Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Electron acoustic envelope solitons in non-Maxwellian plasmas

  • 11 Accesses

Abstract

The NASA Van Allen Probes spacecraft has recently observed broadband electrostatic turbulence in the inner magnetosphere which has been conjectured to be produced by large amplitude electrostatic solitary waves of generally two types [D.M. Malaspina, J.R. Wygant, R.E. Ergun, G.D. Reeves, R.M. Skoug, B.A. Larsen, J. Geophys. Res.: Space Phys. 120, 4246 (2015); C.S. Dillard, I.Y. Vasko, F.S. Mozer, O.V. Agapitov, J.W. Bonnell, Phys. Plasmas 25, 022905, (2018)]. The solitary waves with highly asymmetric bipolar parallel electric field have been recently shown to correspond to the electron-acoustic plasma mode (existing due to two-temperature electron population) [C.S. Dillard, I.Y. Vasko, F.S. Mozer, O.V. Agapitov, J.W. Bonnell, Phys. Plasmas 25, 022905, (2018)]. These findings along with the observations of non-Maxwellian electrons in terrestrial magnetosheath and planetary magnetospheres [W. Masood, S.J. Schwartz, M. Maksimovic, A.N. Fazakerley, Ann. Geophys. 24, 1725 (2006); W. Masood, S.J. Schwartz, J. Geophys. Res. 113, A01216 (2008); M.N.S. Qureshi, W. Nasir, W. Masood, P.H. Yoon, H.A. Shah, S.J. Schwartz, J. Geophys. Res.: Space Phys. 119, 10059 (2014); M.N.S. Qureshi, W. Nasir, R. Bruno, W. Masood, MNRAS 488, 954 (2019)] have prompted us to theoretically investigate the problem of amplitude modulation of the electron acoustic waves (EAWs) in plasmas whose ingredients are stationary ions, inertial cold electrons and warm (r,q) distributed inertialess electrons. The nonlinear Schrödinger equation (NLSE) that governs the modulational instability (MI) of the EAWs has been derived using the standard reductive perturbation technique (RPT). The presence of the warm (r,q) distributed electrons has been shown to influence the existence conditions of MI of the EAWs and both the indices have been found to cause a decrease in the growth rate of MI. A detailed comparison has also been drawn between double spectral index (r,q), kappa and Maxwellian distribution functions and the differences are highlighted. Additionally, the nondimensional parameter α=nc0/ne0 which is the equilibrium density ratio of the cold to hot electron component, has been shown to play an important role in the formation of envelope solitary excitations.

Graphical abstract

This is a preview of subscription content, log in to check access.

References

  1. 1.

    A. Esfandyari-Kalejahi, H. Asgari, Phys. Plasmas 12, 102302 (2005)

  2. 2.

    M. Mohan, B. Buti, Plasma Phys. 21, 713 (1979)

  3. 3.

    X. Bai-song, H. Kai-fen, Chin. Phys. 10, 214 (2001)

  4. 4.

    S.K. El-Labany, W.F. El-Taibany, Phys. Plasmas 10, 989 (2003)

  5. 5.

    B.D. Fried, R.W. Gould, Phys. Fluids 4, 139 (1961)

  6. 6.

    P.K. Shukla, L. Stenflo, M.A. Hellberg, Phys. Rev. E 66, 027403 (2002)

  7. 7.

    R.L. Tokar, S.P. Gary, Geophys. Res. Lett. 11, 1180 (1984)

  8. 8.

    V. Singh, G.S. Lakhina, Planet. Space Sci. 49, 107 (2001)

  9. 9.

    F. Anderegg, C.F. Driscoll, D.H.E. Dubin, T.M. O’Neil, F. Valentini, Phys. Plasmas 16, 055705 (2009)

  10. 10.

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

  11. 11.

    S. Chowdhury, S. Biswas, N. Chakrabarti, R. Pal, Phys. Plasmas 24, 062111 (2017)

  12. 12.

    N. Dubouloz, R. Pottelette, M. Malingre, R.A. Treumann, Geophys. Res. Lett. 18, 155 (1991)

  13. 13.

    R. Pottelette, R.E. Ergun, R.A. Treumann, M. Berthomier, C.W. Carlson, J.P. McFadden, I. Roth, Geophys. Res. Lett. 26, 2629 (1999)

  14. 14.

    H. Matsumoto, H. Kojima, T. Miyatake, Y. Omura, M. Okada, I. Nagano, M. Tsutsui, Geophys. Res. Lett. 21, 2915 (1994)

  15. 15.

    D. Schriver, M. Ashour-Abdalla, Geophys. Res. Lett. 16, 899 (1989)

  16. 16.

    D. Henry, R.A. Treumann, J. Plasma Phys. 8, 311 (1972)

  17. 17.

    K. Watanabe, T. Taniuti, J. Phys. Soc. Jpn. 43, 1819 (1977)

  18. 18.

    T.H. Stix, Waves in Plasma (AIP, New York, 1992)

  19. 19.

    M. Berthomier, R. Pottelette, M. Malingre, Y. Khotyaintsev, Phys. Plasmas 7, 2987 (2000)

  20. 20.

    A.A. Mamun, P.K. Shukla, J. Geophys. Res. 107, 1135 (2002)

  21. 21.

    R. Sabry, M.A. Omran, Astrophys. Space Sci. 344, 455 (2013)

  22. 22.

    R.L. Mace, M.A. Hellberg, Phys. Plasmas 8, 2649 (2001)

  23. 23.

    A.A. Mamun, P.K. Shukla, L. Stenflo, Phys. Plasmas 9, 1474 (2002)

  24. 24.

    P.K. Shukla, A.A. Mamun, B. Eliasson, Geophys. Res. Lett. 31, L07803 (2004)

  25. 25.

    S.K. El-Labany, M. Shalaby, R. Sabry, L.S. El-Sherif, Astrophys. Space Sci. 340, 101 (2012)

  26. 26.

    A.A. Abid, M.Z. Khan, Q. Lu, S.L. Yap, Phys. Plasmas 24, 33702 (2017)

  27. 27.

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

  28. 28.

    M.N.S. Qureshi, H.A. Shah, G. Murtaza, S.J. Schwartz, F. Mahmood, Phys. Plasmas 11, 3819 (2004)

  29. 29.

    S. Zaheer, G. Murtaza, H.A. Shah, Phys. Plasmas 11, 2246 (2004)

  30. 30.

    M.N.S. Qureshi, J.K. Shi, S.Z. Ma, Phys. Plasmas 12, 122902 (2005)

  31. 31.

    S. Zaheer, G. Murtaza, H.A. Shah, Phys. Plasmas 13, 62109 (2006)

  32. 32.

    Z. Kiran, H.A. Shah, M.N.S. Qureshi, G. Murtaza, Sol. Phys. 236, 167 (2006)

  33. 33.

    M.N.S. Qureshi, W. Nasir, W. Masood, P.H. Yoon, H.A. Shah, S.J. Schwartz, J. Geophys. Res.: Space Phys. 119, 10059 (2014)

  34. 34.

    W. Masood, S.J. Schwartz, M. Maksimovic, A.N. Fazakerley, Ann. Geophys. 24, 1725 (2006)

  35. 35.

    W. Masood, S.J. Schwartz, J. Geophys. Res. 113, A01216 (2008)

  36. 36.

    K.H. Shah, M.N.S. Qureshi, W. Masood, H.A. Shah, Phys. Plasmas 25, 042303 (2018)

  37. 37.

    S. Khalid, M.N.S. Qureshi, W. Masood, Astrophys. Space Sci. 363, 9 (2018)

  38. 38.

    J.E. Wahlund, P. Louam, T. Chust, H. de Feraudy, A. Roux, B. Holback, B. Cabrit, A.I. Eriksson, P.M. Kintner, M.C. Kelley, J. Bonnell, S. Chesney, Geophys. Res. Lett. 21, 1835 (1994)

  39. 39.

    M.N.S. Qureshi, W. Nasir, R. Bruno, W. Masood, MNRAS 488, 954 (2019)

  40. 40.

    S. Khalid, M.N.S. Qureshi, W. Masood, Phys. Plasmas 26, 092114 (2019)

  41. 41.

    I. Kourakis, P.K. Shukla, Phys. Rev. E 69, 036411 (2004)

  42. 42.

    H. Demiray, Phys. Plasmas 23, 032109 (2016)

  43. 43.

    R.L. Mace, G. Amery, M.A. Hellberg, Phys. Plasmas 6, 44 (1999)

  44. 44.

    T. Taniuti, N. Yajima, J. Math. Phys. 10, 1369 (1969)

  45. 45.

    N. Asano, T. Taniuti, N. Yajima, J. Math. Phys. 10, 2020 (1969)

  46. 46.

    M.R. Amin, G.E. Morfill, P.K. Shukla, Phys. Rev. E 58, 6517 (1998)

  47. 47.

    R. Fedele, H. Schamel, P.K. Sukla, Phys. Scr. T98, 18 (2002)

  48. 48.

    R. Fedele, H. Schamel, Eur. Phys. J. B 27, 313 (2002)

  49. 49.

    D.M. Malaspina, J.R. Wygant, R.E. Ergun, G.D. Reeves, R.M. Skoug, B.A. Larsen, J. Geophys. Res.: Space Phys. 120, 4246 (2015)

  50. 50.

    C.S. Dillard, I.Y. Vasko, F.S. Mozer, O.V. Agapitov, J.W. Bonnell, Phys. Plasmas 25, 022905 (2018)

Download references

Author information

Correspondence to Shakir Ullah.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Ullah, S., Masood, W. & Siddiq, M. Electron acoustic envelope solitons in non-Maxwellian plasmas. Eur. Phys. J. D 74, 26 (2020). https://doi.org/10.1140/epjd/e2019-100589-1

Download citation

Keywords

  • Plasma Physics