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A small-amplitude study of solitons near critical plasma compositions

Published online by Cambridge University Press:  28 November 2016

Carel P. Olivier ,
Frank Verheest  and
Shimul K. Maharaj
Carel P. Olivier
Affiliation:
South African National Space Agency (SANSA) Space Science, P.O. Box 32, Hermanus 7200, South Africa 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
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Abstract

The properties of small-amplitude solitons are established near critical plasma compositions in a generalized fluid plasma with an arbitrary number of species. The study is conducted via a Taylor series expansion of the Sagdeev potential. It is shown that there are two types of critical compositions, namely rich critical and poor critical compositions. The coexistence of positive and negative polarity solitons is shown to arise at rich critical compositions and near rich critical compositions. At poor critical compositions, no small-amplitude solitons exist, while weak double layers arise near poor critical compositions. A novel analytical expression is obtained for a small-amplitude acoustic speed soliton solution near rich critical compositions. These solitons have a Lorentzian shape with much fatter tails than regular solitons. A case study is also performed for a simple fluid model consisting of cold ions and two Boltzmann electron species. Exact agreement is obtained between the Sagdeev analysis and reductive perturbation theory. For the first time, we derive the same Lorentzian acoustic speed soliton from reductive perturbation theory.

Keywords

plasma nonlinear phenomena
Type
Research Article
Information
Journal of Plasma Physics , Volume 82 , Issue 6 , December 2016 , 905820605
Copyright
© Cambridge University Press 2016 

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References

Baboolal, S., Bharuthram, R. & Hellberg, M. A. 1988 Arbitrary-amplitude rarefactive ion-acoustic double layers in warm multi-fluid plasmas. J. Plasma Phys. 40, 163–178.Google Scholar
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, 1–23.Google Scholar
Baluku, T. K. & Hellberg, M. A. 2008 Dust acoustic solitons in plasmas with kappa-distributed electrons and/or ions. Phys. Plasmas 15, 123705.Google Scholar
Baluku, T. K. & Hellberg, M. A. 2012 Ion acoustic solitons in a plasma with two-temperature kappa-distributed electrons. Phys. Plasmas 19, 012106.Google Scholar
Baluku, T. K., Hellberg, M. A. & Verheest, F. 2010 New light on ion acoustic solitary waves in a plasma with two-temperature electrons. Europhys. Lett. 91, 15001.Google Scholar
Bharuthram, R. & Shukla, P. K. 1986 Large amplitude ion-acoustic double layers in a double Maxwellian electron plasma. Phys. Fluids 29, 3214–3218.Google Scholar
Buti, B. 1980 Ion-acoustic holes in a two-electron-temperature plasma. Phys. Lett. A 76, 251–254.Google Scholar
Cairns, R. A., Mamun, A. A., Bingham, R., Boström, 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
Gardner, C. S., Green, J. M., Kruskal, M. D. & Miura, R. M. 1967 Method for solving the Korteweg–deVries equation. Phys. Rev. Lett. 19, 1095–1097.Google Scholar
Ghosh, S. S., Ghosh, K. K. & Sekar Iyengar, A. N. 1996 Large Mach number ion acoustic rarefactive solitary waves for a two electron temperature warm ion plasma. Phys. Plasmas 3, 3939–3946.CrossRefGoogle Scholar
Gill, T. S. & Kaur, H. 2000 Effect of nonthermal ion distribution and dust temperature on nonlinear dust acoustic solitary waves. Pramana – J. Phys. 55, 855–859.Google Scholar
Goswami, B. N. & Buti, B. 1976 Ion acoustic solitary waves in a two-electron-temperature plasma. Phys. Lett. A 57, 149–150.Google Scholar
Goswami, K. S. & Bujarabarua, S. 1987 Weak electron acoustic double layers in a multicomponent plasma. Pramana – J. Phys. 28, 399–408.Google Scholar
Kakad, A. P., Singh, S. V., Reddy, R. V., Lakhina, G. S., Tagare, S. G. & Verheest, F. 2006 Generation mechanism for electron acoustic solitary waves. Phys. Plasmas 14, 052305.Google Scholar
Maharaj, S. K., Pillay, S. R., Bharuthram, R., Reddy, R. V., Singh, S. V. & Lakhina, G. S. 2006 Arbitrary amplitude dust-acoustic double layers in a non-thermal plasma. J. Plasma Phys. 72, 43–58.CrossRefGoogle Scholar
Mamun, A. A., Cairns, R. A. & Shukla, P. K. 1996 Solitary potentials in dusty plasmas. Phys. Plasmas 3, 702–704.Google Scholar
Mbuli, L. N., Maharaj, S. K., Bharuthram, R., Singh, S. V. & Lakhina, G. S. 2016 Arbitrary amplitude fast electron-acoustic solitons in three-electron component space plasmas. Phys. Plasmas 23, 062302.Google Scholar
Mendoza-Briceño, C. A., Russel, S. M. & Mamun, A. A. 2000 Large amplitude electrostatic solitary structures in a hot non-thermal dusty plasma. Planet. Space Sci. 48, 599–608.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.CrossRefGoogle Scholar
Nakamura, Y. & Tsukabayashi, I. 1985 Modified Korteweg–de Vries ion-acoustic solitons in a plasma. J. Plasma Phys. 34, 401–415.Google Scholar
Nishihara, K. & Tajiri, M. 1981 Rarefaction ion acoustic solitons in two-electron-temperature plasma. J. Phys. Soc. Japan 50, 4047–4053.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
Rice, W. K. M., Hellberg, M. A., Mace, R. L. & Baboolal, S. 1993 Finite electron mass effects on ion-acoustic solitons in a two electron temperature plasma. Phys. Lett. A 174, 416–420.Google Scholar
Sagdeev, R. Z. 1966 Cooperative phenomena and shock waves in collisionless plasmas. In Reviews of Plasma Physics (ed. Leontovich, M. A.), vol. 4, pp. 23–91. Consultants Bureau.Google Scholar
Schamel, H. 1972 Stationary solitary, snoidal and sinusoidal ion acoustic waves. Plasma Phys. 14, 905–924.Google Scholar
Schamel, H. 1973 A modified Korteweg–de Vries equation for ion acoustic waves due to resonant electrons. J. Plasma Phys. 9, 377–387.CrossRefGoogle Scholar
Schamel, H. 2000 Hole equilibria in Vlasov–Poisson systems: a challenge to wave theories of ideal plasmas. Phys. Plasmas 7, 4831–4844.Google Scholar
Tagare, S. G. 1997 Dust-acoustic solitary waves and double layers in dusty plasma consisting of cold dust particles and two-temperature isothermal ions. Phys. Plasmas 4, 3167–3172.CrossRefGoogle Scholar
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, 1175–1178.Google Scholar
Torvén, S. 1981 Modified Korteweg–de Vries equation for propagating double layers in plasmas. Phys. Rev. Lett. 47, 1053–1056.Google Scholar
Tribeche, M., Amour, R. & Shukla, P. K. 2012 Ion acoustic solitary waves in a plasma with nonthermal electrons featuring Tsallis distribution. Phys. Rev.  E 85, 037401.Google Scholar
Tsallis, C. 1988 Possible generalization of Boltzmann–Gibbs statistics. J. Stat. Phys. 52, 479–487.Google Scholar
Verheest, F. 1988 Ion-acoustic solitons in multi-component plasmas including negative ions at critical densities. J. Plasma Phys. 39, 71–79.Google Scholar
Verheest, F. 2010 Nonlinear acoustic waves in nonthermal dusty or pair plasmas. Phys. Plasmas 17, 062302.Google Scholar
Verheest, F. 2015 Critical densities for Korteweg–de Vries-like acoustic solitons in multi-ion plasmas. J. Plasma Phys. 81, 905810605.Google Scholar
Verheest, F. & Hellberg, M. A. 2015a Electrostatic supersolitons and double layers at the acoustic speed. Phys. Plasmas 22, 012301.CrossRefGoogle Scholar
Verheest, F. & Hellberg, M. A. 2015b Effects of hot electron inertia on electron-acoustic solitons and double layers. Phys. Plasmas 22, 072303.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.Google Scholar
Verheest, F., Hellberg, M. A. & Kourakis, I. 2013 Electrostatic supersolitons in three-species plasmas. Phys. Plasmas 20, 012302.Google Scholar
Verheest, F., Olivier, C. P. & Hereman, W. A. 2016 Modified Korteweg–de Vries solitons at supercritical densities in two-electron temperature plasmas. J. Plasma Phys. 82, 905820208.Google Scholar
Verheest, F. & Pillay, S. R. 2008 Large amplitude dust-acoustic solitary waves and double layers in nonthermal plasmas. Phys. Plasmas 15, 013703.Google Scholar
Washimi, H. & Taniuti, T. 1966 Propagation of ion-acoustic solitary waves of small amplitude. Phys. Rev. Lett. 17, 996–998.Google Scholar
Zabusky, N. J. & Kruskal, M. D. 1965 Interaction of ‘solitons’ in a collisionless plasma and the recurrence of initial states. Phys. Rev. Lett. 15, 240–243.Google Scholar