Advertisement

Astrophysics and Space Science

, Volume 343, Issue 1, pp 279–287 | Cite as

Dust-ion-acoustic solitary waves and their multi-dimensional instability in a magnetized nonthermal dusty electronegative plasma

  • N. R. KunduEmail author
  • M. M. Masud
  • K. S. Ashrafi
  • A. A. Mamun
Original Article

Abstract

A rigorous theoretical investigation has been made on multi-dimensional instability of obliquely propagating electrostatic dust-ion-acoustic (DIA) solitary structures in a magnetized dusty electronegative plasma which consists of Boltzmann electrons, nonthermal negative ions, cold mobile positive ions, and arbitrarily charged stationary dust. The Zakharov-Kuznetsov (ZK) equation is derived by the reductive perturbation method, and its solitary wave solution is analyzed for the study of the DIA solitary structures, which are found to exist in such a dusty plasma. The multi-dimensional instability of these solitary structures is also studied by the small-k (long wave-length plane wave) perturbation expansion technique. The combined effects of the external magnetic field, obliqueness, and nonthermal distribution of negative ions, which are found to significantly modify the basic properties of small but finite-amplitude DIA solitary waves, are examined. The external magnetic field and the propagation directions of both the nonlinear waves and their perturbation modes are found to play a very important role in changing the instability criterion and the growth rate of the unstable DIA solitary waves. The basic features (viz. speed, amplitude, width, instability, etc.) and the underlying physics of the DIA solitary waves, which are relevant to many astrophysical situations (especially, auroral plasma, Saturn’s E-ring and F-ring, Halley’s comet, etc.) and laboratory dusty plasma situations, are briefly discussed.

Keywords

Dust-ion-acoustic waves Nonthermal distribution Zakharov-Kuznetsov equation Dusty electronegative plasma Instability Reductive perturbation method 

Notes

Acknowledgements

The research grant for research equipment from the Third World Academy of Sciences (TWAS), ICTP, Trieste, Italy is gratefully acknowledged.

References

  1. Alinejad, H.: Astrophys. Space Sci. 327, 131 (2010) ADSzbMATHCrossRefGoogle Scholar
  2. Annaratone, B.M., Allen, J.E.: J. Phys. D, Appl. Phys. 38, 26 (2005) ADSCrossRefGoogle Scholar
  3. Annaratone, B.M., et al.: Phys. Rev. Lett. 93, 185001 (2004) ADSCrossRefGoogle Scholar
  4. Anowar, M.G.M., Mamun, A.A.: Phys. Plasmas 15, 102111 (2008) ADSCrossRefGoogle Scholar
  5. Anowar, M.G.M., Mamun, A.A.: J. Plasma Phys. 75, 475 (2009) ADSCrossRefGoogle Scholar
  6. Barkan, A., et al.: Planet. Space Sci. 44, 239 (1996) ADSCrossRefGoogle Scholar
  7. Berezhnoj, S.V., et al.: Appl. Phys. Lett. 77, 800 (2000) ADSCrossRefGoogle Scholar
  8. Bogdanov, E.A., Kudryavtsev, A.A.: Tech. Phys. Lett. 27, 905 (2001) ADSCrossRefGoogle Scholar
  9. Buslaev, V., Sulem, C.: Annal. Inst. Henri Poincaré, Anal. Nonlineaire 202, 419 (2003) MathSciNetADSCrossRefGoogle Scholar
  10. Cairns, A.J., et al.: Geophys. Res. Lett. 22, 2709 (1995) ADSCrossRefGoogle Scholar
  11. Chabert, P., et al.: Phys. Plasmas 14, 093502 (2007) ADSCrossRefGoogle Scholar
  12. Chung, T.H.: Phys. Plasmas 16, 063503 (2009) ADSCrossRefGoogle Scholar
  13. Coates, R.A., et al.: Geophys. Res. Lett. 34, L22103 (2007) ADSCrossRefGoogle Scholar
  14. Cuccagna, S.: J. Differ. Equ. 245, 653 (2008) MathSciNetzbMATHCrossRefGoogle Scholar
  15. D’Angelo, N.D.: J. Phys. D 37, 860 (2004) ADSCrossRefGoogle Scholar
  16. Das, P.K., Verheest, F.: J. Plasma Phys. 41, 171 (1989) ADSCrossRefGoogle Scholar
  17. El-Labany, S.K., El-Taibany, W.F.: J. Plasma Phys. 70, 69 (2004) ADSCrossRefGoogle Scholar
  18. El-Labany, S.K., El-Taibany, W.F., El-Fayoumy, M.M.: Astrophys. Space Sci. (2012). doi: 10.1007/s10509-012-1089-3 Google Scholar
  19. Franklin, R.N.: Plasma Sources Sci. Technol. 11, A31 (2002) ADSCrossRefGoogle Scholar
  20. Franklin, R.N., Snell, J.: J. Plasma Phys. 64, 131 (2000) ADSCrossRefGoogle Scholar
  21. Ghim, Y., Hershkowitz, N.: Appl. Phys. Lett. 94, 151503 (2009) ADSCrossRefGoogle Scholar
  22. Goertz, C.K.: Rev. Geophys. 27, 271 (1989) ADSCrossRefGoogle Scholar
  23. Infeld, E.: J. Plasma Phys. 8, 105 (1972) ADSCrossRefGoogle Scholar
  24. Infeld, E.: J. Plasma Phys. 33, 171 (1985) ADSCrossRefGoogle Scholar
  25. Infeld, E., Rowlands, G.: J. Plasma Phys. 10, 293 (1973) ADSCrossRefGoogle Scholar
  26. Kim, S.H., Merlino, R.L.: Phys. Plasmas 13, 052118 (2006) ADSCrossRefGoogle Scholar
  27. Kimura, T., et al.: J. Phys. D, Appl. Phys. 31, 2295 (1998) ADSCrossRefGoogle Scholar
  28. Kirr, E., Zarnescu, A.: J. Differ. Equ. 247, 710 (2009) MathSciNetzbMATHCrossRefGoogle Scholar
  29. Kourakis, I., Shukla, P.K.: Eur. Phys. J., D, At. Mol. Opt. Phys. 30, 97 (2004a) ADSGoogle Scholar
  30. Kourakis, I., Shukla, P.K.: Phys. Scr. 69, 316 (2004b) ADSzbMATHCrossRefGoogle Scholar
  31. Lee, L.C., Kan, J.R.: Phys. Fluids 24, 430 (1981) ADSzbMATHCrossRefGoogle Scholar
  32. Lichtenberg, A.J., et al.: Plasma Sources Sci. Technol. 6, 437 (1997) ADSCrossRefGoogle Scholar
  33. Lieberman, M.A., Lichtenberg, A.: Principle of Plasma Discharges and Materials Processing, 2nd edn. Wiley, New York (2005) CrossRefGoogle Scholar
  34. Mamun, A.A.: Rev. Plasma Phys. 55, 1852 (1997) Google Scholar
  35. Mamun, A.A.: Phys. Plasmas 5, 322 (1998) ADSCrossRefGoogle Scholar
  36. Mamun, A.A., Shukla, P.K.: Phys. Plasmas 65, 1518 (2003) ADSCrossRefGoogle Scholar
  37. Mamun, A.A., et al.: Phys. Lett. A 373, 2355 (2009a) ADSzbMATHCrossRefGoogle Scholar
  38. Mamun, A.A., et al.: Phys. Rev. E 80, 046406 (2009b) ADSCrossRefGoogle Scholar
  39. Masud, M.M., et al.: Astrophys. Space Sci. (2012), doi: 10.1007/s10509-012-1244-x zbMATHGoogle Scholar
  40. Meige, A.J., et al.: Phys. Plasmas 14, 053508 (2007) ADSCrossRefGoogle Scholar
  41. Mendis, D.A., Rosenberg, M.: Annu. Rev. Astron. Astrophys. 32, 419 (1994) ADSCrossRefGoogle Scholar
  42. Merlino, R.L., Goree, J.: Phys. Today 57, 32 (2004) CrossRefGoogle Scholar
  43. Merlino, R.L., Kim, S.H.: Appl. Phys. Lett. 89, 091501 (2006) ADSCrossRefGoogle Scholar
  44. Mizumachi, T.: J. Math. Kyoto Univ. 47, 599 (2007) MathSciNetzbMATHGoogle Scholar
  45. Mizumachi, T.: J. Math. Kyoto Univ. 48, 471 (2008) MathSciNetzbMATHGoogle Scholar
  46. Moslem, W.M., El-Taibany, W.F.: Phys. Plasmas 12, 122309 (2005) ADSCrossRefGoogle Scholar
  47. Pelinovsky, D.E., Stefanov, A.: J. Math. Phys. 53, 073705 (2012) ADSCrossRefGoogle Scholar
  48. Phihon, N., et al.: Phys. Plasmas 14, 013506 (2007) ADSCrossRefGoogle Scholar
  49. Rosenberg, M., Merlino, R.L.: Planet. Space Sci. 55, 1464 (2007) ADSCrossRefGoogle Scholar
  50. Rowlands, G.: J. Plasma Phys. 3, 567 (1969) ADSCrossRefGoogle Scholar
  51. Shukla, P.K., Eliasson, B.: Rev. Mod. Phys. 81, 23 (2009) ADSCrossRefGoogle Scholar
  52. Shukla, P.K., Mamun, A.A.: Introduction to Dusty Plasma Physics. Institute of Physics Publishing, Bristol (2002) CrossRefGoogle Scholar
  53. Shukla, P.K., Silin, V.P.: Phys. Scr. 45, 508 (1992) ADSCrossRefGoogle Scholar
  54. Shukla, P.K., Yu, M.Y.: J. Math. Phys. 19, 2506 (1978) ADSCrossRefGoogle Scholar
  55. Shukla, P.K., et al.: J. Geophys. Res. 96, 21343 (1991) ADSCrossRefGoogle Scholar
  56. Vender, D., et al.: Phys. Rev. E 51, 2436 (1995) ADSCrossRefGoogle Scholar
  57. Washimi, H., Taniuti, T.: Phys. Rev. Lett. 17, 996 (1966) ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • N. R. Kundu
    • 1
    Email author
  • M. M. Masud
    • 1
  • K. S. Ashrafi
    • 1
  • A. A. Mamun
    • 1
  1. 1.Department of PhysicsJahangirnagar UniversityDhakaBangladesh

Personalised recommendations