false hasContentIssue false
  • English
  • Français

Dust acoustic solitary waves in non-thermal plasmas consisting of negatively charged dust grains and isothermal electrons

Published online by Cambridge University Press:  01 August 2009

ANIMESH DAS  and
ANUP BANDYOPADHYAY
ANIMESH DAS
Affiliation:
Department of Mathematics, Jadavpur University, Kolkata 700 032, India ([email protected])
ANUP BANDYOPADHYAY
Affiliation:
Department of Mathematics, Jadavpur University, Kolkata 700 032, India ([email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

A Korteweg–de Vries (KdV) equation is derived here, that describes the nonlinear behaviour of long-wavelength weakly nonlinear dust acoustic waves propagating in an arbitrary direction in a plasma consisting of static negatively charged dust grains, non-thermal ions and isothermal electrons. It is found that the rarefactive or compressive nature of the dust acoustic solitary wave solution of the KdV equation does not depend on the dust temperature if σdc < 0 or σdc > σd*, where σdc is a function of β1, α and μ only, and σd*(<1) is the upper limit (upper bound) of σd. This β1 is the non-thermal parameter associated with the non-thermal velocity distribution of ions, α is the ratio of the average temperature of the non-thermal ions to that of the isothermal electrons, μ is the ratio of the unperturbed number density of isothermal electrons to that of the non-thermal ions, Zdσd is the ratio of the average temperature of the dust particles to that of the ions and Zd is the number of electrons residing on the dust grain surface. The KdV equation describes the rarefactive or the compressive dust acoustic solitary waves according to whether σdc < 0 or σdc > σd*. When 0 ≤ σdc ≤ σd*, the KdV equation describes the rarefactive or the compressive dust acoustic solitary waves according to whether σd > σdc or σd < σdc. If σd takes the value σdc with 0 ≤ σdc ≤ σd*, the coefficient of the nonlinear term of the KdV equation vanishes and, for this case, the nonlinear evolution equation of the dust acoustic waves is derived, which is a modified KdV (MKdV) equation. A theoretical investigation of the nature (rarefactive or compressive) of the dust acoustic solitary wave solutions of the evolution equations (KdV and MKdV) is presented with respect to the non-thermal parameter β1. For any given values of α and μ, it is found that the value of σdc completely defines the nature of the dust acoustic solitary waves except for a small portion of the entire range of the non-thermal parameter β1.

Type
Papers
Information
Journal of Plasma Physics , Volume 75 , Issue 4 , August 2009 , pp. 455 - 474
Copyright
Copyright © Cambridge University Press 2009

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

[1]Verheest, F. 1992 Nonlinear dust–acoustic waves in multispecies dusty plasmas. Planet. Space Sci. 40, 1–6.CrossRefGoogle Scholar
[2]Pillay, S. R., Bharuthram, R. and Verheest, F. 2000 The Jeans–Buneman instability in the presence of an ion beam in a dusty plasma and the influence of dust-size distribution. Phys. Scripta 61, 112–118.CrossRefGoogle Scholar
[3]Verheest, F. 2001 Waves in Dusty Space Plasmas. Dordrecht: Kluwer Academic.Google Scholar
[4]Shukla, P. K. and Mamun, A. A. 2002 Introduction to Dusty Plasma Physics. Bristol: IoP Publishing.CrossRefGoogle Scholar
[5]Rao, N. N., Shukla, P. K. and Yu, M. Y. 1990 Dust–acoustic waves in dusty plasmas. Planet. Space Sci. 38, 543–546.Google Scholar
[6]Shukla, P. K. and Silin, V. P. 1992 Dust ion–acoustic wave. Phys. Scripta 45, 508.CrossRefGoogle Scholar
[7]Verma, 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, 3612–3616.Google Scholar
[8]Rosenberg, M. and Kalman, G. 1997 Dust acoustic waves in strongly coupled dusty plasmas. Phys. Rev. E 56, 7166–7173.Google Scholar
[9]Shukla, P. K. 2001 A survey of dusty plasma physics. Phys. Plasmas 8, 1791–1803.Google Scholar
[10]Goertz, C. K. 1989 Dusty plasmas in the solar system. Rev. Geophys. 27, 271–292.CrossRefGoogle Scholar
[11]Barkan, A., Merlino, R. L. and D'Angelo, , 1995 Laboratory observation of the dust–acoustic wave mode. Phys. Plasmas 2, 3563–3565.CrossRefGoogle Scholar
[12]Pieper, J. B. and Goree, J. 1996 Dispersion of plasma dust acoustic waves in the strong-coupling regime. Phys. Rev. Lett. 77, 3137–3140.CrossRefGoogle ScholarPubMed
[13]Mamun, A. A., Cairns, R. A. and Shukla, P. K. 1996 Solitary potentials in dusty plasmas. Phys. Plasmas 3, 702–704.CrossRefGoogle Scholar
[14]Mamun, A. A., Cairns, R. A. and Shukla, P. K. 1996 Effects of vortex-like and non-thermal ion distributions on non-linear dust–acoustic waves. Phys. Plasmas 3, 2610–2614.CrossRefGoogle Scholar
[15]Washimi, H. and Taniuti, T. 1966 Propagation of ion–acoustic solitary waves of small amplitude. Phys. Rev. Lett. 17, 996–998.Google Scholar
[16]Sagdeev, R. Z. 1966 Reviews of Plasma Physics, Vol. 4 (ed. Leontovich, M. A.). New York: Springer/Consultant Bureau.Google Scholar
[17]Mendoza-Briceño, C. A., Russel, S. M. and Mamun, A. A. 2000 Large amplitude electrostatic solitary structures in a hot non-thermal dusty plasma. Planet. Space Sci. 48, 599–608.CrossRefGoogle Scholar
[18]Maharaj, S. K., Pillay, S. R., Bharuthram, R., Singh, S. V. and Lakhina, G. S. 2004 The effect of dust grain temperature and dust streaming on electrostatic solitary structures in a non-thermal plasma. Phys. Scripta T113, 135–140.CrossRefGoogle Scholar
[19]Maharaj, S. K., Pillay, S. R., Bharuthram, R., Reddy, R. V., Singh, S. V. and Lakhina, G. S. 2006 Arbitrary amplitude dust–acoustic double layers in a non-thermal plasma. J. Plasma Phys. 72, 43–58.Google Scholar
[20]Cairns, R. A., Mamun, A. A., Bingham, R., Böstrom, R., Dendy, R. O., Nairn, C. M. C. and Shukla, P. K. 1995 Electrostatic solitary structures in non-thermal plasmas. Geophys. Res. Lett. 22, 2709–2712.CrossRefGoogle Scholar
[21]Cairns, R. A., Bingham, R., Dendy, R. O., Nairn, C. M. C., Shukla, P. K. and Mamun, A. A. 1995 Ion sound solitary waves with density depressions. J. Phys. (Fr.) 5 (C6), 43–48.Google Scholar
[22]Cairns, R. A., Mamun, A. A., Bingham, R. and Shukla, P. K. 1996 Ion–acoustic solitons in a magnetized plasma with nonthermal electrons. Phys. Scripta T63, 80–86.CrossRefGoogle Scholar
[23]Mamun, A. A. and Cairns, R. A. 1996 Stability of solitary waves in a magnetized non-thermal plasma. J. Plasma Phys. 56, 175–185.CrossRefGoogle Scholar
[24]Bandyopadhyay, A. and Das, K. P. 1999 Stability of solitary waves in a magnetized non-thermal plasma with warm ions. J. Plasma Phys. 62, 255–267.Google Scholar
[25]Bandyopadhyay, A. and Das, K. P. 2001 Growth rate of instability of obliquely propagating ion–acoustic solitons in a magnetized nonthermal plasma. J. Plasma Phys. 65, 131–150.CrossRefGoogle Scholar
[26]Bandyopadhyay, A. and Das, K. P. 2002 Higher order growth rate of instability of obliquely propagating kinetic Alfvén and ion–acoustic solitons in a magnetized nonthermal plasma. J. Plasma Phys. 68, 285–303.CrossRefGoogle Scholar
[27]Bandyopadhyay, A. and Das, K. P. 2000 Ion–acoustic double layers and solitary waves in a magnetized plasma consisting of warm ions and non-thermal electrons. Phys. Scripta 61, 92–96.Google Scholar
[28]Bandyopadhyay, A. and Das, K. P. 2001 Stability of ion–acoustic double layers in a magnetized plasma consisting of warm ions and nonthermal electrons. Phys. Scripta 63, 145–149.Google Scholar
[29]Bandyopadhyay, A. and Das, K. P. 2000 Stability of solitary kinetic Alfvén waves and ion–acoustic waves in a nonthermal plasma. Phys. Plasmas 7, 3227–3237.CrossRefGoogle Scholar
[30]Bandyopadhyay, A. and Das, K. P. 2002 Effect of Landau damping on ion–acoustic solitary waves in a magnetized nonthermal plasma with warm ions. Phys. Plasmas 9, 465–473.Google Scholar
[31]Bandyopadhyay, A. and Das, K. P. 2002 Effect of Landau damping on kinetic Alfvén and ion–acoustic solitary waves in a magnetized nonthermal plasma with warm ions. Phys. Plasmas 9, 3333–3340.CrossRefGoogle Scholar
[32]Das, J., Bandyopadhyay, A. and Das, K. P. 2006 Stability of an alternative solitary wave solution of an ion–acoustic wave obtained from MKdV-KdV-ZK equation in magnetized non-thermal plasma consisting of warm adiabatic ions. J. Plasma Phys. 72, 587–604.CrossRefGoogle Scholar
[33]Das, J., Bandyopadhyay, A. and Das, K. P. 2007 Alternative ion–acoustic solitary waves in magnetized plasma consisting of warm adiabatic ions and non-thermal electrons having vortex-like velocity distribution: existence and stability. J. Plasma Phys. 73, 869–899.CrossRefGoogle Scholar
[34]Das, J., Bandyopadhyay, A. and Das, K. P. 2008 Ion–acoustic double layers in magnetized plasma consisting of warm adiabatic ions and non-thermal electrons having vortex-like velocity distribution: existence and stability. J. Plasma Phys. 74, 163–186.Google Scholar
[35]Das, J., Bandyopadhyay, A. and Das, K. P. 2007 Existence and stability of alternative ion acoustic solitary wave solution of the combined MKdV-KdV-ZK equation in a magnetized non-thermal plasma consisting of warm adiabatic ions. Phys. Plasmas 14, 092304-1–092304-10.CrossRefGoogle Scholar
[36]Verheest, F. and Pillay, S. R. 2008 Large amplitude dust–acoustic solitary waves and double layers in nonthermal plasmas. Phys. Plasmas 15, 013703-1–013703-11.Google Scholar
[37]Shukla, P. K. and Mamun, A. A. 2003 Solitons, shocks and vortices in dusty plasmas. New J. Phys. 5, 17.1–17.37.CrossRefGoogle Scholar
[38]Mamun, A. A., Shukla, P. K. and Verheest, F. 2002 Nonlinear electrostatic waves in dusty plasmas. In: Dust Plasma Interaction in Space (ed. Shukla, P. K.). New York: Nova Science, Chap. 4, p. 209.Google Scholar
[39]Mamun, A. A. 1999 Arbitrary amplitude dust–acoustic solitary structures in a three-component dusty plasma. Astrophys. Space Sci. 268, 443–454.CrossRefGoogle Scholar