Skip to main content
SpringerLink
Log in

Nonlinear Dust Acoustic Waves in Nonuniform Complex Plasma under the Effect of Tsallis Polarization Force

  • WAVES IN PLASMA
  • Published:
Physics of Wave Phenomena Aims and scope Submit manuscript

Abstract

In the present article, we analyzed the effects of Tsallis (or nonextensive) polarization force on nonlinear dust acoustic waves (DAWs). The polarization force acting on dust particles in a nonuniform dusty plasma is then revisited within the theoretical framework of the nonextensive statistical mechanics. The behavior of the polarization force is considerably changed due to the presence of nonextensive ions. Specifically, we showed that, for both experimental and space dusty plasmas, the magnitude of the polarization force (in the case where q > 1) increases as the ion nonextensivity becomes significant. As an application, we studied the changes caused by the nonextensive polarization force on the intrinsic properties of the DAW, namely, the wave profile, the transported energy, and the electric field. In particular, we have shown that due to the presence of nonextensive polarization force, the DA wave profile becomes deeper and the transported energy undergoes depletion. For a good understanding, we have also carried out a comparative study on the effects of the nonextensive polarization force on the DAW and its energy associated with both space and experimental dusty plasmas. We have found that, for a given value of the nonextensive parameter q, the DAW profile of the experimental dusty plasma seems more affected by the presence of the Tsallis polarization force.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.
Fig. 8.
Fig. 9.
Fig. 10.
Fig. 11.
Fig. 12.
Fig. 13.

Similar content being viewed by others

REFERENCES

  1. P. K. Shukla and A.A. Mamun, Introduction to Dusty Plasma Physics (Inst. Phys., Bristol, 2002).

    Book  Google Scholar 

  2. P. K. Shukla and V. P. Silin, “Dust ion-acoustic wave,” Phys. Scr. 45 (5), 508 (1992). https://doi.org/10.1088/0031-8949/45/5/015

    Article  ADS  Google Scholar 

  3. N. N. Rao, P. K. Shukla, and M. Y. Yu, “Dust-acoustic waves in dusty plasmas,” Planet. Space Sci. 38 (4), 543–546 (1990). https://doi.org/10.1016/0032-0633(90)90147-I

    Article  ADS  Google Scholar 

  4. A. E. Dubinov and M. A. Sazonkin, “Supernonlinear ion-acoustic waves in a dusty plasma,” Phys. Wave Phenom. 21 (2), 118–128 (2013). https://doi.org/10.3103/S1541308X13020039

    Article  ADS  Google Scholar 

  5. A. Paul, G. Mandal, A. A. Mamun, and M. R. Amin, “Effects of vortex-like ion distribution on dust-acoustic solitary waves in a self-gravitating opposite polarity dusty plasmas,” Phys. Wave Phenom. 27 (4), 261–267 (2019). https://doi.org/10.3103/S1541308X19040034

    Article  ADS  Google Scholar 

  6. S. Sultana, “Shock waves in magnetized plasmas with superthermal trapped electrons,” Chin. J. Phys. 69, 206–218 (2021). https://doi.org/10.1016/j.cjph.2020.12.005

    Article  MathSciNet  Google Scholar 

  7. A. Berbri, S. Younsi, and M. Laghbeche, “Dust acoustic shock waves in a warm magnetized dusty plasma with kappa distributed electrons and ions,” Phys. Wave Phenom. 30 (6), 378–386 (2022). https://doi.org/10.3103/S1541308X22060024

    Article  ADS  Google Scholar 

  8. R. B. Kian and M. H. Mahdieh, “The compressive and rarefactive dust acoustic solitary waves with two different temperatures for both electrons and ions,” Phys. Wave Phenom. 30 (5), 336–343 (2022). https://doi.org/10.3103/S1541308X22050041

    Article  ADS  Google Scholar 

  9. R. B. Kian and M. H. Mahdieh, “Large amplitude dust acoustic solitary waves with non-thermal distribution for both electrons and ions,” Phys. Wave Phenom. 30 (6), 370–377 (2022). https://doi.org/10.3103/S1541308X22060048

    Article  ADS  Google Scholar 

  10. S. Benaiche, M. Bacha, A. Merriche, and R. Amour, “Effect of Tsallis–Gurevich distributed ions on nonlinear dust-acoustic oscillations in collisionless nonextensive plasma,” Contrib. Plasma Phys. 63 (2), e202200132 (2023). https://doi.org/10.1002/ctpp.202200132

    Article  ADS  Google Scholar 

  11. S. Hamaguchi and R. T. Farouki, “Polarization force on a charged particulate in a nonuniform plasma,” Phys. Rev. E 49 (5), 4430–4441 (1994). https://doi.org/10.1103/PhysRevE.49.4430

    Article  ADS  Google Scholar 

  12. S. Hamaguchi and R. T. Farouki, “Plasma–particulate interactions in nonuniform plasmas with finite flows,” Phys. Plasmas 1, 2110–2118 (1994). https://doi.org/10.1063/1.870608

    Article  ADS  Google Scholar 

  13. S. A. Khrapak, A. V. Ivlev, V. V. Yaroshenko, and G. E. Morfill, “Influence of a polarization force on dust acoustic waves,” Phys. Rev. Lett. 102 (24), 245004 (1990). https://doi.org/10.1103/PhysRevLett.102.245004

    Article  ADS  Google Scholar 

  14. K. S. Ashrafi, A. A. Mamun, and P. K. Shukla, “Polarization force for different dusty plasma situations,” J. Plasma Phys. 80 (1), 1–7 (2014). https://doi.org/10.1017/S0022377813000408

    Article  ADS  Google Scholar 

  15. O. Bouzit and M. Tribeche, “Dust-acoustic waves modulational instability and rogue waves in a polarized dusty plasma,” Phys. Plasmas 22, 103703 (2015). https://doi.org/10.1063/1.4933006

    Article  ADS  Google Scholar 

  16. S. Mayout, K. Bentabet, and M. Tribeche, “Polarization force-induced changes in the dust sheath formation,” Phys. Plasmas 22, 093705 (2015). https://doi.org/10.1063/1.4931173

    Article  ADS  Google Scholar 

  17. S. Mayout, K. Bentabet, and M. Tribeche, “Effect of the polarization force on the dust-acoustic soliton energy,” Contrib. Plasma Phys. 56 (2), 99–103 (2016). https://doi.org/10.1002/ctpp.201500068

    Article  ADS  MATH  Google Scholar 

  18. M. Asaduzzaman and A. A. Mamun, “Effects of nonthermal ions and polarization force on dust-acoustic waves in a density-varying dusty plasma,” Phys. Rev. E 86 (1), 016409 (2012). https://doi.org/10.1103/PhysRevE.86.016409

    Article  ADS  Google Scholar 

  19. K. Bentabet, S. Mayout, and M. Tribeche, “Generalized polarization force acting on dust grains in a dusty plasma,” Phys. A 44, 492–501 (2017). https://doi.org/10.1016/j.physa.2016.09.055

    Article  MathSciNet  MATH  Google Scholar 

  20. K. Bentabet and M. Tribeche, “Dust-acoustic solitons in a polarized dusty plasma with nonthermal ions,” IEEE Trans. Plasma Sci. 45 (4), 736–741 (2017). https://doi.org/10.1109/TPS.2017.2677203

    Article  ADS  Google Scholar 

  21. N. Arab, R. Amour, and M. Benzekka, “Effect of Cairns–Gurevich polarization force on dust-acoustic solitons in collisionless dusty plasmas,” Eur. Phys. J. Plus 135 (11), 872 (2020). https://doi.org/10.1140/epjp/s13360-020-00892-w

    Article  Google Scholar 

  22. N. Arab, R. Amour, and T. H. Zerguini, “Low-frequency solitary wave propagations in complex plasmas: The effect of trapped non-thermal polarization force,” Waves Random Complex Media 33 (1), 163–180 (2021). https://doi.org/10.1080/17455030.2021.1876280

    Article  ADS  MathSciNet  Google Scholar 

  23. B. Belaifa and M. Benzekka, “Effect of Gurevich polarization force on arbitrary amplitude dust-acoustic waves and double-layer structures in a collisionless complex plasma,” IEEE Trans. Plasma Sci. 50 (9), 3229–3237 (2022). https://doi.org/10.1109/TPS.2022.3198332

    Article  ADS  Google Scholar 

  24. C. Tsallis, “Possible generalization of Boltzmann–Gibbs statistics,” J. Stat. Phys. 52 (1–2), 479–487 (1988). https://doi.org/10.1007/bf01016429

  25. J. A. S. Lima, R. Silva, Jr., and J. Santos, “Plasma oscillations and nonextensive statistics,” Phys. Rev. E 61 (3), 3260–3263 (2000). https://doi.org/10.1103/physreve.61.3260

    Article  ADS  Google Scholar 

  26. R. Silva, Jr., R. Plastino, and J. A. S. Lima, “A Maxwellian path to the q-nonextensive velocity distribution function,” Phys. Lett. A 249 (5–6), 401–408 (1998). https://doi.org/10.1016/S0375-9601(98)00710-5

  27. J. Du, “Nonextensivity in nonequilibrium plasma systems with Coulombian long-range interactions,” Phys. Lett. A 329 (4–5), 262–267 (2004). https://doi.org/10.1016/j.physleta.2004.07.010

  28. F. Sattin, “Non-extensive entropy from incomplete knowledge of Shannon entropy?” Phys. Scr. 71 (5), 443–446 (2005). https://doi.org/10.1238/Physica.Regular.071a00443

    Article  ADS  MathSciNet  MATH  Google Scholar 

  29. N. G. de Almeida, “Formal equivalence between Tsallis and extended Boltzmann–Gibbs statistics,” Phys. A 387 (12), 2745–2749 (2008). https://doi.org/10.1016/j.physa.2008.01.066

    Article  MathSciNet  Google Scholar 

  30. L. Liu and J. Du, “Ion acoustic waves in the plasma with the power-law q-distribution in nonextensive statistics,” Phys. A 387 (19–20), 4821–4827 (2008). https://doi.org/10.1016/j.physa.2008.04.016

  31. V. Latora, A. Rapisarda, and C. Tsallis, “Non-Gaussian equilibrium in a long-range Hamiltonian system,” Phys. Rev. E 64 (5), 056134 (2001). https://doi.org/10.1103/physreve.64.056134

    Article  ADS  Google Scholar 

  32. M. P. Leubner, “A nonextensive entropy approach to kappa-distribution,” Astrophys. Space Sci. 282, 573–579 (2002). https://doi.org/10.1023/a:1020990413487

    Article  ADS  Google Scholar 

  33. M. P. Leubner, “Fundamental issues on kappa-distributions in space plasmas and interplanetary proton distributions,” Phys. Plasmas 11, 1308–1316 (2004). https://doi.org/10.1063/1.1667501

    Article  ADS  Google Scholar 

  34. R. Amour and M. Tribeche, “Semi-analytical study of variable charge dust acoustic solitary waves in a dusty plasma with a q-nonextensive ion velocity distribution,” Commun. Nonlinear Sci. Numer. Simul. 16 (9), 3533–3539 (2011). https://doi.org/10.1016/j.cnsns.2010.12.037

    Article  ADS  MATH  Google Scholar 

  35. R. Amour and M. Tribeche, “Nonextensive electron and ion dust charging currents,” Phys. Plasmas 18, 033706 (2011). https://doi.org/10.1063/1.3561826

    Article  ADS  Google Scholar 

  36. M. Tribeche, R. Amour, and P. K. Shukla, “Ion acoustic solitary waves in a plasma with nonthermal electrons featuring Tsallis distribution,” Phys. Rev. E 85 (3), 037401 (2012). https://doi.org/10.1103/PhysRevE.85.037401

    Article  ADS  Google Scholar 

  37. M. M. Hatami, “Nonextensive statistics and the sheath criterion in collisional plasmas,” Phys. Plasmas 22 (1), 013508 (2015). https://doi.org/10.1063/1.4906355

    Article  ADS  Google Scholar 

  38. S. Bhowmick and B. Sahu, “Propagation properties of dust-electron-acoustic waves in weakly magnetized dusty nonthermal plasmas,” Contrib. Plasma Phys. 61 (1), e202000091 (2021). https://doi.org/10.1002/ctpp.202000091

    Article  Google Scholar 

  39. M. Farooq, M. Ahmad, and Q Jan, “Polarization force in an opposite polarity dusty plasma with hybrid Cairns–Tsallis distributed electrons,” Contrib. Plasma Phys. 61 (6), e202000170 (2021). https://doi.org/10.1002/ctpp.202000170

    Article  Google Scholar 

  40. A. Merriche, M. Benzekka, and R. Amour, “Head-on collision of two ion-acoustic solitons in pair-ion plasmas with nonthermal electrons featuring Tsallis distribution,” Z. Naturforsch., A: Phys. Sci. 76 (5), 445–454 (2021). https://doi.org/10.1515/zna-2020-0319

    Article  Google Scholar 

  41. C. K. Goertz, Linhua-Shan, and O. Havnes, “Electrostatic forces in planetary rings,” Geophys. Res. Lett. 15 (1), 84–87 (1988). https://doi.org/10.1029/gl015i001p00084

    Article  ADS  Google Scholar 

  42. P. Bandypadhyay, G. Prasad, A. Sen, and P. K. Kaw, “Experimental study of nonlinear dust acoustic solitary waves in a dusty plasma,” Phys. Rev. Lett. 101 (6–8), 065006 (2008). https://doi.org/10.1103/physrevlett.101.065006

  43. M. Asaduzzaman, A. A. Mamun, and K. S. Ashrafi, “Dust-acoustic waves in nonuniform dusty plasma in presence of polarization force,” Phys. Plasmas 18, 113704 (2011). https://doi.org/10.1063/1.3657432

    Article  ADS  Google Scholar 

  44. H. Washimi and T. Taniuti, “Propagation of ion-acoustic solitary waves of small amplitude,” Phys. Rev. Lett. 17 (19), 996–998 (1966). https://doi.org/10.1103/physrevlett.17.996

    Article  ADS  Google Scholar 

  45. A. A. Mamun, “Arbitrary amplitude dust-acoustic solitary structures in a three-component dusty plasma,” Astrophys. Space Sci. 268, 443–454 (1999). https://doi.org/10.1023/A:1002031022895

    Article  ADS  Google Scholar 

Download references

ACKNOWLEDGMENTS

The constructive suggestions of the anonymous referees are gratefully acknowledged.

Funding

This work was supported in part by the Direction Générale de la Recherche Scientifique et du Développement Technologique.

Author information

Authors and Affiliations

  1. Laboratoire de Physique des Particules et Physique Statistique, École Normale Supérieur Kouba, B.P. 92, Vieux-Kouba, 16050, Algiers, Algeria

    Moufida Benzekka & Nedjma Bouchemla

  2. Department of Physics, Akli Mohand Oulhadj University of Bouira, 10000, Bouira, Algeria

    Nedjma Bouchemla & Abderrzak Merriche

  3. Plasma Physics Group, Theoretical Physics Laboratory, Faculty of Physics, University of Bab-Ezzouar, USTHB, B.P. 32, El Alia, 16111, Algiers, Algeria

    Abderrzak Merriche

Authors
  1. Moufida Benzekka
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nedjma Bouchemla
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Abderrzak Merriche
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Moufida Benzekka.

Ethics declarations

The authors declare that they have no conflicts of interest.

Additional information

The text was submitted by the author in English.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Benzekka, M., Bouchemla, N. & Merriche, A. Nonlinear Dust Acoustic Waves in Nonuniform Complex Plasma under the Effect of Tsallis Polarization Force. Phys. Wave Phen. 31, 281–292 (2023). https://doi.org/10.3103/S1541308X23040088

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1541308X23040088

Keywords:

Search

Navigation