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

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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.

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References

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  3. Lieberman, M.A., Lichtenberg, A.: Principles of Plasma Discharges and Material Processing, 2nd edn. Wiley, New Jersey (2005)

    Book  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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. Baalrud, S.D.: Influence of ion streaming instabilities on transport near plasma boundaries. Plasma Sources Sci. Technol. 25(2), 025008 (2016)

    Article  Google Scholar 

  8. Gary, S.P., Omidi, N.: The ion–ion acoustic instability. J. Plasma Phys. 37(1), 45–61 (2009)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  17. Medvedev, Y.V.: Evolution of a density disturbance in a collisionless plasma. Plasma Phys. Control. Fusion 56(2), 025005 (2014)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  20. Ohno, Y., Yoshida, Z.: Nonlinear ion acoustic waves scattered by vortexes. Commun. Nonlinear Sci. Numer. Simul. 38, 277–287 (2016)

    Article  MathSciNet  Google Scholar 

  21. Wazwaz, A.M.: Partial Differential Equations and Solitary Waves Theory. Nonlinear Physical Science. Higher Education Press, Beijing (2009)

    Book  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  24. Verheest, F., Yaroshenko, V.V.: Nonlinear electrostatic modes in astrophysical plasmas with charged dust distributions. Astron. Astrophys. 503, 683–690 (2009)

    Article  MATH  Google Scholar 

  25. Verheest, F., Hellberg, M.A., Herman, W.A.: Head-on collisions of electrostatic solitons in multi-ion plasmas. Phys. Plasmas 19, 092302 (2012)

    Article  Google Scholar 

  26. Khrapak, S.A., Morfill, G.E.: Ionization instability of ion-acoustic waves. Phys. Plasmas 17(6), 062111 (2010). (4pp)

    Article  Google Scholar 

  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. 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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

  31. Arnold, V.I.: Mathematical Methods of Classical Mechanics, 2nd edn. Springer, New York (1989). (Translated by K. Vogtmann and A. Weinstein)

    Book  Google Scholar 

  32. Hershkowitz, N.: Sheaths: more complicated than you think. Phys. Plasmas 12, 055502 (2005)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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. 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)

    Article  MathSciNet  MATH  Google Scholar 

  36. Dehghan, M., Shokri, A.: A numerical method for kdv equation using collocation and radial basis functions. Nonlinear Dyn. 50, 111–120 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  37. Lifshitz, E.M., Pitaevskii, L.P.: Physical Kinetics. Butterworth-Heinemann, Oxford (1981)

    Google Scholar 

  38. Abramovitz, M., Stegun, I.A.: Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, 4th edn. National Bureau of Standards, Washington (1964)

    MATH  Google Scholar 

  39. John, P.I., Saxena, Y.C.: Propagation of ion acoustic solitons in plasma density gradients. Pays. Lett. A 56(5), 385–386 (1976)

    Article  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  42. Klostermann, H., Pierre, T.: Frequency modulation of the ion-acoustic instability. Phys. Rev. E 61(6), 7034–7038 (2000)

    Article  Google Scholar 

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  1. Material Research School, Tehran, 14155-1239, Iran

    Nora Nassiri-Mofakham

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Nassiri-Mofakham, N. Evolution of ion–ion acoustic instability in multi-ion plasma sheaths. Nonlinear Dyn 93, 2301–2314 (2018). https://doi.org/10.1007/s11071-018-4326-7

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