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Nonlinear theory of ion-acoustic waves in an electron-positron-ion plasma

  • Plasma Oscillations and Waves
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Abstract

An analytical nonlinear gasdynamic theory of ion-acoustic waves in an e-p-i plasma is developed for the case in which all the plasma components in the wave undergo polytropic compression and rarefaction. An exact solution to the basic equations is found and analyzed by the Bernoulli pseudopotential method. The parameter range in which periodic waves can propagate and the range in which solitary waves (solitons) exist are determined. It is shown that the propagation velocity of a solitary is always higher than the linear ion sound velocity. The profiles of all the physical quantities in both subsonic and supersonic waves are calculated. The results obtained agree well with both the data from other papers and particular limiting cases.

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References

  1. W. H. Lee, E. Ramirez-Ruiz, and D. Page, Astrophys. J. 632, 421 (2005).

    Article  ADS  Google Scholar 

  2. V. S. Beskin, Stationary Axisymmetric Flows in Astrophysics (Fizmatlit, Moscow, 2006) [in Russian].

    Google Scholar 

  3. V. M. Lipunov, Astrophysics of Neutron Stars (Nauka, Moscow, 1987) [in Russian].

    Google Scholar 

  4. F. C. Michel, Rev. Mod. Phys. 54, 1 (1982).

    Article  ADS  Google Scholar 

  5. M. C. Begelman, R. D. Blandford, and M. J. Rees, Rev. Mod. Phys. 56, 255 (1984).

    Article  ADS  Google Scholar 

  6. B. Kozlovsky, R. J. Murphy, and G. H. Share, Astrophys. J. 604, 892 (2004).

    Article  ADS  Google Scholar 

  7. V. V. Zheleznyakov and S. A. Koryagin, Pis’ma Astron. Zh. 28, 809 (2002) [Astron. Lett. 28, 727 (2002)].

    Google Scholar 

  8. V. V. Zheleznyakov and S. A. Koryagin, Pis’ma Astron. Zh. 31, 819 (2005) [Astron. Lett. 31, 713 (2005)].

    Google Scholar 

  9. E. V. Derishev, V. V. Kocharovskii, Vl. V. Kocharovskii, and V. Yu. Mart’yanov, Nonlinear Waves (IPF RAN, Nizhni Novgorod, 2007), p. 268 [in Russian].

    Google Scholar 

  10. Ya. B. Zeldovich and I. D. Novikov, Relativistic Astrophysics (Nauka, Moscow, 1967, 1975; University of Chicago Press, Chicago, 1971, 1983), Vols. 1, 2.

    Google Scholar 

  11. H. Alfven, Rev. Mod. Phys. 37, 652 (1965).

    Article  ADS  Google Scholar 

  12. H. Alfven, Cosmic Plasma (Reidel, Dordrecht, 1981; Mir, Moscow, 1983).

    Google Scholar 

  13. V. I. Berezhiani, D. D. Tskhakaya, and P. K. Shukla, Phys. Rev. A 46, 6608 (1992).

    Article  ADS  Google Scholar 

  14. E. P. Liang, S. C. Wilks, and M. Tabak, Phys. Rev. Lett. 81, 4890 (1998).

    Google Scholar 

  15. Y. I. Salamin, S. X. Hu, K. Z. Hatsagortsyan, and C. H. Keitel, Phys. Rep. 427(2–3), 41 (2006).

    Article  ADS  Google Scholar 

  16. C. M. Surko, M. Leventhal, W. S. Crane, et al., Rev. Sci. Instrum. 57, 1862 (1986).

    Article  ADS  Google Scholar 

  17. C. M. Surko and T. J. Murphy, Phys. Fluids 2, 1372 (1990).

    Article  Google Scholar 

  18. R. G. Greaves and C. M. Surko, Phys. Rev. Lett. 75, 3846 (1995).

    Article  ADS  Google Scholar 

  19. H. Kakati and K. S. Goswami, Phys. Plasmas 5, 4229 (1998).

    Article  Google Scholar 

  20. H. Saleem and S. Mahmood, Phys. Plasmas 10, 2612 (2003).

    Article  ADS  Google Scholar 

  21. S. Mahmood and H. Saleem, Phys. Plasmas 10, 4680 (2003).

    Article  ADS  Google Scholar 

  22. H. Saleem, Q. Haque, and J. Vranjes, Phys. Rev. E 67, 057402 (2003).

    Google Scholar 

  23. Q. Haque and H. Saleem, Chin. Phys. Lett 21, 884 (2004).

    Article  ADS  Google Scholar 

  24. A. Mushtaq and H. A. Shah, Phys. Plasmas 12, 012301 (2005).

    Google Scholar 

  25. H. Kakati and K. S. Goswami, Phys. Plasmas 7, 808 (2000).

    Article  ADS  Google Scholar 

  26. B. Eliasson and P. K. Shukla, Phys. Plasmas 12, 104501 (2005).

    Google Scholar 

  27. V. I. Berezhiani, M. Y. El-Ashry, and U. A. Mofiz, Phys. Rev. E 50, 448 (1994).

    Article  ADS  Google Scholar 

  28. V. I. Berezhiani and S. M. Mahajan, Phys. Rev. E 52, 1968 (1995).

    Article  ADS  Google Scholar 

  29. P. K. Shukla, L. Stenflo, and R. Fedele, Phys. Plasmas 10, 310 (2003).

    Article  ADS  Google Scholar 

  30. J. O. Hall and P. K. Shukla, Phys. Plasmas 12, 084507 (2005).

    Google Scholar 

  31. N. L. Shatashvili and N. N. Rao, Phys. Plasmas 6, 66 (1999).

    Article  ADS  Google Scholar 

  32. Q. Haque, H. Saleem, and J. Vranjes, Phys. Plasmas 5, 474 (2002).

    Article  ADS  Google Scholar 

  33. N. L. Shatashvili, J. I. Javakhishvili, and H. Kaya, Astrophys. Space Sci. 250, 109 (1997).

    Article  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

  35. R. S. Tiwari, A. Kaushik, and M. K. Mishra, Phys. Lett. A 365, 335 (2007).

    Article  ADS  Google Scholar 

  36. Y. N. Nejoh, Phys. Plasmas 3, 1447 (1996).

    Article  ADS  Google Scholar 

  37. Y. N. Nejoh, Austral. J. Phys. 50, 309 (1997).

    ADS  Google Scholar 

  38. M. Salahuddin, H. Saleem, and M. Saddiq, Phys. Rev. E 66, 036407 (2002).

    Google Scholar 

  39. S. Mahmood, A. Mushtaq, and H. Saleem, New J. Phys. 5, 28.1 (2003).

    Article  Google Scholar 

  40. Q. Haque and H. Saleem, Phys. Plasmas 10, 3793 (2003).

    Article  ADS  Google Scholar 

  41. H. Alinejad, S. Sobhanian, and J. Mahmoodi, Phys. Plasmas 13, 012 304 (2006).

    Google Scholar 

  42. A. Mushtaq and S. A. Khan, Phys. Plasmas 14(5), 052307 (2007).

  43. S. Ali, W. M. Moslem, P. K. Shukla, and R. Schlickeiser, Phys. Plasmas 14, 082 307 (2007).

    Google Scholar 

  44. K. Roy, A. P. Misra, and P. Chatterjee, Phys. Plasmas 15, 032 310 (2008).

    Google Scholar 

  45. N. Jehan, S. Mahmood, and A. M. Mirza, Phys. Scr. 76, 661 (2007).

    Article  MATH  ADS  Google Scholar 

  46. W. M. Moslem, P. K. Shukla, and R. Schlickeiser, Phys. Plasmas 14, 102901 (2007).

    Google Scholar 

  47. T. S. Gill, A. Singh, H. Kaur, et al., Phys. Lett. A 361, 364 (2007).

    Article  MATH  ADS  Google Scholar 

  48. J. F. McKenzie, Phys. Plasmas 9, 800 (2002).

    Article  ADS  MathSciNet  Google Scholar 

  49. J. F. McKenzie, J. Plas. Phys. 67, 353 (2002).

    ADS  Google Scholar 

  50. J. F. McKenzie, F. Verheest, T. B. Doyle, and M. A. Hellberg, Phys. Plasmas 11, 1762 (2004).

    Article  ADS  Google Scholar 

  51. A. E. Dubinov, Prikl. Mekh. Tekh. Fiz. 48(5), 3 (2007) [J. Appl. Mech. Tech. Phys. 48, 621 (2007)].

    Google Scholar 

  52. A. E. Dubinov and A. A. Dubinova, Fiz. Plazmy 33, 935 (2007) [Plasma Phys. Rep. 33, 859 (2007)].

    Google Scholar 

  53. A. E. Dubinov and M. A. Sazonkin, Zh. Tekh. Fiz. 78(9), 29 (2008) [Tech. Phys. 53, 1129 (2008)].

    Google Scholar 

  54. A. E. Dubinov and A. A. Dubinova, Fiz. Plazmy 34, 442 (2008) [Plasma Phys. Rep. 34, 403 (2008)].

    Google Scholar 

  55. A. E. Dubinov, Fiz. Plazmy 34, 239 (2007) [Plasma Phys. Rep. 34, 210 (2007)].

    Google Scholar 

  56. Ch. Sack and H. Schamel, Plasma Phys. Controlled Fusion 27, 717 (1985).

    Article  ADS  Google Scholar 

  57. A. G. Khrapak and I. T. Yakubov, Electrons in Dense Gases and Plasmas (Nauka, Moscow, 1981) [in Russian].

    Google Scholar 

  58. K. Iwata, R. G. Greaves, and T. J. Murphy, Phys. Rev. A 51, 473 (1995).

    Article  ADS  Google Scholar 

  59. S. A. Kaplan and V. N. Tsytovich, Usp. Fiz. Nauk 97, 77 (1969) [Sov. Phys. Usp. 12, 42 (1969)].

    Google Scholar 

  60. V. F. Zaitsev and A. D. Polyanin, Handbook of Ordinary Differential Equations (Nauka, Moscow, 2001) [in Russian].

    Google Scholar 

  61. A. E. Dubinov and I. D. Dubinova, J. Plasma Phys. 71, 715 (2005).

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Sarov State Physical and Technical Institute, ul. Dukhova 6, Sarov, Nizhni Novgorod oblast, 607186, Russia

    A. E. Dubinov & M. A. Sazonkin

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  1. A. E. Dubinov
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  2. M. A. Sazonkin
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Original Russian Text © A.E. Dubinov, M.A. Sazonkin, 2009, published in Fizika Plazmy, 2009, Vol. 35, No. 1, pp. 18–28.

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Dubinov, A.E., Sazonkin, M.A. Nonlinear theory of ion-acoustic waves in an electron-positron-ion plasma. Plasma Phys. Rep. 35, 14–24 (2009). https://doi.org/10.1134/S1063780X09010024

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  • DOI: https://doi.org/10.1134/S1063780X09010024

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