Solar Physics

, Volume 290, Issue 10, pp 3033–3049 | Cite as

Generation of Weak Double Layers and Low-Frequency Electrostatic Waves in the Solar Wind

  • G. S. Lakhina
  • S. V. Singh


We propose that the mechanism for the generation of weak double layers (WDLs) and low-frequency coherent electrostatic waves, observed by Wind in the solar wind at 1 AU, might be slow and fast ion-acoustic solitons and double layers. The solar wind plasma is modelled as a fluid of hot protons and hot \(\alpha\) particles streaming with respect to protons, and suprathermal electrons having a \(\kappa\)-distribution. The fast ion-acoustic mode is similar to the ion-acoustic mode of a proton–electron plasma and can support only positive-potential solitons. The slow ion-acoustic mode is a new mode that occurs due to the presence of \(\alpha\) particles. This mode can support both positive and negative solitons and double layers. The slow ion-acoustic mode can exist even when the relative streaming, \(U_{0}\), between \(\alpha\) particles and protons is zero, provided that the \(\alpha\) temperature, \(T_{i}\), is not exactly equal to four times the proton temperature, \(T_{p}\). An increase of the \(\kappa\)-index leads to an increase in the critical Mach number, maximum Mach number, and the maximum amplitude of both slow and fast ion-acoustic solitons. The slow ion-acoustic double layer can explain the amplitudes and widths, but not the shapes, of the observed WDLs in the solar wind at 1 AU by Wind spacecraft. The Fourier transform of the slow ion-acoustic solitons/double layers would produce broadband low-frequency electrostatic waves having main peaks between 0.35 kHz to 1.6 kHz, with an electric field in the range of \(E = (0.01\,\mbox{--}\,0.7)~\mbox{mV}\,\mbox{m}^{-1}\), in excellent agreement with the observed low-frequency electrostatic wave activity in the solar wind at 1 AU.


Solar wind, shock waves Waves, plasma Plasma physics 



GSL thanks the National Academy of Sciences, India for the support under the NASI-Senior Scientist Platinum Jubilee Fellowship Scheme.


  1. Asbridge, J.R., Bame, S.J., Feldman, W.C., Montgomery, M.D.: 1976, Helium and hydrogen velocity differences in the solar wind. J. Geophys. Res. 81, 2719.  DOI. CrossRefADSGoogle Scholar
  2. Baboolal, S., Bharuthram, R., Hellberg, M.A.: 1990, Cut-off conditions and existence domains for large-amplitude ion-acoustic solitons and double layers in fluid plasmas. J. Plasma Phys. 44, 1.  DOI. CrossRefADSGoogle Scholar
  3. Berthomier, M., Pottelette, R., Malingre, M.: 1998, Solitary waves and weak double layers in a two-electron temperature auroral plasma. J. Geophys. Res. 103, 4261.  DOI. CrossRefADSGoogle Scholar
  4. Borovsky, J.E., Gary, S.P.: 2014, How important are the alpha–proton relative drift and the electron heat flux for the proton heating of the solar wind in the inner heliosphere? J. Geophys. Res. 119, 5210.  DOI. CrossRefGoogle Scholar
  5. Bostrom, R., Gustafsson, G., Holback, B., Holmgreen, G., Koskinen, H., Kintner, P.: 1988, Characteristics of solitary waves and weak double layers in the magnetospheric plasma. Phys. Rev. Lett. 61, 82.  DOI. CrossRefADSGoogle Scholar
  6. Bounds, S.R., Pfaff, R.F., Knowlton, S.F., Mozer, F.S., Temerin, M.A., Kletzing, C.A.: 1999, Solitary potential structures associated with ion and electron beams near 1 \(r_{e}\) altitude. J. Geophys. Res. 104, 28709.  DOI. CrossRefADSGoogle Scholar
  7. Bourouaine, S., Marsch, E., Neubauer, F.M.: 2011, On the relative speed and temperature ratio of solar wind alpha particles and protons: collisions versus wave effects. Astrophys. J. Lett. 728, L3.  DOI. CrossRefADSGoogle Scholar
  8. Buti, B.: 1980, Ion-acoustic holes in a two-electron-temperature plasma. Phys. Lett. A 76, 251.  DOI. CrossRefADSGoogle Scholar
  9. Cattell, C.A., Dombeck, J., Wygant, J.R., Hudson, M.K., Mozer, F.S., Temerin, M.A., Peterson, W.K., Kletzing, C.A., Russell, C.T., Pfaff, R.F.: 1999, Comparisons of polar satellite observations of solitary wave velocities in the plasma sheet boundary and the high altitude cusp to those in the auroral zone. Geophys. Res. Lett. 26, 425.  DOI. CrossRefADSGoogle Scholar
  10. Devanandhan, S., Singh, S.V., Lakhina, G.S., Bharuthram, R.: 2015, Small amplitude electron acoustic solitary waves in a magnetized superthermal plasma. Commun. Nonlinear Sci. Numer. Simul. 22, 1322.  DOI. MathSciNetCrossRefADSGoogle Scholar
  11. Dovner, P.O., Eriksson, A.I., Bostrom, R., Holback, B.: 1980, Freja multiprobe observations of electrostatic solitary structures. Geophys. Res. Lett. 21, 1827.  DOI. CrossRefADSGoogle Scholar
  12. Ergun, R.E., Carlson, C.W., McFadden, J.P., Mozer, F.S., Delory, G.T., Peria, W., Chaston, C.C., Temerin, M., Roth, I., Muschietti, L., Elphic, R., Strangeway, R., Pfaff, R., Cattell, C.A., Klumpar, D., Shelley, E., Peterson, W., Moebius, E., Kistler, L.: 1998a, Fast satellite observations of large-amplitude solitary structures. Geophys. Res. Lett. 25, 2041.  DOI. CrossRefADSGoogle Scholar
  13. Ergun, R.E., Calrson, C.W., McFadden, J.P., Mozer, F.S., Muschietti, L., Roth, I., Strangeway, R.J.: 1998b, Debye-scale plasma structures associated with magnetic-field-aligned electric fields. Phys. Rev. Lett. 81, 826.  DOI. CrossRefADSGoogle Scholar
  14. Franz, J.R., Kintner, P.M., Pickett, J.S.: 1998, Polar observations of coherent electric field structures. Geophys. Res. Lett. 25, 1277.  DOI. CrossRefADSGoogle Scholar
  15. Franz, J.R., Kintner, P.M., Pickett, J.S., Chen, L.-J.: 2005, Properties of small-amplitude electron phase-space holes observed by polar. J. Geophys. Res. 110, A09212.  DOI. ADSGoogle Scholar
  16. Ghosh, S.S., Iyengar, A.N.S.: 1997, Anomalous width variations forion acoustic rarefactive solitary waves in a warm ion plasma with two electron temperatures. Phys. Plasmas 5, 3204.  DOI. CrossRefADSGoogle Scholar
  17. Ghosh, S.S., Lakhina, G.S.: 2004, Anomalous width variation of rarefactive ion acoustic solitary waves in the context of auroral plasmas. Nonlinear Process. Geophys. 11, 219.  DOI. CrossRefADSGoogle Scholar
  18. Ghosh, S.S., Ghosh, K.K., Iyengar, A.N.S.: 1996, Large mach number ion acoustic rarefactive solitary waves for a two electron temperature warm ion plasma. Phys. Plasmas 4, 3939.  DOI. CrossRefADSGoogle Scholar
  19. Goldman, M.V., Oppenheim, M.M., Newman, D.L.: 1999, Nonlinear two-stream instabilities as an explanation for the auroral bipolar wave structures. Geophys. Res. Lett. 26, 1821.  DOI. CrossRefADSGoogle Scholar
  20. Gurnett, D.A., Anderson, R.R.: 1977, Plasma wave electric fields in the solar wind: initial results from helios 1. J. Geophys. Res. 82, 632.  DOI. CrossRefADSGoogle Scholar
  21. Gurnett, D.A., Frank, L.A.: 1978, Ion acoustic waves in the solar wind. J. Geophys. Res. 83, 58.  DOI. CrossRefADSGoogle Scholar
  22. Hirshberg, J., Asbridge, J.R., Robbins, D.E.: 1974, The helium component of solar wind velocity streams. J. Geophys. Res. 79, 934.  DOI. CrossRefADSGoogle Scholar
  23. Kakad, A.P., Singh, S.V., Reddy, R.V., Lakhina, G.S., Tagare, S.G., Verheest, F.: 2007, Generation mechanism for electron acoustic solitary waves. Phys. Plasmas 14, 052305.  DOI. CrossRefADSGoogle Scholar
  24. Kojima, H., Matsumoto, H., Chikuba, S., Horiyama, S., Ashour-Abdalla, M., Anderson, R.R.: 1996, Geotail waveform observations of broadband/narrowband electrostatic noise in the distant tail. J. Geophys. Res. 102, 14439.  DOI. CrossRefADSGoogle Scholar
  25. Koskinen, H.E.J., Lundin, R., Holback, B.: 1990, On the plasma environment of solitary waves and weak double layers. J. Geophys. Res. 95, 5921.  DOI. CrossRefADSGoogle Scholar
  26. Kurth, W.S., Gurnett, D.A., Frank, L.A.: 1979, High-resolution spectrograms of ion acoustic waves in the solar wind. J. Geophys. Res. 84, 3413.  DOI. CrossRefADSGoogle Scholar
  27. Lacombe, C., Salem, C., Mangeney, A., Hubert, D., Perche, C., Bougeret, J.-L., Kellogg, P.J., Bosqued, J.-M.: 2002, Evidence for the interplanetary electric potential? Wind observations of electrostatic fluctuations. Ann. Geophys. 20, 609.  DOI. CrossRefADSGoogle Scholar
  28. Lakhina, G.S., Singh, S.V., Kakad, A.P.: 2011, Ion- and electron- acoustic solitons and double layers in multi-component space plasmas. Adv. Space Res. 47, 1558.  DOI. CrossRefADSGoogle Scholar
  29. Lakhina, G.S., Singh, S.V., Kakad, A.P.: 2014, Ion acoustic solitons/double layers in two-ion plasma revisited. Phys. Plasmas 21, 062311.  DOI. CrossRefADSGoogle Scholar
  30. Lakhina, G.S., Kakad, A.P., Singh, S.V., Verheest, F.: 2008a, Ion- and electron-acoustic solitons in two-electron temperature space plasmas. Phys. Plasmas 15, 062903.  DOI. CrossRefADSGoogle Scholar
  31. Lakhina, G.S., Singh, S.V., Kakad, A.P., Verheest, F., Bharuthram, R.: 2008b, Study of nonlinear ion- and electron-acoustic waves in multi-component space plasmas. Nonlinear Process. Geophys. 15, 903.  DOI. CrossRefADSGoogle Scholar
  32. Lakhina, G.S., Singh, S.V., Kakad, A.P., Goldstein, M.L., Vinas, A.F., Pickett, J.S.: 2009, A mechanism for electrostatic solitary structures in the Earth’s magnetosheath. J. Geophys. Res. 114, A09212.  DOI. ADSGoogle Scholar
  33. Lakhina, G.S., Singh, S.V., Kakad, A.P., Pickett, J.S.: 2011, Generation of electrostatic solitary waves in the plasma sheet boundary layer. J. Geophys. Res. 116, A10218.  DOI. CrossRefADSGoogle Scholar
  34. Livadiotis, G.: 2015, Introduction to special section on origins and properties of kappa distributions: Statistical background and properties of kappa distributions in space plasmas. J. Geophys. Res. 120, 1.  DOI. Google Scholar
  35. Mace, R.L., Hellberg, M.A.: 1995, A dispersion function for plasmas containing superthermal particles. Phys. Plasmas 2, 2098.  DOI. CrossRefADSGoogle Scholar
  36. Maharaj, S.K., Bharuthram, R., Singh, S.V., Lakhina, G.S.: 2012, Existence domains of arbitrary amplitude nonlinear structures in two-electron temperature space plasmas. I. Low-frequency ion-acoustic solitons. Phys. Plasmas 19, 072320.  DOI. CrossRefADSGoogle Scholar
  37. Maksimovic, M., Pierrard, V., Riley, P.: 1997, Ulysses electron distributions fitted with kappa functions. Geophys. Res. Lett. 24, 1151.  DOI. CrossRefADSGoogle Scholar
  38. Mangeney, A., Salem, C., Lacombe, C., Bougeret, J.-L., Perche, C., Manning, R., Kellogg, P.J., Goetz, K., Monson, S.J., Bosqued, J.-M.: 1999, Wind observations of coherent electrostatic waves in the solar wind. Ann. Geophys. 17, 307.  DOI. CrossRefADSGoogle Scholar
  39. Marsch, E., Muhlhauser, K.-H., Rosenbauer, H., Schwenn, R., Neubauer, F.M.: 1982, Solar wind helium ions: Observations of the Helios solar probes between 0.3 and 1 AU. J. Geophys. Res. 87, 35.  DOI. CrossRefADSGoogle Scholar
  40. Matsumoto, H., Kojima, H., Miyatake, T., Omura, Y., Okada, Y.M., Nagano, I., Tsutui, M.: 1994, Electrostatic solitary waves (esw) in the magnetotail: Ben wave forms observed by geotail. Geophys. Res. Lett. 21, 2915.  DOI. CrossRefADSGoogle Scholar
  41. Mottez, F., Perraut, S., Roux, A., Louarn, P.: 1997, Coherent structures in the magnetotail triggered by counterstreaming electron beams. J. Geophys. Res. 102, 11399.  DOI. CrossRefADSGoogle Scholar
  42. Mozer, F.S., Ergun, R.E., Temerin, M., Cattell, C., Dombeck, J., Wygant, J.: 1997, New features of time domain electric field structures in the auroral acceleration region. Phys. Rev. Lett. 79, 1281.  DOI. CrossRefADSGoogle Scholar
  43. Omura, Y., Matsumoto, H., Miyake, T., Kojima, H.: 1996, Electron beam instabilities as generation mechanism of electrostatic solitary waves in the magnetotail. J. Geophys. Res. 101, 2685.  DOI. CrossRefADSGoogle Scholar
  44. Omura, Y., Kojima, H., Miki, N., Mukai, T., Matsumoto, H., Anderson, R.: 1999, Electrostatic solitary waves carried by diffused electron beams observed by the geotail spacecraft. J. Geophys. Res. 104, 14627.  DOI. CrossRefADSGoogle Scholar
  45. Pickett, J.S., Chen, L.-J., Kahler, S.W., Santolik, O., Gurnett, D.A., Tsurutani, B.T., Balogh, A.: 2004, Isolated electrostatic structures observed throughout the cluster orbit: relationship to magnetic field strength. Ann. Geophys. 22, 2515.  DOI. CrossRefADSGoogle Scholar
  46. Pickett, J.S., Chen, L.-J., Kahler, S.W., Santolík, O., Goldstein, M.L., Lavraud, B., Décréau, P.M.E., Kessel, R., Lucek, E., Lakhina, G.S., Tsurutani, B.T., Gurnett, D.A., Cornilleau-Wehrlin, N., Fazakerley, A., Réme, H., Balogh, A.: 2005, On the generation of solitary waves observed by cluster in the near-Earth magnetosheath. Nonlinear Process. Geophys. 12, 181.  DOI. CrossRefADSGoogle Scholar
  47. Pickett, J.S., Chen, L.-J., Mutel, R.L., Christopher, I.H., Santolik, O., Lakhina, G.S., Singh, S.V., Reddy, R.V., Gurnett, D.A., Tsurutani, B.T., Lucek, E.: 2008, Furthering our understanding of electrostatic solitary waves through cluster multi-spacecraft observations and theory. Adv. Space Res. 41, 1643.  DOI. CrossRefGoogle Scholar
  48. Pierrard, V.: 2012, Solar wind electron transport: interplanetary electric field and heat conduction. Space Sci. Rev. 172, 315.  DOI. CrossRefADSGoogle Scholar
  49. Pierrard, V., Lemaire, J.: 1996, Lorentzian ion exosphere model. J. Geophys. Res. 101, 7923.  DOI. CrossRefADSGoogle Scholar
  50. Pierrard, V., Maksimovic, M., Lemaire, J.: 1999, Electronic velocity distribution functions from the solar wind to the corona. J. Geophys. Res. 104, 17021.  DOI. CrossRefADSGoogle Scholar
  51. Reddy, R.V., Lakhina, G.S.: 1991, Ion acoustic double layers and solitons in auroral plasma. Planet. Space Sci. 39, 1343.  DOI. CrossRefADSGoogle Scholar
  52. Reddy, R.V., Lakhina, G.S., Verheest, F.: 1992, Ion-acoustic double layers and solitons in multispecies auroral beam-plasmas. Planet. Space Sci. 40, 1055.  DOI. CrossRefADSGoogle Scholar
  53. Rufai, O.R., Bharuthram, R., Singh, S.V., Lakhina, G.S.: 2012, Low frequency solitons and double layers in a magnetized plasma with two temperature electrons. Phys. Plasmas 19, 122308.  DOI. CrossRefADSGoogle Scholar
  54. Rufai, O.R., Bharuthram, R., Singh, S.V., Lakhina, G.S.: 2014, Effect of hot ion temperature on obliquely propagating ion-acoustic solitons and double layers in an auroral plasma. Commun. Nonlinear Sci. Numer. Simul. 19, 1338.  DOI. MathSciNetCrossRefADSGoogle Scholar
  55. Sagdeev, R.Z.: 1966, Cooperative phenomena and shock waves in collisionless plasmas. In: Leontovich, M.A. (ed.) Reviews of Plasma Physics 4, Consultants Bureau, New York. Google Scholar
  56. Salem, C., Lacombe, C., Mangeney, A., Kellogg, P.J., Bougeret, J.-L.: 2003, Weak double layers in the solar wind and their relation to the interplanetary electric field. In: Velli, M., Bruno, R., Malara, F. (eds.) CP679, Solar Wind 10: Proceedings of the Tenth International Sola Wind Conference, Am. Inst. of Phys., New York, 513.  DOI. Google Scholar
  57. Singh, N.: 2003, Space-time evolution of electron-beam driven electron holes and their effects on the plasma. Nonlinear Process. Geophys. 10, 53.  DOI. CrossRefADSGoogle Scholar
  58. Singh, S.V., Reddy, R.V., Lakhina, G.S.: 2001, Broadband electrostatic noise due to nonlinear electron-acoustic waves. Adv. Space Res. 28, 1643.  DOI. CrossRefADSGoogle Scholar
  59. Singh, S.V., Lakhina, G.S., Bharuthram, R., Pillay, S.R.: 2011, Electrostatic solitary structures in presence of non-thermal electrons and a warm electron beam on the auroral field lines. Phys. Plasmas 18, 122306.  DOI. CrossRefADSGoogle Scholar
  60. Singh, S.V., Devanandhan, S., Lakhina, G.S., Bharuthram, R.: 2013, Effect of ion temperature on ion-acoustic solitary waves in a magnetized plasma in presence of superthermal electrons. Phys. Plasmas 20, 012306.  DOI. CrossRefADSGoogle Scholar
  61. Steinberg, J.T., Lazaras, A.J., Ogilvie, K.W., Lepping, R., Byrnes, J.: 1996, Differential flow between solar wind protons and alpha particles: first wind observations. Geophys. Res. Lett. 23, 1183.  DOI. CrossRefADSGoogle Scholar
  62. Temerin, M., Cerny, K., Lotko, W., Mozer, F.S.: 1982, Observations of double layers and solitary waves in the auroral plasma. Phys. Rev. Lett. 48, 1175.  DOI. CrossRefADSGoogle Scholar
  63. Tsurutani, B.T., Arballo, J.K., Lakhina, G.S., Ho, C.M., Buti, B., Pickett, J.S., Gurnett, D.A.: 1998, Plasma waves in the dayside polar cap boundary layer: bipolar and monopolar electric pulses and whistler mode waves. Geophys. Res. Lett. 25, 4117.  DOI. CrossRefADSGoogle Scholar
  64. Washimi, H., Taniuti, T.: 1966, Propagation of ion-acoustic solitary waves of small amplitude. Phys. Rev. Lett. 17, 996.  DOI. CrossRefADSGoogle Scholar

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Authors and Affiliations

  1. 1.Indian Institute of GeomagnetismNavi MumbaiIndia

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