Astrophysics and Space Science

, Volume 355, Issue 1, pp 33–41 | Cite as

Freak waves in Saturn’s magnetosphere

Original Article


Properties of planar as well as nonplanar ion acoustic freak waves that propagate in a plasma composed of warm ions and two-temperature electron plasma having kappa-distribution are reported. The dynamics of the nonlinear freak waves is governed by a modified nonlinear Schrödinger equation. The possible region for the freak waves to exist is defined precisely for typical parameters of Saturn’s magnetosphere. For planar case, stability/instability analyses reveals that there is a critical value (f cr ) of f (i.e., the equilibrium density ratio of the hot-to-cold electron species) exists for low wave number k. For large wave number k, the stability domain is always a decreasing function in f. Low κ values, which indicate that an excess of suprathermal particles in the tail of the distribution, shifts f cr to higher values. Also, there exists a modulation instability period for the cylindrical and spherical envelope excitations, which does not exist in the one-dimensional case. Furthermore, cylindrical and spherical freak waves are investigated numerically. Spherical ion-acoustic freak waves are found to grow faster than the cylindrical waves.


Nonlinear wave modulation Cylindrical and spherical rogue waves Ion-acoustic wavepackets Saturn’s magnetosphere Super-thermal electron distribution 



The author dedicate this work to the memory of Prof. Padma Kant Shukla.


  1. Abraham-Shrauner, B., Feldman, W.C.: J. Plasma Phys. 17, 123 (1977) ADSCrossRefGoogle Scholar
  2. Abraham-Shrauner, B., Asbridge, J.R., Bame, S.J., Feldman, W.C.: J. Geophys. Res. 84, 553 (1979) ADSCrossRefGoogle Scholar
  3. Ankiewicz, A., Devine, N., Akhmediev, N.: Phys. Lett. A 373, 3997 (2009) ADSCrossRefGoogle Scholar
  4. Armstrong, T.P., Paonessa, M.T., Bell, E.V. II, Krimigis, S.M.: J. Geophys. Res. 88, 8893 (1983) ADSCrossRefGoogle Scholar
  5. Baluku, T.K., Hellberg, M.A.: Phys. Plasmas 19, 012106 (2012) ADSCrossRefGoogle Scholar
  6. Barbosa, D.D., Kurth, W.S.: J. Geophys. Res.-Space Phys. 98, 9351 (1993) ADSCrossRefGoogle Scholar
  7. Bludov, Yu.V., Konotop, V.V., Akhmediev, N.: Opt. Lett. 34, 3015 (2009a) ADSCrossRefGoogle Scholar
  8. Bludov, Yu.V., Konotop, V.V., Akhmediev, N.: Phys. Rev. A 80, 033610 (2009b) ADSCrossRefGoogle Scholar
  9. Christon, P., Mitchell, D.G., Williams, D.J., Frank, L.A., Huang, C.Y., Eastman, T.E.: J. Geophys. Res. 93, 2562 (1988) ADSCrossRefGoogle Scholar
  10. Chuang, S.-H., Haul, L.-N.: Phys. Plasmas 16, 022901 (2009) ADSCrossRefGoogle Scholar
  11. El-Labany, S.K., Sabry, R., Moslem, W.M., Elghmaz, E.A.: Astrophys. Space Sci. 349, 773 (2014) ADSCrossRefGoogle Scholar
  12. El-Wakil, S.A., Abulwafa, E.M., Elgarayhi, A., El-Shewy, E.K., Mahmoud, A.A., Tawfik, A.M.: Astrophys. Space Sci. 350, 591 (2014) ADSCrossRefGoogle Scholar
  13. Ganshin, A.N., Efimov, V.B., Kolmakov, G.V., Mezhov-Deglin, L.P., McClintock, P.V.E.: Phys. Rev. Lett. 101, 065303 (2008) ADSCrossRefGoogle Scholar
  14. Genty, G., de Sterke, C.M., Bang, O., Dias, F., Akhmediev, N., Dudley, J.M.: Phys. Lett. A 374, 989 (2010) ADSCrossRefGoogle Scholar
  15. Gill, T.S., Bedi, C., Bains, A.S.: Phys. Scr. 81, 055503 (2010) ADSCrossRefGoogle Scholar
  16. Gosling, J.T., Asbridge, J.R., Bame, S.J., Feldman, W.C., Zwickl, R.D., Paschman, G., Sckopke, N., Hynds, R.J.: J. Geophys. Res. 86, 547 (1981) ADSCrossRefGoogle Scholar
  17. Hellberg, M.A., Mace, R.L.: Phys. Plasmas 9, 1495 (2002) ADSCrossRefGoogle Scholar
  18. Hussain, S., Mahmood, S.: Phys. Plasmas 18, 123701 (2011) ADSCrossRefGoogle Scholar
  19. Hussain, S., Mahmood, S.: Astrophys. Space Sci. 342, 117 (2012) ADSCrossRefGoogle Scholar
  20. Jukui, X.: Phys. Plasmas 11, 1860 (2004) ADSCrossRefGoogle Scholar
  21. Jukui, X., Lang, H.: Phys. Plasmas 10, 339 (2003) ADSCrossRefGoogle Scholar
  22. Lazar, M., Schlickeiser, R., Poedts, S., Tautz, R.C.: Mon. Not. R. Astron. Soc. 168, 390 (2008) Google Scholar
  23. Leubner, M.P.: J. Geophys. Res. 87, 6335 (1982) ADSCrossRefGoogle Scholar
  24. Leubner, M.P.: Phys. Plasmas 11, 1308 (2004) ADSCrossRefGoogle Scholar
  25. Lui, A.T.Y., Krimigis, S.M.: Geophys. Res. Lett. 8, 527 (1981) ADSCrossRefGoogle Scholar
  26. Maksimovic, M., Pierrard, V., Lemaire, J.F.: Astron. Astrophys. 324, 725 (1997) ADSGoogle Scholar
  27. Mendis, D.A., Rosenberg, M.: Annu. Rev. Astron. Astrophys. 32, 419 (1994) ADSCrossRefGoogle Scholar
  28. Moslem, W.M.: Phys. Plasmas 18, 032301 (2011) ADSCrossRefGoogle Scholar
  29. Moslem, W.M., Sabry, R., Shukla, P.K.: Phys. Plasmas 17, 032305 (2010) ADSCrossRefGoogle Scholar
  30. Moslem, W.M., Sabry, R., El-Labany, S.K., Shukla, P.K.: Phys. Rev. E 84, 066402 (2011a) ADSCrossRefGoogle Scholar
  31. Moslem, W.M., Shukla, P.K., Eliasson, B.: Europhys. Lett. 96, 25002 (2011b) ADSCrossRefGoogle Scholar
  32. Pierrard, V., Lemaire, J.: J. Geophys. Res. 101, 7923 (1996) ADSCrossRefGoogle Scholar
  33. Ruban, V., Kodama, Y., Ruderman, M., et al.: Eur. Phys. J. Spec. Top. 185, 5 (2010) CrossRefGoogle Scholar
  34. Sabry, R., Omran, M.A.: Astrophys. Space Sci. 344, 455 (2013) ADSCrossRefGoogle Scholar
  35. Sabry, R., El-Labany, S.K., Shukla, P.K.: Phys. Plasmas 15, 122310 (2008) ADSCrossRefGoogle Scholar
  36. Sabry, R., Moslem, W.M., Shukla, P.K.: Plasma Phys. Control. Fusion 54, 035010 (2012a) ADSCrossRefGoogle Scholar
  37. Sabry, R., Moslem, W.M., Shukla, P.K.: Phys. Plasmas 19, 122903 (2012b) ADSCrossRefGoogle Scholar
  38. Sabry, R., Moslem, W.M., Shukla, P.K.: Phys. Rev. E 86, 036408 (2012c) ADSCrossRefGoogle Scholar
  39. Sahu, B.: Astrophys. Space Sci. 346, 415 (2013) ADSCrossRefGoogle Scholar
  40. Schippers, P., Blanc, M., Andre, N., Dandouras, I., Lewis, G.R., Gilbert, L.K., Persoon, A.M., Krupp, N., Gurnett, D.A., Coates, A.J., Krimigis, S.M., Young, D.T., Dougherty, M.K.: J. Geophys. Res.-Space Phys. 113, A07208 (2008). doi: 10.1029/2008JA013098 ADSCrossRefGoogle Scholar
  41. Shatz, M., Punzmann, H., Xia, H.: Phys. Rev. Lett. 104, 104503 (2010) ADSCrossRefGoogle Scholar
  42. Sittler, E.C., Ogilvie, K.W., Scudder, J.D.: J. Geophys. Res.-Space Phys. 88, 8847 (1983). doi: 10.1029/JA088iA11p08847 ADSCrossRefGoogle Scholar
  43. Solli, D.R., Ropers, C., Koonath, P., Jalali, B.: Nature 450, 1054 (2007) ADSCrossRefGoogle Scholar
  44. Stenflo, L., Marklund, M.: J. Plasma Phys. 76, 293 (2010) ADSCrossRefGoogle Scholar
  45. Taniuti, T., Yajima, N.: J. Math. Phys. 10, 1369 (1969) ADSCrossRefGoogle Scholar
  46. Williams, D.J., Mitchell, D.G., Christon, S.P.: Geophys. Res. Lett. 15, 303 (1988) ADSCrossRefGoogle Scholar
  47. Xue, J.K.: Europhys. Lett. 68(5), 645 (2004) ADSCrossRefGoogle Scholar
  48. Yan, Z.: Commun. Theor. Phys. 54, 947 (2010) ADSCrossRefGoogle Scholar
  49. Yeom, D.-I., Eggleton, B.: Nature 450, 953 (2007) ADSCrossRefGoogle Scholar
  50. Young, D.T., Berthelier, J.J., Blanc, M., Burch, J.L., Bolton, S., Coates, A.J., Crary, F.J., Goldstein, R., Grande, M., Hill, T.W., Johnson, R.E., Baragiola, R.A., Kelha, V., McComas, D.J., Mursula, K., Sittler, E.C., Svenes, K.R., Szego, K., Tanskanen, P., Thomsen, M.F., Bakshi, S., Barraclough, B.L., Bebesi, Z., Delapp, D., Dunlop, M.W., Gosling, J.T., Furman, J.D., Gilbert, L.K., Glenn, D., Holmlund, C., Illiano, J.M., Lewis, G.R., Linder, D.R., Maurice, S., McAndrews, H.J., Narheim, B.T., Pallier, E., Reisenfeld, D., Rymer, A.M., Smith, H.T., Tokar, R.L., Vilppola, J., Zinsmeyer, C.: Science 307, 1262 (2005) ADSCrossRefGoogle Scholar

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© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Theoretical Physics Group, Department of Physics, Faculty of ScienceDamietta UniversityNew DamiettaEgypt
  2. 2.Department of Physics, College of Science and Humanitarian StudiesSalman bin Abdulaziz UniversityAlkharjKingdom of Saudi Arabia

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