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Finite ion temperature effects on oblique modulational stability and envelope excitations of dust-ion acoustic waves

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Abstract.

Theoretical and numerical investigations are carried out for the amplitude modulation of dust-ion acoustic waves (DIAW) propagating in an unmagnetized weakly coupled collisionless fully ionized plasma consisting of isothermal electrons, warm ions and charged dust grains. Modulation oblique (by an angle \(\theta\)) to the carrier wave propagation direction is considered. The stability analysis, based on a nonlinear Schrödinger-type equation (NLSE), exhibits a sensitivity of the instability region to the modulation angle \(\theta\), the dust concentration and the ion temperature. It is found that the ion temperature may strongly modify the wave’s stability profile, in qualitative agreement with previous results, obtained for an electron-ion plasma. The effect of the ion temperature on the formation of DIAW envelope excitations (envelope solitons) is also discussed.

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References

  1. P.K. Shukla, A.A. Mamun, Introduction to Dusty Plasma Physics (Institute of Physics Publishing Ltd., Bristol, 2002)

  2. N.N. Rao, P.K. Shukla, M.Y. Yu, Planet. Space Sci. 38, 543 (1990)

    Article  Google Scholar 

  3. P.K. Shukla, V.P. Silin, Phys. Scripta 45, 508 (1992)

    Google Scholar 

  4. A. Barkan, R. Merlino, N. D’Angelo, Phys. Plasmas 2, 3563 (1995)

    Article  Google Scholar 

  5. J. Pieper, J. Goree, Phys. Rev. Lett. 77, 3137 (1996)

    Article  Google Scholar 

  6. A. Barkan, N. D’Angelo, R. Merlino, Planet. Space Sci. 44, 239 (1996)

    Article  Google Scholar 

  7. F. Verheest, Waves in Dusty Space Plasmas (Kluwer Academic Publishers, Dordrecht, 2001)

  8. N.A. Krall, A.W. Trivelpiece, Principles of plasma physics (McGraw-Hill, New York, 1973)

  9. Th. Stix, Waves in Plasmas (American Institute of Physics, New York, 1992)

  10. T. Taniuti, N. Yajima, J. Math. Phys. 10, 1369 (1969)

    Google Scholar 

  11. N. Asano, T. Taniuti, N. Yajima, J. Math. Phys. 10, 2020 (1969)

    Google Scholar 

  12. A.S. Davydov, Solitons in Molecular Systems (Kluwer Academic Publishers, Dordrecht, 1985)

  13. A. Hasegawa, Optical Solitons in Fibers (Springer-Verlag, 1989)

  14. E. Infeld, G. Rowlands, Nonlinear Waves, Solitons and Chaos (Cambridge University Press, Cambridge, England, 1990)

  15. M. Remoissenet, Waves Called Solitons (Springer-Verlag, Berlin, 1994)

  16. K. Shimizu, H. Ichikawa, J. Phys. Soc. Jpn 33, 789 (1972)

    Google Scholar 

  17. M. Kako, Prog. Theor. Phys. Suppl. 55, 1974 (1974)

    Google Scholar 

  18. T. Kakutani, N. Sugimoto, Phys. Fluids 17, 1617 (1974)

    Google Scholar 

  19. M. Kako, A. Hasegawa, Phys. Fluids 19, 1967 (1976)

    Article  Google Scholar 

  20. R. Chhabra, S. Sharma, Phys. Fluids 29, 128 (1986)

    Article  Google Scholar 

  21. M. Mishra, R. Chhabra, S. Sharma, Phys. Plasmas 1, 70 (1994)

    MATH  Google Scholar 

  22. V. Chan, S. Seshadri, Phys. Fluids 18, 1294 (1975)

    Article  Google Scholar 

  23. I. Durrani, Phys. Fluids 22, 791 (1979)

    Article  Google Scholar 

  24. J.-K. Xue, W.-S. Duan, L. He, Chin. Phys. 11, 1184 (2002)

    Article  Google Scholar 

  25. This remark excludes e.g. the electron plasma mode, which was found to be stable to parallel perturbations for all carrier wavelengths

  26. M.R. Amin, G.E. Morfill, P.K. Shukla, Phys. Rev. E 58, 6517 (1998)

    Article  Google Scholar 

  27. R.-A. Tang, J.-K. Xue, Phys. Plasmas 10, 3800 (2003)

    Article  Google Scholar 

  28. I. Kourakis, P.K. Shukla, J. Math. Phys. (2003, submitted)

  29. Xue Jukui, Lang He, Phys. Plasmas 10, 339 (2003)

    Article  Google Scholar 

  30. I.Kourakis, P.K. Shukla, Phys. Plasmas 10, 3459 (2003)

    Article  Google Scholar 

  31. M.R. Amin, G.E. Morfill, P.K. Shukla, Phys. Plasmas 5, 2578 (1998)

    Article  Google Scholar 

  32. I. Kourakis, Proceedings of the 29th EPS meeting on Controlled Fusion and Plasma Physics, European Conference Abstracts (ECA), Vol. 26B P-4.221 (European Physical Society, Petit-Lancy, Switzerland, 2002)

  33. Notice that the parameters \(\alpha\), \(\alpha'\), \(\beta\) all take positive values of similar order of magnitude (for Z i =1) and may not be neglected

  34. As a matter of fact, the numerical factor \(1/3\) in reference [16] is exactly obtained here upon setting \(\alpha = 1/2\), \(\alpha' = 1/6\), \(\beta = 1\) and \(\sigma = 0\), into our formulae

  35. W. Watanabe, J. Plasma Phys. 17, 487 (1977)

    MATH  Google Scholar 

  36. W. Watanabe, J. Plasma Phys. 14, 353 (1975)

    Google Scholar 

  37. Q.-Z. Luo, N. D’Angelo, R. Merlino, Phys. Plasmas 5, 2868 (1998)

    Article  Google Scholar 

  38. Y. Nakamura, H. Bailung, P.K. Shukla, Phys. Rev. Lett. 83, 1602 (1999)

    Article  Google Scholar 

  39. P.K. Shukla, Phys. Plasmas 10, 1619 (2003)

    Article  Google Scholar 

  40. A. Hasegawa, Plasma Instabilities and Nonlinear Effects (Springer-Verlag, Berlin, 1975)

  41. R. Fedele, H. Schamel, Eur. Phys. J. B 27, 313 (2002)

    Article  Google Scholar 

  42. This expression is readily obtained from reference [41], by shifting the variables therein to our notation as: \(x \rightarrow \zeta\), \(s \rightarrow \tau\), \(\rho_m \rightarrow \rho_0\), \(\alpha \rightarrow 2 P\), \(q_0 \rightarrow - 2 P Q\), \(\Delta \rightarrow L\), \(E \rightarrow \Omega\), \(V_0 \rightarrow u\).

  43. S. Flach, C. Willis, Phys. Rep. 295, 181 (1998)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Institut für Theoretische Physik IV, Fakultät für Physik und Astronomie, Ruhr-Universität Bochum, 44780, Bochum, Germany

    I. Kourakis & P. K. Shukla

Authors
  1. I. Kourakis
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  2. P. K. Shukla
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Correspondence to I. Kourakis.

Additional information

Received: 2 September 2003, Published online: 21 October 2003

PACS:

52.27.Lw Dusty or complex plasmas; plasma crystals - 52.35.Fp Electrostatic waves and oscillations (e.g., ion-acoustic waves) - 52.35.Mw Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.) - 52.35.Sb Solitons; BGK modes

I. Kourakis: On leave from: U.L.B., Université Libre de Bruxelles, Faculté des Sciences Apliquées, C.P. 165/81 Physique Générale, avenue F.D. Roosevelt 49, 1050 Brussels, Belgium.

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Kourakis, I., Shukla, P.K. Finite ion temperature effects on oblique modulational stability and envelope excitations of dust-ion acoustic waves. Eur. Phys. J. D 28, 109–117 (2004). https://doi.org/10.1140/epjd/e2003-00292-4

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