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Properties of cylindrical and spherical heavy ion-acoustic solitary and shock structures in a multispecies plasma with superthermal electrons

  • Nonlinear Phenomena
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Abstract

A theoretical investigation on heavy ion-acoustic (HIA) solitary and shock structures has been accomplished in an unmagnetized multispecies plasma consisting of inertialess kappa-distributed superthermal electrons, Boltzmann light ions, and adiabatic positively charged inertial heavy ions. Using the reductive perturbation technique, the nonplanar (cylindrical and spherical) Kortewg–de Vries (KdV) and Burgers equations have been derived. The solitary and shock wave solutions of the KdV and Burgers equations, respectively, have been numerically analyzed. The effects of superthermality of electrons, adiabaticity of heavy ions, and nonplanar geometry, which noticeably modify the basic features (viz. polarity, amplitude, phase speed, etc.) of small but finite amplitude HIA solitary and shock structures, have been carefully investigated. The HIA solitary and shock structures in nonplanar geometry have been found to distinctly differ from those in planar geometry. Novel features of our present attempt may contribute to the physics of nonlinear electrostatic perturbation in astrophysical and laboratory plasmas.

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References

  1. H. Washimi and T. Taniuti, Phys. Rev. Lett. 17, 996 (1966).

    Article  ADS  Google Scholar 

  2. M. Temirin, K. Cerny, W. Lotko, and F. S. Mozer, Phys. Rev. Lett. 48, 1175 (1982).

    Article  ADS  Google Scholar 

  3. S. I. Popel, S. V. Vladimirov, and P. K. Shukla, Phys. Plasmas 2, 716 (1995).

    Article  ADS  Google Scholar 

  4. A. A. Mamun and P. K. Shukla, Phys. Plasmas 9, 1468 (2002).

    Article  ADS  MathSciNet  Google Scholar 

  5. P. K. Shukla, Phys. Plasmas 7, 1044 (2000).

    Article  ADS  Google Scholar 

  6. A. Rahman, F. Sayed, and A. A. Mamun, Phys. Plasmas 14, 034503 (2007).

    Article  ADS  Google Scholar 

  7. A. A. Mamun and N. Jahan, Europhys. Lett. 84, 35001 (2008).

    Article  ADS  Google Scholar 

  8. S. Tasnim, S. Islam, and A. A. Mamun, Phys. Plasmas 19, 033706 (2012).

    Article  ADS  Google Scholar 

  9. M. Hasan, M. M. Hossain, and A. A. Mamun, Astrophys. Space Sci. 345, 113 (2013).

    Article  ADS  Google Scholar 

  10. J. K. Chawla, M. K. Mishra, and R. S. Tiwari, Astrophys. Space Sci. 347, 283 (2013).

    Article  ADS  Google Scholar 

  11. S. Ata-ur-Rahman, S. Ali, A. M. Mirza, and A. Qamar, Phys. Plasmas 20, 042305 (2013).

    Article  ADS  Google Scholar 

  12. H. Alinejad, Astrophys. Space Sci. 345, 85 (2013).

    Article  ADS  Google Scholar 

  13. H. K. Andersen, N. D’Angelo, P. Michelsen, and P. Nielsen, Phys. Rev. Lett. 19, 149 (1967).

    Article  ADS  Google Scholar 

  14. H. Ikezi, R. Taylor, and D. Baker, Phys. Rev. Lett. 25, 11 (1970).

    Article  ADS  Google Scholar 

  15. K. E. Longren, J. Plasma Phys. 25, 943 (1983).

    Article  ADS  Google Scholar 

  16. F. F. Chen, Introduction to Plasma Physics (Plenum, New York, 1984).

    Google Scholar 

  17. K. Roy, A. P. Misra, and P. Chatterjee, Phys. Plasmas 15, 032310 (2008).

    Article  ADS  Google Scholar 

  18. J. K. Xue, Phys. Lett. A 322, 225 (2004).

    Article  ADS  Google Scholar 

  19. M. R. Hossen, L. Nahar, S. Sultana, and A. A. Mamun, High Energy Density Phys. 13, 13 (2014).

    Article  ADS  Google Scholar 

  20. M. R. Hossen, L. Nahar, and A. A. Mamun, Phys. Scr. 89, 105603 (2014).

    Article  ADS  Google Scholar 

  21. M. R. Hossen, L. Nahar, S. Sultana, and A. A. Mamun, Astrophys. Space Sci. 353, 123 (2014).

    Article  ADS  Google Scholar 

  22. M. R. Hossen, L. Nahar, and A. A. Mamun, J. Korean Phys. Soc. 65, 1863 (2014).

    Article  ADS  Google Scholar 

  23. C. O. Hines, J. Atmos. Terr. Phys. 11, 36 (1957).

    Article  ADS  Google Scholar 

  24. F. Sayed and A. A. Mamun, Phys. Plasmas 14, 034503 (2007).

    Article  ADS  Google Scholar 

  25. S. Mahmood and N. Akhtar, Eur. Phys. J. D 49, 217 (2008).

    Article  ADS  Google Scholar 

  26. F. Tanjia and A. A. Mamun, J. Plasma Phys. 75, 99 (2008).

    Article  ADS  Google Scholar 

  27. V. M. Vasyliunas, J. Geophys. Res. 73, 2839 (1968).

    Article  ADS  Google Scholar 

  28. M. P. Leubner, J. Geophys. Res. 87, 6335 (1982).

    Article  ADS  Google Scholar 

  29. D. Summers and R. M. Thorne, Phys. Fluids B 3, 1835 (1991).

    Article  ADS  Google Scholar 

  30. R. M. Thorne and R. B. Horne, J. Geophys. Res. 99, 17249 (1994).

    Article  ADS  Google Scholar 

  31. R. L. Mace and M. A. Hellberg, Phys. Plasmas 2, 2098 (1995).

    Article  ADS  Google Scholar 

  32. T. K. Baluka and M. A. Hellberg, Phys. Plasmas 15, 123705 (2008).

    Article  ADS  Google Scholar 

  33. T. K. Baluku, M. A. Hellberg, I. Kourakis, and N. S. Saini, Phys. Plasmas 17, 053702 (2010).

    Article  ADS  Google Scholar 

  34. M. S. Alam, M. M. Masud, and A. A. Mamun, Plasma Phys. Rep. 39, 1011 (2013).

    Article  ADS  Google Scholar 

  35. V. Formisano, G. Moreno, and F. Palmiotto, J. Geophys. Res. 78, 3714 (1973).

    Article  ADS  Google Scholar 

  36. E. Marsch, K. H. Muhlhauser, R. Schwenn, H. Rosenbauer, W. Pilipp, and F. M. Neubauer, J. Geophys. Res. 87, 52 (1982).

    Article  ADS  Google Scholar 

  37. J. D. Scudder, E. C. Sittler, and H. S. Bridge, J. Geophys. Res. 86, 8157 (1981).

    Article  ADS  Google Scholar 

  38. G. Gloeckler and L. A. Fisk, Astrophys. J. 648, L63 (2006).

    Article  ADS  Google Scholar 

  39. C. Vocks, G. Mann, and G. Rausche, Astron. Astrophys. 480, 527 (2008).

    Article  ADS  Google Scholar 

  40. E. Fourkal, V. Y. Bychenkov, W. Rozmus, R. Sydora, C. Kirkby, C. E. Capjack, S. H. Glenzer, and H. A. Baldis, Phys. Plasmas 8, 550 (2001).

    Article  ADS  Google Scholar 

  41. Y. Yagi, V. Antoni, M. Bagatin, D. Desideri, E. Martines, G. Serianni, and F. Vallone, Plasma Phys. Controlled Fusion 39, 1915 (1997).

    Article  ADS  Google Scholar 

  42. M. A. Hellberg, R. L. Mace, R. J. Armstrong, and G. Karlstad, J. Plasma Phys. 64, 433 (2000).

    Article  ADS  Google Scholar 

  43. B. Basu, Phys. Plasmas 15, 042108 (2008).

    Article  ADS  Google Scholar 

  44. T. Cattaert, M. A. Helberg, and R. L. Mace, Phys. Plasmas 14, 082111 (2007).

    Article  ADS  Google Scholar 

  45. T. K. Baluku and M. A. Hellberg, Phys. Plasmas 19, 012106 (2012).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  47. S. I. Popel and M. Y. Yu, Contrib. Plasma Phys. 35, 103 (1995).

    Article  ADS  Google Scholar 

  48. S. I. Popel, M. Y. Yu, and V. N. Tsytovich, Phys. Plasmas 3, 4313 (1996).

    Article  ADS  Google Scholar 

  49. P. K. Shukla and A. A. Mamun, Introduction to Dusty Plasma Physics (IOP, Bristol, 2002).

    Book  Google Scholar 

  50. S. I. Popel, A. P. Golub, T. V. Losseva, A. V. Ivlev, S. A. Khrapak, and G. Morfill, Phys. Rev. E 67, 056402 (2003).

    Article  ADS  Google Scholar 

  51. S. I. Kopnin, I. N. Kosarev, S. I. Popel, and M. Y. Yu, Plasma Phys. Rep. 31, 198 (2005).

    Article  ADS  Google Scholar 

  52. T. V. Losseva, S. I. Popel, A. P. Golub, and P. K. Shukla, Phys. Plasmas 16, 093704 (2009).

    Article  ADS  Google Scholar 

  53. B. Sahu, Europhys. Lett. 101, 55002 (2013).

    Article  ADS  Google Scholar 

  54. H. R. Pakzad, Astrophys. Space Sci. 331, 169 (2011).

    Article  ADS  Google Scholar 

  55. T. K. Baluku, M. A. Hellberg, and R. L. Mace, J. Geophys. Res. 116, A04227 (2011).

    Article  ADS  Google Scholar 

  56. M. Shahmansouri, Chin. Phys. Lett. 29, 105201 (2012).

    Article  Google Scholar 

  57. H. Ainejad, M. Mahdavi, and M. Shahmansouri, Eur. Phys. J. Plus 129, 99 (2014).

    Article  Google Scholar 

  58. A. E. Dubinov, Phys. Scr. 80, 035504 (2009).

    Article  ADS  Google Scholar 

  59. A. E. Dubinov, Plasma Phys. Rep. 35, 991 (2009).

    Article  ADS  Google Scholar 

  60. P. Eslami, M. Mottaghizadeh, and H. R. Pakzad, Canad. J. Phys. 90, 661 (2012).

    Article  Google Scholar 

  61. M. S. Alam, M. J. Uddin, M. M. Masud, and A. A. Mamun, Chaos 24, 033130 (2014).

    Article  ADS  MathSciNet  Google Scholar 

  62. M. G. Shah, M. R. Hossen, and A. A. Mamun, Braz. J. Phys. 45, 219 (2015).

    Article  ADS  Google Scholar 

  63. S. Maxon and J. Viecelli, Phys. Rev. Lett. 32, 4 (1974).

    Article  ADS  Google Scholar 

  64. M.-J. Lee, Phys. Plasmas 14, 032112 (2007).

    Article  ADS  Google Scholar 

  65. K. Jilani, A. M. Mirza, and T. A. Khan, Astrophys. Space Sci. 344, 135 (2013).

    Article  ADS  Google Scholar 

  66. D. A. Mendis and M. Rosenberg, Annu. Rev. Astron. Astrophys. 32, 419 (1994).

    Article  ADS  Google Scholar 

  67. C. K. Goertz, Rev. Geophys. 27, 271 (1989).

    Article  ADS  Google Scholar 

  68. G. S. Selwyn, Jpn. J. Appl. Phys. 32, 3068 (1993).

    Article  ADS  Google Scholar 

  69. J. Winter, Plasma Phys. Controlled Fusion 340, 1201 (1998).

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Physics, Jahangirnagar University, Savar, Dhaka, 1342, Bangladesh

    M. G. Shah, M. M. Rahman & A. A. Mamun

  2. Department of Natural Sciences, Daffodil International University, Dhanmondi, Dhaka, 1207, Bangladesh

    M. R. Hossen

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  1. M. G. Shah
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  2. M. M. Rahman
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  3. M. R. Hossen
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  4. A. A. Mamun
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Correspondence to M. G. Shah.

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Shah, M.G., Rahman, M.M., Hossen, M.R. et al. 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). https://doi.org/10.1134/S1063780X16020069

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