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Asymptotic analysis of solitons and double layers at the acoustic speed

Published online by Cambridge University Press:  16 November 2017

Carel P. Olivier ,
Frank Verheest  and
Shimul K. Maharaj
Carel P. Olivier*
Affiliation:
Centre for Space Research, North-West University, Potchefstroom 2520, South Africa
Frank Verheest
Affiliation:
Sterrenkundig Observatorium, Universiteit Gent, Krijgslaan 281, B–9000 Gent, Belgium School of Chemistry and Physics, University of KwaZulu-Natal, Durban 4000, South Africa
Shimul K. Maharaj
Affiliation:
South African National Space Agency (SANSA) Space Science, P. O. Box 32, Hermanus 7200, South Africa Department of Physics, University of the Western Cape, Robert Sobukwe Road, Bellville 7535, South Africa
*
†Email address for correspondence: carel.olivier@nwu.ac.za
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Abstract

In this paper, we consider the asymptotic behaviour of solitons and double layers. By using the Sagdeev pseudopotential formalism, a Taylor series expansion is used to derive the asymptotic behaviour. For solitons and supersolitons that propagate faster than the acoustic speed, an exponential decay rate is derived. In contrast, for acoustic speed solitons and supersolitons, we show that the decay rate is algebraic, resulting in much fatter tails. These results can be extended to double layers. However, the double layer velocity affects only one side of the tail. The other side of the tail is affected by the multiplicity of the double layer root. All the results are illustrated by means of a case study.

Keywords

plasma nonlinear phenomenaplasma waves
Type
Research Article
Information
Journal of Plasma Physics , Volume 83 , Issue 6 , December 2017 , 905830605
Copyright
© Cambridge University Press 2017 

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References

Baluku, T. K. & Hellberg, M. A. 2011 Ion acoustic solitary waves in an electron-positron-ion plasma with non-thermal electrons. Plasma Phys. Control. Fusion 53, 095007.CrossRefGoogle Scholar
Baluku, T. K. & Hellberg, M. A. 2012 Ion acoustic solitons in a plasma with two-temperature kappa-distributed electrons. Phys. Plasmas 19, 012106.CrossRefGoogle Scholar
Baluku, T. K., Hellberg, M. A., Kourakis, I. & Saini, N. S. 2010a Dust ion acoustic solitons in a plasma with kappa-distributed electrons. Phys. Plasmas 17, 053702.CrossRefGoogle Scholar
Baluku, T. K., Hellberg, M. A. & Verheest, F. 2010b New light on ion acoustic solitary waves in a plasma with two-temperature electrons. Europhys. Lett. 91, 15001.CrossRefGoogle Scholar
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, 28709–28717.Google Scholar
Buti, B. 1980 Ion-acoustic holes in a two-electron-temperature ion plasma. Phys. Lett. 76, 251–254.Google Scholar
Cairns, R. A., Mamun, A. A., Bingham, R., Böstrom, R., Dendy, R. O., Nairn, C. M. C. & Shukla, P. K. 1995 Electrostatic solitary structures in non-thermal plasmas. Geophys. Res. Lett. 22, 2709–2712.Google Scholar
Jenab, S. M. & Spanier, F. 2017 Simulation study of overtaking of ion-acoustic solitons in the fully kinetic regime. Phys. Plasmas 24, 032305.Google Scholar
Kakad, B., Kakad, A. & Omura, Y. 2014 Nonlinear evolution of ion acoustic solitary waves in space plasmas: fluid and particle-in-cell simulations. J. Geophys. Res. 119, 5589–5599.CrossRefGoogle Scholar
Kakad, A., Lotekar, A. & Kakad, B. 2016 First-ever model simulation of the new subclass of solitons ‘Supersolitons’ in plasma. Phys. Plasmas. 23, 110702.CrossRefGoogle Scholar
Kakad, A., Omura, Y. & Kakad, B. 2013 Experimental evidence of ion acoustic soliton chain formation and validation of nonlinear fluid theory. Phys. Plasmas. 20, 062103.CrossRefGoogle Scholar
Koskinen, H. E. J., Lundin, R. & Holback, B. 1990 On the plasma environment of solitary waves and weak double layers. J. Geophys. Res. 95, 5921–5929.CrossRefGoogle Scholar
Lakhina, G. S., Singh, S. V. & Kakad, A. P. 2014 Ion acoustic solitons/double layers in two-ion plasma revisited. Phys. Plasmas 21, 062311.CrossRefGoogle Scholar
Lotekar, A., Kakad, A. & Kakad, B. 2016 Fluid simulation of dispersive and nondispersive ion acoustic waves in the presence of superthermal electrons. Phys. Plasmas 23, 102108.CrossRefGoogle Scholar
Mälkki, A., Eriksson, A. I., Dovner, P. O., Boström, R., Holback, B., Holmgren, G. & Koskinen, H. E. J. 1993 A statistical survey of auroral solitary waves and weak double layers: 1. Occurence and net voltage. J. Geophys. Res. 98, 15521–15530.Google Scholar
Nakamura, Y. & Tsukabayashi, I. 1984 Observation of modified Korteweg-de Vries solitons in a multicomponent plasma with negative ions. Phys. Rev. Lett. 52, 2356–2359.Google Scholar
Olivier, C. P., Maharaj, S. K. & Bharuthram, R. 2015 Ion-acoustic solitons, double layers and supersolitons in a plasma with two ion- and two electron species. Phys. Plasmas 22, 082312.Google Scholar
Olivier, C. P., Verheest, F. & Maharaj, S. K. 2016 A small-amplitude study of solitons near critical plasma compositions. J. Plasma Phys. 82, 905820605.Google Scholar
Temerin, M., Cerny, K., Lotko, W. & Mozer, F. S. 1982 Observation of double layers and solitary waves in the auroral plasma. Phys. Rev. Lett. 48, 1175–1178.CrossRefGoogle Scholar
Verheest, F. 2011 Dust-acoustic solitary modes in plasmas with isothermal and nonthermal ions: polarity switches and coexistence domains. Phys. Plasmas 18, 083701.Google Scholar
Verheest, F. & Hellberg, M. A. 2015 Electrostatic supersolitons and double layers at the acoustic speed. Phys. Plasmas 22, 012301.Google Scholar
Verheest, F., Hellberg, M. A. & Baluku, T. K. 2012 Arbitrary amplitude ion-acoustic soliton coexistence and polarity in a plasma with two ion species. Phys. Plasmas 19, 032305.CrossRefGoogle Scholar
Verheest, F., Hellberg, M. A., Saini, N. S. & Kourakis, I. 2011 Large acoustic solitons and double layers in plasmas with two positive ion species. Phys. Plasmas 18, 042309.Google Scholar
Washimi, H. & Taniuti, T. 1966 Propagation of ion-acoustic solitary waves of small amplitude. Phys. Rev. Lett. 17, 996–998.Google Scholar