Head-on Collision of Ion-Acoustic Shock and Solitary Waves in Collisionless Plasma with Pair Ions and Electrons

  • M. S. Alam
  • M. R. TalukderEmail author
General and Applied Physics


Unmagnetized collisionless plasma system consisting of positive and negative ions and electrons is considered to study the head-on collision of ion-acoustic shock and solitary waves (IASWs) and its effects on the formation of shock (monotonic and oscillatory) waves and phase shift. The soliton solution is derived from the two-sided Korteweg-de Vries Burger (KdVB) equations. The KdVB equations are obtained using extend Poincaré-Lighthill-Kuo (ePLK) method. It is assumed that the negative ions are immobile and the electrons follow the Boltzmann energy distribution in the plasma. The effects of plasma parameters such as density ratios and kinematic viscosities on electrostatic shock profiles, phase shift, amplitudes, and formation of shock (monotonic and oscillatory) as well as on the soliton solution are investigated. It is found that the density ratio of negative to positive ions plays a vital role on the formation of shock waves and phase shift after collision.


Collisionless plasma Pair ions IASWs ePLK method Phase shift Soliton solution 



  1. 1.
    M. Washimi, T. Taniuti, Propagation of ion-acoustic solitary waves of small amplitude. Phys. Rev. Lett. 17, 996–998 (1966)ADSCrossRefGoogle Scholar
  2. 2.
    H. Ikezi, R.J. Taylor, D.R. Baker, Formation and interaction of ion-acoustic solitions. Phys. Rev. Lett. 25, 11–14 (1970)ADSCrossRefGoogle Scholar
  3. 3.
    E. Infeld, G. Rowlands, Nonlinear Waves, Solitons and Chaos (Cambridge University Press, Cambridge, 2000)CrossRefGoogle Scholar
  4. 4.
    J.K. Xue, Head-on collision of dust-acoustic solitary waves. Phys. Rev. E 69, 016403 (2004)ADSCrossRefGoogle Scholar
  5. 5.
    J.-N. Han, J.-X. Li, Y.-L. He, Z.-H. Han, G.-X. Dong, Y.-G. Nan, Phys. Plasmas 20, 072109 (2013)ADSCrossRefGoogle Scholar
  6. 6.
    E.F. El-Shamy, Head-on collision of ion thermal waves in a magnetized pair-ion plasma containing charged dust impurities. Phys. Plasmas 16, 113704 (2009)ADSCrossRefGoogle Scholar
  7. 7.
    M. Bacal, G.W. Hamilton, H− and D− production in plasmas. Phys. Rev. Lett. 42, 1538–1540 (1979)ADSCrossRefGoogle Scholar
  8. 8.
    L. Boufendi, A. Bouchoule, Industrial developments of scientific insights in dusty plasmas. Plasma Sources Sci. Technol. 11, A211–A218 (2002)ADSCrossRefGoogle Scholar
  9. 9.
    N. D’Angelo, S.V. Goeler, T. Ohe, Propagation and damping of ion waves in a plasma with negative ions. Phys. Fluids 9, 1605 (1966)ADSCrossRefGoogle Scholar
  10. 10.
    A.Y. Wong, D.L. Mamas, D. Arnush, Negative ion plasmas. Phys. Fluids 18, 1489 (1975)ADSCrossRefGoogle Scholar
  11. 11.
    T. Intrator, N. Hershkowitz, Beam–plasma interactions in a positive ion–negative ion plasma. Phys. Fluids 26, 1942 (1983)ADSCrossRefGoogle Scholar
  12. 12.
    H. Amemiya, B.M. Annaratone, J.E. Allen, The collection of positive ions by spherical and cylindrical probes in an electronegative plasma. Plasma Sources Sci.Technol. 8, 179–190 (1999)ADSCrossRefGoogle Scholar
  13. 13.
    Y.I. Portnyagin, O.F. Klyuev, A.A. Shidlovsky, A.N. Evdokimov, T.W. Buzdigar, P.G. Matukhin, S.G. Pasynkov, K.N. Shamshev, V.V. Sokolov, N.D. Semkin, Adv. Space Res. 11, 89–92 (1991)ADSCrossRefGoogle Scholar
  14. 14.
    J. Jacquinot, B.D. McVey, J.E. Scharer, Mode conversion of the fast magnetosonic wave in a deuterium-hydrogen tokamak plasma. Phys. Rev. Lett. 39, 88–91 (1977)ADSCrossRefGoogle Scholar
  15. 15.
    R. Ichiki, S. Yoshimura, T. Watanabe, Y. Nakamura, Y. Kawai, Experimental observation of dominant propagation of the ion-acoustic slow mode in a negative ion plasma and its application. Phys. Plasmas 9, 4481–4487 (2002)ADSCrossRefGoogle Scholar
  16. 16.
    W. Oohara, R. Hatakeyama, Pair-ion plasma generation using fullerenes. Phys. Rev. Lett. 91, 205005 (2003)ADSCrossRefGoogle Scholar
  17. 17.
    S. Von Goeler, T. Ohe, N. D’Angelo, Production of a thermally ionized plasma with negative ions. J. Appl. Phys. 37, 2519–2520 (1966)ADSCrossRefGoogle Scholar
  18. 18.
    B. Song, D. Suszcynsky, N. D’Angelo, R.L. Merlino, Electrostatic ion‐cyclotron waves in a plasma with negative ions. Phys. Fluids B 1, 2316–2318 (1989)ADSCrossRefGoogle Scholar
  19. 19.
    N. D’Angelo, Negative ions in the night ionosphere and the continuous sub-ELF emissions. J. Geophys. Res. 72, 1541–1546 (1967)ADSCrossRefGoogle Scholar
  20. 20.
    M. Galvez, S.P. Gary, Electrostatic beam instabilities in a positive/negative ion plasma. Phys. Fluids 29, 4085 (1986)ADSCrossRefGoogle Scholar
  21. 21.
    Y. Nakamura, T. Odagiri, I. Tsukubayashi, Ion-acoustic waves in a multicomponent plasma with negative ions, Comments Plasma Phys. Control. Fusion 39, 105 (1977)Google Scholar
  22. 22.
    A. Weingarten, R. Arad, Y. Maron, A. Fruchtman, Ion separation due to magnetic field penetration into a multispecies plasma, Phys. Rev. Lett. 87, 115004 (2001)Google Scholar
  23. 23.
    N. Sato, A variety of plasmas, edited by A. Sen and P. K. Kaw. Plasma Sources Sci. Technol. 3, 395 (1994) 79ADSCrossRefGoogle Scholar
  24. 24.
    A.J. Coates, F.J. Crary, G.R. Lewis, D.T. Young, J.H. Waite, E.C. Sittler Jr., Geophys. Res. Lett. 34, 22103 (2007)ADSCrossRefGoogle Scholar
  25. 25.
    R.J. Taylor, D.R. Baker, H. Ikezi, Observation of collisionless electrostatic shocks. Phys. Rev. Lett. 24, 206–209 (1970)ADSCrossRefGoogle Scholar
  26. 26.
    B. Song, N. D’Angelo, R.L. Merlino, Phys. Fluids B 284, 3 (1991)Google Scholar
  27. 27.
    M. Tajiri, M. Tuda, On large amplitude ion acoustic solitons in plasma with negative ions. J. Phys. Soc. Jpn. 54, 19–22 (1985)ADSCrossRefGoogle Scholar
  28. 28.
    T. E. Sheridan, Some properties of large-amplitude, negative-potential solitary waves in a three-component plasma, J. Plasma Phys. 60, 17 (1998)Google Scholar
  29. 29.
    D.A. Tidman, N.A. Krall, Shock Waves in Collisionless Plasmas (Wiley Interscience, New York, 1971)Google Scholar
  30. 30.
    A. Bret, arXiv: 1502.00626V1 [Physics. Plasma-Ph], (2015)Google Scholar
  31. 31.
    N. Hershkowitz, Double layers and electrostatic shocks. J. Geophys. Res. 86, 3307 (1981)ADSCrossRefGoogle Scholar
  32. 32.
    M.E. Dieckmann, G. Sarri, D. Doria, H. Ahmed, M. Borghesi, Evolution of slow electrostatic shock into a plasma shock mediated by electrostatic turbulence. New J. Phys. 16, 073001 (2014)ADSCrossRefGoogle Scholar
  33. 33.
    M.G. Shah, M.R. Hossen, S. Sultana, A. A. Mamun, Positron-acoustic shock waves in a degenerate multi-component plasma, Chin. Phys. Lett. 32, 8 (2015) 085203Google Scholar
  34. 34.
    T. Takeuchi, S. Iizuka, N. Sato, Ion acoustic shocks formed in a collisionless plasma with negative ions. Phys. Rev. Lett. 80, 77–80 (1998)ADSCrossRefGoogle Scholar
  35. 35.
    T.S. Gill, A.S. Bains, C. Bedi, Ion acoustic shock waves in weakly relativistic multicomponent quantum plasma. J. Phys. Conf. Ser. 208, 012040 (2010)CrossRefGoogle Scholar
  36. 36.
    P. Chaizy et al., Negative-ions in the coma of comet Halley. Nature 349, 393 (1991)Google Scholar
  37. 37.
    Y. Nakamura, H. Bailung, P.K. Shukla, Observation of ion-acoustic shocks in a dusty plasma. Phys. Rev. Lett. 83, 1602–1605 (1999)ADSCrossRefGoogle Scholar
  38. 38.
    K. Roy, A.P. Misra, P. Chatterjee, Ion-acoustic shocks in quantum electron-positron-ion plasmas. Phys. Plasmas 15, 032310 (2008)ADSCrossRefGoogle Scholar
  39. 39.
    Y. Nakamura, A. Sarma, Observation of ion-acoustic solitary waves in a dusty plasma. Phys. Plasmas 8, 3921–3926 (2001)ADSCrossRefGoogle Scholar
  40. 40.
    Q.-Z. Luo, N. D’Angelo, R.L. Merlino, Shock formation in a negative ion plasma. Phys. Plasmas 5, 2868–2870 (1998)ADSCrossRefGoogle Scholar
  41. 41.
    A. Adak, A. Sikdar, S. Ghosh, M. Khan, Magnetosonic shock wave in collisional pair-ion plasma. Phys. Plasmas 23, 062124 (2016)ADSCrossRefGoogle Scholar
  42. 42.
    A. Adak, S. Ghosh, N. Chakrabarty, Ion acoustic shock wave in collisional equal mass plasma, Phys. Plasmas 22, 102307 (2015)Google Scholar
  43. 43.
    S. Hussain, N. Akhtar, S. Mahmood, Propagation of ion acoustic shock waves in negative ion plasma with nonextensive electrons, Phys Plasmas 20, 092303 (2013)Google Scholar
  44. 44.
    R. Saeed, A. Mushtaq, Ion acoustic waves in pair-ion plasma: Linear and nonlinear analyses, Phys. Plasmas 16, 032307 (2009)Google Scholar
  45. 45.
    W. Craig, P. Guyenne, and {\it et al}, Solitary wave interactions, Phys. Fluids 18, 057106 (2006)Google Scholar
  46. 46.
    T. Marchant, N. Smyth, Soliton interaction for the extended Korteweg-de Vries equation. IMA J. Appl. Math. 56, 157–176 (1996)ADSMathSciNetCrossRefGoogle Scholar
  47. 47.
    T. Maxworthy, Experiments on collisions between solitary waves. J. Fluid Mech. 76, 177 (1976)ADSCrossRefGoogle Scholar
  48. 48.
    R. W. Gould, Excitation of ion-acoustic waves, Phys. Rev. 136, A991 (1964)Google Scholar
  49. 49.
    J.L. Hirshfield, J.H. Jacob, Free-streaming and spatial Landau damping, Phys Fluids 11, 411 (1968)Google Scholar
  50. 50.
    N. Sato, A. Sasaki, Spatial evolution of low-frequency perturbations produced by a grid in a plasma. Phys. Fluids 15, 508 (1972)ADSCrossRefGoogle Scholar
  51. 51.
    N. Sato, H. Sugai, R. Hatakeyama, Spatial evolution of velocity-modulated ion beams in a plasma. Phys. Rev. Lett. 34, 931–934 (1975)ADSCrossRefGoogle Scholar
  52. 52.
    V. Vanek, T.C. Marshall, Ion-acoustic collisionless shocks in a Q-machine. Plasma Phys. 14, 925–934 (1972)ADSCrossRefGoogle Scholar
  53. 53.
    Z. Feng, On travelling wave solutions of the Burgers–Korteweg–de Vries equation. Nonlinearity 20, 343–356 (2007)ADSMathSciNetCrossRefGoogle Scholar
  54. 54.
    F. S. Crawford, Waves, Berkeley Physics Course, Cambridge University Press (1968)Google Scholar
  55. 55.
    R. D. Guenther, Modern Optics, John Wiley & Sons, Inc. (1990)Google Scholar

Copyright information

© Sociedade Brasileira de Física 2019

Authors and Affiliations

  1. 1.Department of Applied MathematicsUniversity of RajshahiRajshahiBangladesh
  2. 2.Plasma Science and Technology Lab, Department of Applied Physics and Electronic EngineeringUniversity of RajshahiRajshahiBangladesh
  3. 3.Department of MathematicsChittagong University of Engineering and TechnologyChittagongBangladesh

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