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Nonlinear Dynamics

, Volume 93, Issue 4, pp 2301–2314 | Cite as

Evolution of ion–ion acoustic instability in multi-ion plasma sheaths

  • Nora Nassiri-Mofakham
Original Paper
  • 62 Downloads

Abstract

The generation of ion-acoustic solitary waves is investigated in a nonuniform multicomponent collisional plasma sheath containing cold ions and Boltzmann electrons to probe the formation and physics of modulation of nonlinear ion-acoustic waves. The new model for the plasma is adapted to include the effects of ion production-loss and momentum loss terms due to ion-neutral collisions, and implementation related to space and laboratory plasma applications are discussed. The discrete modes, the instability conditions and the growth rate of the streaming instability with the effect of the present plasma parameters are calculated based on the approximate but yet precise complex dispersion relation. The marginal stability curve, characterized by mode bifurcation, cutoff, and complex fold point, indicates a growth rate of a few percents of effective plasma frequency. The damping of ion-acoustic is affected by heavy neutrals, and its maximum rate found near the ion-neutral collision frequency. The variable-coefficient Korteweg-de Vries equation is derived via reductive perturbation method to govern the dynamics of small- as well as large-amplitude solitons. It is found that the propagating nonlinear coherent structures through the created ion phase-space vortices lead to ion trapping and acceleration, and the modulation of ion-acoustic instabilities in the turbulent region. The effect of ion streaming motion on the driven solitons and modulation instability for the variable-coefficient Korteweg-de Vries equation is numerically investigated in detail. The theoretical results can be applied to the observation of electrostatic waves in space plasmas, in industrial pair-ion plasmas as well as in laboratory dusty plasmas.

Keywords

Ion-beam-plasma Ion-acoustic solitary waves Modulation instability Ion acceleration 

Notes

Acknowledgements

All data for this paper are properly cited and referred to in the reference list.

Compliance with ethical standards

Conflict of interest

The author confirms that this paper content has no conflict of interest.

References

  1. 1.
    Yip, C.H., Hershkowitz, N., Severn, G.: Verifying effects of instability enhanced ion–ion coulomb collisions on ion velocity distribution functions near the sheath edge in low temperature plasmas. Plasma Sources Sci. Technol. 24(1), 015018 (2015)CrossRefGoogle Scholar
  2. 2.
    Kella, V.P., Ghosh, J., Chattopadhyay, P.K., Sharma, D., Saxena, Y.C.: Observation of ion–ion counter streaming instability in presheath–sheath region of a mesh grid immersed in low temperature plasma. Phys. Plasmas 24(3), 032110 (2017)CrossRefGoogle Scholar
  3. 3.
    Lieberman, M.A., Lichtenberg, A.: Principles of Plasma Discharges and Material Processing, 2nd edn. Wiley, New Jersey (2005)CrossRefGoogle Scholar
  4. 4.
    Rufai, O.R., Bains, A.S., Ehsan, Z.: Arbitrary amplitude ion acoustic solitary waves and double layers in a magnetized auroral plasma with q-nonextensive electrons. Astrophys. Space Sci. 357(2), 102 (2015)CrossRefGoogle Scholar
  5. 5.
    Lakhina, G.S., Singh, S.V.: Generation of weak double layers and low-frequency electrostatic waves in the solar wind. Sol. Phys. 290(10), 3033–3049 (2015)CrossRefGoogle Scholar
  6. 6.
    Akhiezer, A.I., Akhiezer, I.A., Polovin, R.V., Sitenko, A.G., Stepanov, K.W.: Plasma ELectrodynamics: Linear Theory, 2nd edn. Pergamon Press, Oxford (1975)Google Scholar
  7. 7.
    Baalrud, S.D.: Influence of ion streaming instabilities on transport near plasma boundaries. Plasma Sources Sci. Technol. 25(2), 025008 (2016)CrossRefGoogle Scholar
  8. 8.
    Gary, S.P., Omidi, N.: The ion–ion acoustic instability. J. Plasma Phys. 37(1), 45–61 (2009)CrossRefGoogle Scholar
  9. 9.
    Gary, S.P., Jian, L.K., Broiles, T.W., Stevens, M.L., Podesta, J.J., Kasper, J.C.: Ion-driven instabilities in the solar wind: wind observations of 19 March 2005. J. Geophys. Res. Space Phys. 121(1), 30–41 (2016)CrossRefGoogle Scholar
  10. 10.
    King, M., Gray, R.J., Powell, H.W., Capdessus, R., McKenna, P.: Energy exchange via multi-species streaming in laser-driven ion acceleration. Plasma Phys. Control. Fusion 59(1), 014003 (2017)CrossRefGoogle Scholar
  11. 11.
    Dalui, S., Bandyopadhyay, A., Das, K.P.: Modulational instability of ion acoustic waves in a multi-species collisionless unmagnetized plasma consisting of nonthermal and isothermal electrons. Phys. Plasmas 24(4), 042305 (2017)CrossRefGoogle Scholar
  12. 12.
    Guo, S., Mei, L., He, Y., Li, Y.: Modulation instability and ion-acoustic rogue waves in a strongly coupled collisional plasma with nonthermal nonextensive electrons. Plasma Phys. Control. Fusion 58(2), 025014 (2016)CrossRefGoogle Scholar
  13. 13.
    Qu, Z.S., Hole, M.J., Fitzgerald, M.: Energetic geodesic acoustic modes associated with two-stream-like instabilities in tokamak plasmas. Phys. Rev. Lett. 116, 095004 (2016)CrossRefGoogle Scholar
  14. 14.
    Shah, M.G., Rahman, M.M., Hossen, M.R., Mamun, A.A.: Properties of cylindrical and spherical heavy ion-acoustic solitary and shock structures in a multispecies plasma with superthermal electrons. Plasma Phys. Rep. 42, 168–176 (2016)CrossRefGoogle Scholar
  15. 15.
    Schaeffer, D.B., Winske, D., Larson, D.J., Cowee, M.M., Constantin, C.G., Bondarenko, A.S., Clark, S.E., Niemann, C.: On the generation of magnetized collisionless shocks in the large plasma device. Phys. Plasmas 24(4), 041405 (2017)CrossRefGoogle Scholar
  16. 16.
    Rapson, C., Grulke, O., Matyash, K., Klinger, T.: The effect of boundaries on the ion acoustic beam-plasma instability in experiment and simulation. Phys. Plasmas 21(5), 052103 (2014)CrossRefGoogle Scholar
  17. 17.
    Medvedev, Y.V.: Evolution of a density disturbance in a collisionless plasma. Plasma Phys. Control. Fusion 56(2), 025005 (2014)CrossRefGoogle Scholar
  18. 18.
    Maity, B., Ghosh, S., Bharuthram, R.: Nonlinear ion acoustic wave in a pair-ion plasma in a uniform weak magnetic field. Phys. Scr. 90(4), 045604 (2015)CrossRefGoogle Scholar
  19. 19.
    Khattak, N., Mushtaq, M., Qamar, A.: Ion streaming instabilities in pair ion plasma and localized structure with non-thermal electrons. Braz. J. Phys. 45(6), 633–642 (2015)CrossRefGoogle Scholar
  20. 20.
    Ohno, Y., Yoshida, Z.: Nonlinear ion acoustic waves scattered by vortexes. Commun. Nonlinear Sci. Numer. Simul. 38, 277–287 (2016)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Wazwaz, A.M.: Partial Differential Equations and Solitary Waves Theory. Nonlinear Physical Science. Higher Education Press, Beijing (2009)CrossRefzbMATHGoogle Scholar
  22. 22.
    Wazwaz, A.M., El-Tantawy, S.A.: A new integrable (3+1)-dimensional kdv-like model with its multiple-soliton solutions. Nonlinear Dyn. 83(3), 1529–1534 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Champneys, A.R., McKenna, P.J., Zegeling, P.A.: Solitary waves in nonlinear beam equations: stability, fission and fusion. Nonlinear Dyn. 21(1), 31–53 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Verheest, F., Yaroshenko, V.V.: Nonlinear electrostatic modes in astrophysical plasmas with charged dust distributions. Astron. Astrophys. 503, 683–690 (2009)CrossRefzbMATHGoogle Scholar
  25. 25.
    Verheest, F., Hellberg, M.A., Herman, W.A.: Head-on collisions of electrostatic solitons in multi-ion plasmas. Phys. Plasmas 19, 092302 (2012)CrossRefGoogle Scholar
  26. 26.
    Khrapak, S.A., Morfill, G.E.: Ionization instability of ion-acoustic waves. Phys. Plasmas 17(6), 062111 (2010). (4pp)CrossRefGoogle Scholar
  27. 27.
    Zaqarshvili, T.V., Khodachenko, M.L., Rucker, H.O.: Damping of Alfvén waves in solar partially ionized plasmas: effect of neutral helium in multi-fluid approach. Astron. Astrophys. 534(A93), 1–7 (2011)Google Scholar
  28. 28.
    Crumley, J.P., Cattell, C.A., Lysak, R.L., Dombeck, J.P.: Studies of ion solitary waves using simulations including hydrogen and oxygen beams. J. Geophys. Res. 106(A4), 6007–6015 (2001)CrossRefGoogle Scholar
  29. 29.
    Main, D.S., Newman, D.L., Ergun, R.E.: Double layers and ion phase-space holes in the auroral upward-current region. Phys. Rev. Lett. 97, 185001 (2006). (4pp)CrossRefGoogle Scholar
  30. 30.
    Yau, A.W., Lockwood, M.: Vertical ion flow in the polar ionosphere. In: Moore, T.E., Waite, J.H., Moorehead, T.W., Hanson, W.B. (eds.) pp. 229–240. American Geophysical Union, Washington (2013)Google Scholar
  31. 31.
    Arnold, V.I.: Mathematical Methods of Classical Mechanics, 2nd edn. Springer, New York (1989). (Translated by K. Vogtmann and A. Weinstein)CrossRefGoogle Scholar
  32. 32.
    Hershkowitz, N.: Sheaths: more complicated than you think. Phys. Plasmas 12, 055502 (2005)CrossRefGoogle Scholar
  33. 33.
    Yip, C.S., Hershkowitz, N., Callen, J.D.: Experimental test of instability-enhanced collisional friction for determining ion loss in two ion species plasmas. Phys. Rev. Lett. 104(22), 225003 (2010). (4pp)CrossRefGoogle Scholar
  34. 34.
    Wazwaz, A.M.: Chapter 9, the kdv equation. In: Dafermos, C.M., Pokorny, M. (eds.) Handbook of Differential Equations: Evolutionary Equations, vol. 4, 1st edn, pp. 485–568. North-Holland, Amsterdam (2008)Google Scholar
  35. 35.
    El-Wakil, S.A., Abulwafa, E.M., Zahran, M.A., Mahmoud, A.A.: Time-fractional kdv equation: formulation and solution using variational methods. Nonlinear Dyn. 65, 55–63 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  36. 36.
    Dehghan, M., Shokri, A.: A numerical method for kdv equation using collocation and radial basis functions. Nonlinear Dyn. 50, 111–120 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  37. 37.
    Lifshitz, E.M., Pitaevskii, L.P.: Physical Kinetics. Butterworth-Heinemann, Oxford (1981)Google Scholar
  38. 38.
    Abramovitz, M., Stegun, I.A.: Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, 4th edn. National Bureau of Standards, Washington (1964)zbMATHGoogle Scholar
  39. 39.
    John, P.I., Saxena, Y.C.: Propagation of ion acoustic solitons in plasma density gradients. Pays. Lett. A 56(5), 385–386 (1976)CrossRefGoogle Scholar
  40. 40.
    Liu, Y., Gao, Y.T., Sun, Z.Y., Yu, X.: Multi-soliton solutions of the forced variable-coefficient extended Korteweg-de Vries equation arisen in fluid dynamics of internal solitary waves. Nonlinear Dyn. 66, 575–587 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  41. 41.
    Bonhomme, G., Pierre, T., Leclert, G., Trulsen, J.: Ion phase space vortices in ion beam-plasma systems and their relation with the ion acoustic instability: numerical and experimental results. Plasma Phys. Control. Fusion 33, 507–520 (1991)CrossRefGoogle Scholar
  42. 42.
    Klostermann, H., Pierre, T.: Frequency modulation of the ion-acoustic instability. Phys. Rev. E 61(6), 7034–7038 (2000)CrossRefGoogle Scholar

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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Material Research SchoolTehranIran

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