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Chaos in positive ion–negative ion magnetized plasmas

Published online by Cambridge University Press:  09 November 2020

Samiran Ghosh Open the ORCID record for Samiran Ghosh [Opens in a new window] ,
Biplab Maity  and
Swarup Poria
Samiran Ghosh*
Affiliation:
Department of Applied Mathematics, University of Calcutta, 92, Acharya Prafulla Chandra Road, Kolkata700009, India
Biplab Maity
Affiliation:
Government General Degree College, Dantan – II, Paschim Medinipur721445, West Bengal, India
Swarup Poria
Affiliation:
Department of Applied Mathematics, University of Calcutta, 92, Acharya Prafulla Chandra Road, Kolkata700009, India
*
†Email addresses for correspondence: [email protected], [email protected]
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Abstract

The dynamical behaviour of weakly nonlinear, low-frequency sound waves are investigated in a plasma composed of only positive and negative ions incorporating the effects of a weak external uniform magnetic field. In the plasma model the mass (temperature) of the positive ions is smaller (larger) than that of the negative ions. The dynamics of the nonlinear wave is shown to be governed by a novel nonlinear equation. The stationary plane wave (analytical and numerical) nonlinear analysis on the basis of experimental parameters reveals that the nonlinear wave does have quasi-periodic and chaotic solutions. The Poincarè return map analysis confirms these observed complex structures.

Keywords

plasma nonlinear phenomena
Type
Research Article
Information
Journal of Plasma Physics , Volume 86 , Issue 6 , December 2020 , 905860604
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Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press

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References

REFERENCES

Adak, A., Ghosh, S. & Chakrabarti, N. 2015 Ion acoustic shock wave in collisional equal mass plasma. Phys. Plasmas 22, 102307.CrossRefGoogle Scholar
Arnold, V. I. 1989 Mathematical Methods of Classical Mechanics. Springer.CrossRefGoogle Scholar
Economou, D. J. 2007 Fundamentals and applications of ion–ion plasmas. Appl. Surf. Sci. 253, 6672–6680.CrossRefGoogle Scholar
Ghosh, S., Adak, A. & Khan, M. 2014 Dissipative solitons in pair-ion plasmas. Phys. Plasmas 21, 12303.CrossRefGoogle Scholar
Greaves, R. G. & Surko, C. M. 2000 Inward transport and compression of a positron plasma by a rotating electric field. Phys. Rev. Lett. 85, 1883–1886.CrossRefGoogle ScholarPubMed
Intrator, T., Hershkowitz, N. & Stern, R. 1983 Beam–plasma interactions in a positive ion–negative ion plasma. Phys. Fluids 26, 1942–1948.CrossRefGoogle Scholar
Iwamoto, N. 1993 Collective modes in nonrelativistic electron-positron plasmas. Phys. Rev. E 47, 604–611.CrossRefGoogle ScholarPubMed
Kadomtsev, B. B. & Petviashvili, V. I. 1970 On the stability of solitary waves in weakly dispersing media. Sov. Phys. Dokl. 15, 539–541.Google Scholar
Karney, C. F. F. & Bers, A. 1977 Stochastic ion heating by a perpendicularly propagating electrostatic wave. Phys. Rev. Lett. 39, 550–554.CrossRefGoogle Scholar
Kelly, M. C. & Heelis, R. A. 1989 The Earth's Ionosphere: Plasma Physics and Electrodynamics. Academic Press.Google Scholar
Kim, S. H., Henrich, J. R. & Merlino, R. L. 2008 Electrostatic ion-cyclotron waves in a plasma with heavy negative ions. Planet. Space Sci. 56, 1552–1559.CrossRefGoogle Scholar
Kim, S. H. & Merlino, R. L. 2007 Electron attachment to ${\mathrm {C}}_{7}{\mathrm {F}}_{14}$ and ${\mathrm {SF}}_{6}$ in a thermally ionized potassium plasma. Phys. Rev. E 76, 035401.CrossRefGoogle Scholar
Kim, S. H., Merlino, R. L., Meyer, J. K. & Rosenberg, M. 2013 Low-frequency electrostatic waves in a magnetized, current-free, heavy negative ion plasma. J. Plasma Phys. 79, 1107–1111.CrossRefGoogle Scholar
Kourakis, I., Verheest, F. & Crammer, N. F. 2007 Nonlinear perpendicular propagation of ordinary mode electromagnetic wave packets in pair plasmas and electron-positron-ion plasmas. Phys. Plasmas 14, 022306.CrossRefGoogle Scholar
Laedke, E. W. & Spatschek, K. H. 1982 Nonlinear ion-acoustic waves in weak magnetic fields. Phys. Fluids 25, 985–989.CrossRefGoogle Scholar
Lichtenberg, A. J. & Lieberman, M. A. 1992 Regular and Chaotic Dynamics. Springer.CrossRefGoogle Scholar
Lorenz, E. N. 1963 Deterministic nonperiodic flow. J. Atmos. Sci. 20, 130–141.2.0.CO;2>CrossRefGoogle Scholar
Maity, B., Ghosh, S. & Bharuthram, R. 2015 Nonlinear ion acoustic wave in a pair-ion plasma in a uniform weak magnetic field. Phys. Scr. 90, 045604.CrossRefGoogle Scholar
Merlino, R. L. & Kim, S. H. 2008 Measurement of the electron attachment rates for SF6 and C7F14 at $\textrm {Te}=0.2 \textrm {eV}$ in a magnetized $Q$ machine plasma. J. Chem. Phys. 129, 224310.CrossRefGoogle Scholar
Molenaar, D., Clercx, H. J. H. & van Heijst, G. J. F. 2005 Transition to chaos in a confined two-dimensional fluid flow. Phys. Rev. Lett. 95, 104503.CrossRefGoogle Scholar
Moslem, W. M., Kourakis, I. & Shukla, P. K. 2007 Finite amplitude envelope solitons in a pair-ion plasma. Phys. Plasmas 14, 032107.CrossRefGoogle Scholar
Oohara, W. & Hatakeyama, R. 2005 Electrostatic waves in a paired fullerene-ion plasma. Phys. Rev. Lett. 95, 175003.CrossRefGoogle Scholar
Poria, S. & Ghosh, S. 2016 Chaotic behavior of collective ion dynamics in the presence of an external static magnetic field. Phys. Plasmas 23, 062315.CrossRefGoogle Scholar
Ratcliffe, J. A. 1972 An Introduction to the Ionosphere and Magnetosphere. Cambridge University Press.Google Scholar
Rosenberg, M. & Merlino, R. L. 2009 Instability of higher harmonic electrostatic ion cyclotron waves in a negative ion plasma. J. Plasma Phys. 75, 495–508.CrossRefGoogle Scholar
Rosenberg, M. & Merlino, R. L. 2013 Drift instability in a positive ion–negative ion plasma. J. Plasma Phys. 79, 949–952.CrossRefGoogle Scholar
Shukla, P. K., Bingham, R., Phelps, A. D. R. & Stenflo, L. 2009 Dark and grey electromagnetic electron-cyclotron envelope solitons in an electron-positron magnetoplasma. J. Plasma Phys. 75, 575–580.CrossRefGoogle Scholar
Shukla, P. K., Eliasson, B. & Stenflo, L. 2011 Electromagnetic solitary pulses in a magnetized electron-positron plasma. Phys. Rev. E 84, 037401.CrossRefGoogle Scholar
Sirovich, L. 1989 Chaotic dynamics of coherent structures. Physica D 37, 126–145.CrossRefGoogle Scholar
Stenflo, L., Shukla, P. K. & Yu, M. Y. 1985 Nonlinear propagation of electromagnetic waves in magnetized electron-positron plasmas. Astrophys. Space Sci. 117, 303–308.CrossRefGoogle Scholar
Strogatz, S. H. 1994 Nonlinear Dynamics and Chaos: with applications to Physics, Biology, Chemistry and Engineering. Addision-Wesley Publishing Company.Google Scholar
Taniuti, T. 1974 Reductive perturbation method and far fields of wave equations. Suppl. Prog. Theor. Phys. 55, 1–35.CrossRefGoogle Scholar
Witham, G. B. 1999 Linear and Nonlinear Waves. John-Wiley and Sons.CrossRefGoogle Scholar
Yu, M. Y., Shukla, P. K. & Stenflo, L. 1986 Alfven vortices in a strongly magnetized electron – positron plasma. Astrophys. J. Lett. 309, L63–L66.CrossRefGoogle Scholar
Zakharov, V. E. & Kuznetsov, E. A. 1974 Three-dimensional solitons. Sov. Phys. JETP 39, 285–286.Google Scholar
Zank, G. P. & Greaves, R. G. 1995 Linear and nonlinear modes in nonrelativistic electron-positron plasmas. Phys. Rev. E 51, 6079–6090.CrossRefGoogle ScholarPubMed