Skip to main content Accessibility help

Nonlinear electrostatic solitary waves in electron–positron plasmas

  • I. J. Lazarus (a1), R. Bharuthram (a2), S. Moolla (a3), S. V. Singh (a4) and G. S. Lakhina (a4)...


The generation of nonlinear electrostatic solitary waves (ESWs) is explored in a magnetized four component two-temperature electron–positron plasma. Fluid theory is used to derive a set of nonlinear equations for the ESWs, which propagate obliquely to an external magnetic field. The electric field structures are examined for various plasma parameters and are shown to yield sinusoidal, sawtooth and bipolar waveforms. It is found that an increase in the densities of the electrons and positrons strengthen the nonlinearity while the periodicity and nonlinearity of the wave increases as the cool-to-hot temperature ratio increases. Our results could be useful in understanding nonlinear propagation of waves in astrophysical environments and related laboratory experiments.


Corresponding author

Email address for correspondence:


Hide All
Asseo, E. & Riazuelo, A. 2000 Relativistic anisotropic pair plasmas. Mon. Not. R. Astron. Soc. 318, 9831004.
Bharuthram, R. 1992 Arbitrary amplitude double layers in a multi-species electron–positron plasma. Astrophys. Space Sci. 189, 213222.
Bhattacharyya, R., Janaki, M. S. & Dasgupta, B. 2003 Relaxation in electron–positron plasma: a possibility. Phys. Lett. A 315, 120125(6).
Ergun, R. E., Carlson, C. W., McFadden, J. P., Mozer, F. S., Delroy, G. T., Peria, W., Chaston, C. C., Temerin, M., Elphic, R., Strangeway, R. et al. 1998 FAST satellite observations of large-amplitude solitary wave structures. Geophys. Res. Lett. 25, 20412044.
Esfandyari-Kalejahi, A., Kourakis, Y. & Shukla, P. K. 2006 Oblique modulation of electrostatic modes and envelope excitations in pair-ion and electron–positron plasmas. Phys. Plasmas 13, 122310122318.
Franz, J. R., Kintner, P. M. & Pickett, J. S. 1998 POLAR observations of coherent electric field structures. Geophys. Res. Lett. 25, 12771280.
Goldreich, P. & Julian, W. H. 1969 Pulsar electrodynamics. Astrophys. J. 157, 869880.
Greaves, R. G. & Surko, C. M. 1995 An electron–positron beam-plasma experiment. Phys. Rev. Lett. 75, 38463849.
Hasegawa, A. 1975 Plasma Instabilities and Nonlinear Effects, p. 194. Springer.
Iwamoto, N. 1993 Collective modes in nonrelativistic electron–positron plasmas. Phys. Rev. E 47, 604611.
Kashiyama, K., Ioka, K. & Kawanaka, N. 2011 White dwarf pulsars as possible cosmic ray electron–positron factories. Phys. Rev. D 83, 023002023022.
Kojima, H., Matsumoto, H., Miyatake, T., Nagano, I., Fujita, A., Frank, L. A., Mukai, T., Paterson, W. R., Saito, Y., Machida, S. et al. 1994 Relation between electrostatic solitary waves and hot plasma flow in the plasma sheet boundary layer: GEOTAIL observations. Geophys. Res. Lett. 21, 29192922.
Kojima, H., Ohtsuka, K., Matsumoto, H., Omura, Y., Anderson, R. R., Saito, Y., Mukai, T., Kokubun, S. & Yamamoto, T. 1999 Plasma waves in slow-mode shocks observed by GEOTAIL spacescraft. Adv. Space Res. 24, 5154.
Lazarus, I. J., Bharuthram, R. & Hellberg, M. A. 2008 Modified Korteweg–de Vries–Zakharov–Kuznetsov solitons in symmetric two-temperature electron–positron plasmas. J. Plasma Phys. 74, 519529.
Lazarus, I. J., Bharuthram, R., Singh, S. V., Pillay, S. R. & Lakhina, G. S. 2012 Linear electrostatic waves in two temperature electron–positron plasmas. J. Plasma Phys. 78, 621628.
Liu, Y. & Liu, S. Q. 2011 Nonlinear behavior of electromagnetic waves in ultra-relativistic electron–positron plasmas. Contrib. Plasma Phys. 51, 698706.
Lu, G., Liu, Y., Wang, Y., Stenflo, L., Popel, S. I. & Yu, M. Y. 2010 Fully nonlinear electrostatic waves in electron–positron plasmas. J. Plasma Phys. 76, 267275.
Luo, Q. 1998 Plasma processes in pulsar magnetospheres and eclipsing binary pulsar systems. Braz. J. Phys. 28, 191202.
Matsumoto, H., Kojima, H., Kasaba, Y., Miyake, T., Anderson, R. R. & Mukai, T. 1997 Plasma waves in the upstream and bow shock regions observed by GEOTAIL. Adv. Space Res. 20, 683693.
Matsumoto, H., Kojima, H., Miyatake, T., Omura, Y., Okada, M., Nagano, I. & Tsutsui, M. 1994 Electrostatic solitary waves (ESW) in the magnetotail: BEN wave forms observed by GEOTAIL. Geophys. Res. Lett. 21, 29152918.
Michel, F. C. 1982 Theory of pulsar magnetospheres. Rev. Mod. Phys. 54, 166.
Miller, H. R. & Witta, P. J. 1987 Active Galactic Nuclei, p. 202. Springer.
Mofiz, U. A. & Amin, M. R. 2013 Langmuir dark solitons in dense ultrarelativistic electron–positron gravito-plasma in pulsar magnetosphere. Astrophys. Space Sci. 345, 119124.
Mofiz, U. A. & Mamun, A. A. 1992 Spiky Langmuir solitons in a dense ultrarelativistic electron–positron plasma. Phys. Fluids B 4, 38063807.
Moolla, S., Bharuthram, R., Singh, S. V. & Lakhina, G. S. 2003 Non-linear high-frequency waves in the magnetosphere. Pramana J. Phys. 61, 12091214.
Moolla, S., Bharuthram, R., Singh, S. V., Lakhina, G. S. & Reddy, R. V. 2007 An explanation for high-frequency broadband electrostatic noise in the Earth’s magnetosphere. J. Geophys. Res. 112, A07214p1-23.
Omura, Y., Kojima, H. & Matsumoto, H. 1994 Computer simulation of electrostatic solitary waves: a nonlinear model of broadband electrostatic noise. Geophys. Res. Lett. 21, 29232926.
Piran, T. 2005 The physics of gamma-ray bursts. Rev. Mod. Phys. 76, 11431210.
Press, W. H., Teukolsky, S. A., Vetterling, W. T. & Flannery, B. P. 1996 Numerical Receipes in Fortran 90 – ‘The Art of Parallel Scientific Computing’, vol. 2, pp. 702704, 731, 740, 1297, 1308. Cambridge University Press.
Reddy, R. V., Lakhina, G. S., Singh, N. & Bharuthram, R. 2002 Spiky parallel electrostatic ion cyclotron and ion acoustic waves. Nonlinear Process. Geophys. 9, 2529.
Stark, C. R., Diver, D. A., da Costa, A. A. & Laing, E. W. 2007 Nonlinear mode coupling in pair plasmas. Astron. Astrophys. 476, 1730.
Sturrock, P. A. 1971 A model of pulsars. Astrophys. J. 164, 529556.
Temerin, M. A., Cerny, K., Lotko, W. & Mozer, F. S. 1982 Observations of double layers and solitary waves in the auroral plasma. Phys. Rev. Lett. 48, 11751179.
Verheest, F., Hellberg, M. A., Gray, G. J. & Mace, R. L. 1996 Electrostatic solitons in multispecies electron–positron plasmas. Astrophys. Space Sci. 239, 125139.
Weise, J. & Melrose, D. B. 2002 One-photon pair production in pulsars: non-relativistic and relatrivistic regimes. Mon. Not. R. Astron. Soc. 329, 115125.
Zank, G. P. & Greaves, R. G. 1995 Linear and nonlinear modes in nonrelativistic electron–positron plasmas. Phys. Rev. E 51, 60796090.
MathJax is a JavaScript display engine for mathematics. For more information see

Nonlinear electrostatic solitary waves in electron–positron plasmas

  • I. J. Lazarus (a1), R. Bharuthram (a2), S. Moolla (a3), S. V. Singh (a4) and G. S. Lakhina (a4)...


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed