Home Arbitrary amplitude ion acoustic solitons, double layers and supersolitons in a collisionless magnetized plasma consisting of non-thermal and isothermal electrons
Article
Licensed
Unlicensed Requires Authentication

Arbitrary amplitude ion acoustic solitons, double layers and supersolitons in a collisionless magnetized plasma consisting of non-thermal and isothermal electrons

  • Sandip Dalui ORCID logo EMAIL logo , Sankirtan Sardar ORCID logo and Anup Bandyopadhyay
Published/Copyright: March 8, 2021
Zeitschrift für Naturforschung A
From the journal Zeitschrift für Naturforschung A Volume 76 Issue 5

Abstract

Using Sagdeev pseudo-potential technique, we have studied the arbitrary amplitude ion acoustic solitons, double layers and supersolitons in a collisionless plasma consisting of adiabatic warm ions, non-thermal hot electrons and isothermal cold electrons immersed in an external uniform static magnetic field. We have used the phase portraits of the dynamical system describing the non-linear behaviour of ion acoustic waves to confirm the existence of different solitary structures. We have found that the system supports (a) positive potential solitons, (b) negative potential solitons, (c) coexistence of both positive and negative potential solitons, (d) negative potential double layers, (e) negative potential supersolitons and (f) positive potential supersolitons. Again, we have seen that the amplitude of the positive potential solitons decreases or increases with increasing nch according to whether 0<nch<nch(c) or nch(c)<nch≤1, where nch is the ratio of isothermal cold and non-thermal hot electron number densities, and nch(c) is a critical value of nch. Also, we have seen that the amplitude of the positive potential solitons decreases with increasing βe, where βe is the non-thermal parameter. We have also investigated the transition of different negative potential solitary structures: negative potential soliton (before the formation of negative potential double layer) → negative potential double layer → negative potential supersoliton → negative potential soliton (after the formation of negative potential double layer) by considering the variation of θ only, where θ is angle between the direction of the external uniform static magnetic field and the direction of propagation of the ion acoustic wave.

Keywords: ion acoustic solitary waves; non-thermal electrons; phase portraits; soliton; supersoliton
Corresponding author: Sandip Dalui, Department of Mathematics, Jadavpur University, Kolkata700032, India, E-mail:

Acknowledgements

The authors are grateful to both the reviewers for their constructive comments, without which this paper could not have been written in its present form. The authors are also grateful to Prof. Manoranjan Khan, Emeritus Professor, Department of Instrumentation Science & Centre for Plasma studies, Jadavpur University for his helpful suggestions.

  1. Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: None declared.

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

References

[1] W. C. Feldman, J. R. Asbridge, S. J. Bame, M. D. Montgomery, and S. P. Gary, “Solar wind electrons,” J. Geophys. Res., vol. 80, p. 4181, 1975. https://doi.org/10.1029/ja080i031p04181.Search in Google Scholar

[2] M. Temerin, K. Cerny, W. Lotko, and F. S. Mozer, “Observations of double layers and solitary waves in the auroral plasma,” Phys. Rev. Lett., vol. 48, p. 1175, 1982. https://doi.org/10.1103/physrevlett.48.1175.Search in Google Scholar

[3] W. D. Jones, A. Lee, S. M. Gleman, and H. J. Doucet, “Propagation of ion-acoustic waves in a two-electron-temperature plasma,” Phys. Rev. Lett., vol. 35, p. 1349, 1975. https://doi.org/10.1103/physrevlett.35.1349.Search in Google Scholar

[4] N. Hershkowitz, “Review of recent laboratory double layer experiments,” Space Sci. Rev., vol. 41, p. 351, 1985. https://doi.org/10.1007/bf00190655.Search in Google Scholar

[5] Y. Nishida and T. Nagasawa, “Excitation of ion-acoustic rarefactive solitons in a two-electron-temperature plasma,” Phys. Fluids, vol. 29, p. 345, 1986. https://doi.org/10.1063/1.865717.Search in Google Scholar

[6] G. Hairapetian and R. L. Stenzel, “Observation of a stationary, current-free double layer in a plasma,” Phys. Rev. Lett., vol. 65, p. 175, 1990. https://doi.org/10.1103/physrevlett.65.175.Search in Google Scholar

[7] R. E. Ergun, C. W. Carlson, J. P. McFadden, et al.., “FAST satellite observations of electric field structures in the auroral zone,” Geophys. Res. Lett., vol. 25, p. 2025, 1998. https://doi.org/10.1029/98gl00635.Search in Google Scholar

[8] R. E. Ergun, C. W. Carlson, J. P. McFadden, et al.., “FAST satellite wave observations in the AKR source region,” Geophys. Res. Lett., vol. 25, p. 2061, 1998. https://doi.org/10.1029/98gl00570.Search in Google Scholar

[9] G. T. Delory, R. E. Ergun, C. W. Carlson, et al.., “FAST observations of electron distributions within AKR source regions,” Geophys. Res. Lett., vol. 25, p. 2069, 1998. https://doi.org/10.1029/98gl00705.Search in Google Scholar

[10] R. Pottelette, R. E. Ergun, R. A. Treumann, et al.., “Modulated electron-acoustic waves in auroral density cavities: FAST observations,” Geophys. Res. Lett., vol. 26, p. 2629, 1999. https://doi.org/10.1029/1999gl900462.Search in Google Scholar

[11] J. P. McFadden, C. W. Carlson, R. E. Ergun, et al.., “FAST observations of ion solitary waves,” J. Geophys. Res., vol. 108, p. 8018, 2003. https://doi.org/10.1029/2002JA009485.Search in Google Scholar

[12] R. Boström, G. Gustafsson, B. Holback, G. Holmgren, H. Koskinen, and P. Kintner, “Characteristics of solitary waves and weak double layers in the magnetospheric plasma,” Phys. Rev. Lett., vol. 61, p. 82, 1988. https://doi.org/10.1103/physrevlett.61.82.Search in Google Scholar

[13] R. Boström, “Observations of weak double layers on auroral field lines,” IEEE Trans. Plasma Sci., vol. 20, p. 756, 1992. https://doi.org/10.1109/27.199524.Search in Google Scholar

[14] H. Matsumoto, H. Kojima, T. Miyatake, et al.., “Electrostatic solitary waves (ESW) in the magnetotail: BEN wave forms observed by GEOTAIL,” Geophys. Res. Lett., vol. 21, p. 2915, 1994. https://doi.org/10.1029/94gl01284.Search in Google Scholar

[15] J. R. Franz, P. M. Kintner, and J. S. Pickett, “POLAR observations of coherent electric field structures,” Geophys. Res. Lett., vol. 25, p. 1277, 1998. https://doi.org/10.1029/98gl50870.Search in Google Scholar

[16] C. A. Cattell, J. Dombeck, J. R. Wygant, et al.., “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., vol. 26, p. 425, 1999. https://doi.org/10.1029/1998gl900304.Search in Google Scholar

[17] P. O. Dovner, A. I. Eriksson, R. Boström, and B. Holback, “Freja multiprobe observations of electrostatic solitary structures,” Geophys. Res. Lett., vol. 21, p. 1827, 1994. https://doi.org/10.1029/94gl00886.Search in Google Scholar

[18] R. A. Cairns, A. A. Mamum, R. Bingham, et al.., “Electrostatic solitary structures in non-thermal plasmas,” Geophys. Res. Lett., vol. 22, p. 2709, 1995. https://doi.org/10.1029/95gl02781.Search in Google Scholar

[19] O. R. Rufai, R. Bharuthram, S. V. Singh, and G. S. Lakhina, “Ion acoustic solitons and supersolitons in a magnetized plasma with nonthermal hot electrons and Boltzmann cool electrons,” Phys. Plasmas, vol. 21, 2014, Art no. 082304. https://doi.org/10.1063/1.4891877.Search in Google Scholar

[20] S. V. Singh and G. S. Lakhina, “Ion-acoustic supersolitons in the presence of non-thermal electrons,” Commun. Nonlinear Sci. Numer. Simulat., vol. 23, p. 274, 2015. https://doi.org/10.1016/j.cnsns.2014.11.017.Search in Google Scholar

[21] O. Rufai, R. Bharuthram, S. V. Singh, and G. S. Lakhina, “Nonlinear low frequency electrostatic structures in a magnetized two-component auroral plasma,” Phys. Plasmas, vol. 23, 2016, Art no. 032309. https://doi.org/10.1063/1.4944669.Search in Google Scholar

[22] S. Dalui, A. Bandyopadhyay, and K. P. Das, “Modulational instability of ion acoustic waves in a multi-species collisionless unmagnetized plasma consisting of nonthermal and isothermal electrons,” Phys. Plasmas, vol. 24, 2017, Art no. 042305. https://doi.org/10.1063/1.4980837.Search in Google Scholar

[23] H. Kaur, T. S. Gill, and P. Bala, “Propagation characteristics of ion-acoustic double layer in multicomponent inhomogeneous auroral zone plasma,” Pramana, vol. 89, p. 28, 2017. https://doi.org/10.1007/s12043-017-1429-5.Search in Google Scholar

[24] S. Dalui, A. Bandyopadhyay, and K. P. Das, “Modulational instability of ion acoustic waves in a multi-species collisionless magnetized plasma consisting of nonthermal and isothermal electrons,” Phys. Plasmas, vol. 24, p. 102310, 2017. https://doi.org/10.1063/1.4991806.Search in Google Scholar

[25] S. Dalui and A. Bandyopadhyay, “Modulation instability of obliquely propagating ion acoustic waves in a collisionless magnetized plasma consisting of nonthermal and isothermal electrons,” Astrophys. Space Sci., vol. 364, p. 182, 2019. https://doi.org/10.1007/s10509-019-3672-3.Search in Google Scholar

[26] S. Dalui and A. Bandyopadhyay, “Effect of Landau damping on ion acoustic solitary waves in a collisionless unmagnetized plasma consisting of nonthermal and isothermal electrons,” Indian J. Phys., vol. 95, pp. 367–381, 2020. https://doi.org/10.1007/s12648-020-01731-5.Search in Google Scholar

[27] R. Z. Sagdeev and M. A. Leontovich, Reviews of Plasma Physics, vol. 4, New York, Consultants Bureau, 1966.Search in Google Scholar

[28] H. Washimi and T. Taniuti, “Propagation of ion-acoustic solitary waves of small amplitude,” Phys. Rev. Lett., vol. 17, p. 996, 1966. https://doi.org/10.1103/physrevlett.17.996.Search in Google Scholar

[29] M. Y. Yu, P. K. Shukla, and S. Bujarbarua, “Fully nonlinear ion-acoustic solitary waves in a magnetized plasma,” Phys. Fluids, vol. 23, p. 2146, 1980. https://doi.org/10.1063/1.862872.Search in Google Scholar

[30] K. Nishihara and M. Tajiri, “Rarefaction ion acoustic solitons in two-electron-temperature plasma,” J. Phys. Soc. Jpn., vol. 50, p. 4047, 1981. https://doi.org/10.1143/jpsj.50.4047.Search in Google Scholar

[31] R. Bharuthram and P. K. Shukla, “Large amplitude ion-acoustic double layers in a double Maxwellian electron plasma,” Phys. Fluids, vol. 29, p. 3214, 1986. https://doi.org/10.1063/1.865839.Search in Google Scholar

[32] S. Baboolal, R. Bharuthram, and M. A. Hellberg, “Arbitrary-amplitude rarefactive ion-acoustic double layers in warm multi-fluid plasmas,” J. Plasma Phys., vol. 40, p. 163, 1988. https://doi.org/10.1017/s0022377800013180.Search in Google Scholar

[33] S. Baboolal, R. Bharuthram, and M. A. Hellberg, “Arbitrary-amplitude theory of ion-acoustic solitons in warm multi-fluid plasmas,” J. Plasma Phys., vol. 41, p. 341, 1989. https://doi.org/10.1017/s002237780001391x.Search in Google Scholar

[34] S. Baboolal, R. Bharuthram, and M. A. Hellberg, “Cut-off conditions and existence domains for large-amplitude ion-acoustic solitons and double layers in fluid plasmas,” J. Plasma Phys., vol. 44, p. 1, 1990. https://doi.org/10.1017/S0022377800014975.Search in Google Scholar

[35] R. A. Cairns, A. A. Mamun, R. Bingham, and P. K. Shukla, “Ion-acoustic solitons in a magnetized plasma with nonthermal electrons,” Phys. Scripta, vol. T63, p. 80, 1996. https://doi.org/10.1088/0031-8949/1996/t63/012.Search in Google Scholar

[36] S. G. Tagare, “Ion-acoustic solitons and double layers in a two-electron temperature plasma with hot isothermal electrons and cold ions,” Phys. Plasmas, vol. 7, p. 883, 2000. https://doi.org/10.1063/1.873885.Search in Google Scholar

[37] S. V. Singh and G. S. Lakhina, “Electron acoustic solitary waves with non-thermal distribution of electrons,” Nonlinear Process. Geophys., vol. 11, p. 275, 2004. https://doi.org/10.5194/npg-11-275-2004.Search in Google Scholar

[38] C. R. Choi, C. M. Ryu, N. C. Lee, and D. Y. Lee, “Ion acoustic solitary waves in a dusty plasma obliquely propagating to an external magnetic field,” Phys. Plasmas, vol. 12, 2005, Art no. 022304. https://doi.org/10.1063/1.1843820.Search in Google Scholar

[39] A. E. Dubinov and D. Y. Kolotkov, “Ion-acoustic super solitary waves in dusty multispecies plasmas,” IEEE Trans. Plasma Sci., vol. 40, p. 1429, 2012. https://doi.org/10.1109/tps.2012.2189026.Search in Google Scholar

[40] A. E. Dubinov and D. Y. Kolotkov, “Interpretation of ion-acoustic solitons of unusual form in experiments in SF6-Ar plasma,” High Energy Chem., vol. 46, p. 349, 2012. https://doi.org/10.1134/s0018143912060033.Search in Google Scholar

[41] A. E. Dubinov and D. Y. Kolotkov, “Ion-acoustic supersolitons in plasma,” Plasma Phys. Rep., vol. 38, p. 909, 2012. https://doi.org/10.1134/s1063780x12100054.Search in Google Scholar

[42] Y. Nakamura and I. Tsukabayashi, “Modified Korteweg-de Vries ion-acoustic solitons in a plasma,” J. Plasma Phys., vol. 34, p. 401, 1985. https://doi.org/10.1017/s0022377800002968.Search in Google Scholar

[43] Y. Nakamura, J. L. Ferreira, and G. O. Ludwig, “Experiments on ion-acoustic rarefactive solitons in a multicomponent plasma with negative ions,” J. Plasma Phys., vol. 33, p. 237, 1985 https://doi.org/10.1017/S0022377800002476.Search in Google Scholar

[44] A. E. Dubinov and D. Y. Kolotkov, “Above the weak nonlinearity: super-nonlinear waves in astrophysical and laboratory plasmas,” Rev. Mod. Plasma Phys., vol. 2, p. 2, 2018. https://doi.org/10.1007/s41614-018-0014-9.Search in Google Scholar

[45] H. Ikezi, “Experiments on ion-acoustic solitary waves,” Phys. Fluids, vol. 16, p. 1668, 1973. https://doi.org/10.1063/1.1694194.Search in Google Scholar

[46] F. S. Mozer, R. Ergun, M. Temerin, C. Cattell, J. Dombeck, and J. Wygant, “New features of time domain electric-field structures in the auroral acceleration region,” Phys. Rev. Lett., vol. 79, p. 1281, 1997. https://doi.org/10.1103/physrevlett.79.1281.Search in Google Scholar

[47] R. E. Ergun, C. W. Carlson, J. P. McFadden, et al.., “Debye-scale plasma structures associated with magnetic-field-aligned electric fields,” Phys. Rev. Lett., vol. 81, p. 826, 1998. https://doi.org/10.1103/physrevlett.81.826.Search in Google Scholar

[48] G. Gustafsson, M. André, T. Carozzi, et al.., “First results of electric field and density observations by cluster EFW based on initial months of operation,” Ann. Geophys., vol. 19, p. 1219, 2001. https://doi.org/10.5194/angeo-19-1219-2001.Search in Google Scholar

[49] V. M. Nakariakov and E. Verwichte, “Coronal waves and oscillations,” Living Rev. Sol. Phys., vol. 2, p. 3, 2005. https://doi.org/10.12942/lrsp-2005-3.Search in Google Scholar

[50] J. R. Franz, P. M. Kintner, J. S. Pickett, and L. J. Chen, “Properties of small-amplitude electron phase-space holes observed by polar,” J. Geophys. Res. Space Phys., vol. 110, 2005. https://doi.org/10.1029/2005ja011095.Search in Google Scholar

[51] V. M. Nakariakov, A. R. Inglis, I. V. Zimovets, et al.., “Oscillatory processes in solar flares,” Plasma Phys. Contr. Fusion, vol. 52, 2010, Art no. 124009. https://doi.org/10.1088/0741-3335/52/12/124009.Search in Google Scholar

[52] V. M. Nakariakov, V. Pilipenko, B. Heilig, et al.., “Magnetohydrodynamic oscillations in the solar corona and Earth’s magnetosphere: towards consolidated understanding,” Space Sci. Rev., vol. 200, p. 75, 2016. https://doi.org/10.1007/s11214-015-0233-0.Search in Google Scholar

[53] D. J. Pascoe, C. R. Goddard, G. Nisticò, S. Anfinogentov, and V. M. Nakariakov, “Damping profile of standing kink oscillations observed by SDO/AIA,” Astron. Astrophys., vol. 585, p. L6, 2016. https://doi.org/10.1051/0004-6361/201527835.Search in Google Scholar

[54] M. A. Hellberg, T. K. Baluku, F. Verheest, and I. Kourakis, “Dust-acoustic supersolitons in a three-species dusty plasma with kappa distributions,” J. Plasma Phys., vol. 79, p. 1039, 2013. https://doi.org/10.1017/s0022377813001153.Search in Google Scholar

[55] S. K. Maharaj, R. Bharuthram, S. V. Singh, and G. S. Lakhina, “Existence domains of dust-acoustic solitons and supersolitons,” Phys. Plasmas, vol. 20, 2013, Art no. 083705. https://doi.org/10.1063/1.4818439.Search in Google Scholar

[56] F. Verheest, M. A. Hellberg, and I. Kourakis, “Dust-ion-acoustic supersolitons in dusty plasmas with nonthermal electrons,” Phys. Rev. E, vol. 87, 2013, Art no. 043107. https://doi.org/10.1103/physreve.87.043107.Search in Google Scholar

[57] F. Verheest, M. A. Hellberg, and I. Kourakis, “Ion-acoustic supersolitons in plasmas with two-temperature electrons: Boltzmann and kappa distributions,” Phys. Plasmas, vol. 20, 2013, Art no. 012302. https://doi.org/10.1063/1.4775085.Search in Google Scholar

[58] F. Verheest, M. A. Hellberg, and I. Kourakis, “Ion-acoustic supersolitons in plasmas with two-temperature electrons: Boltzmann and kappa distributions,” Phys. Plasmas, vol. 20, 2013, Art no. 082309. https://doi.org/10.1063/1.4818888.Search in Google Scholar

[59] C. P. Olivier, S. K. Maharaj, and R. Bharuthram, “Ion-acoustic solitons, double layers and supersolitons in a plasma with two ion-and two electron species,” Phys. Plasmas, vol. 22, 2015, Art no. 082312. https://doi.org/10.1063/1.4928884.Search in Google Scholar

[60] A. Paul, A. Bandyopadhyay, and K. P. Das, “Dust ion acoustic solitary structures in presence of nonthermally distributed electrons and positrons,” Phys. Plasmas, vol. 24, 2017, Art no. 013707. https://doi.org/10.1063/1.4975089.Search in Google Scholar

[61] D. Debnath, A. Bandyopadhyay, and K. P. Das, “Ion acoustic solitary structures in a magnetized nonthermal dusty plasma,” Phys. Plasmas, vol. 25, 2018, Art no. 033704. https://doi.org/10.1063/1.5021127.Search in Google Scholar

Received: 2020-10-17
Accepted: 2021-02-16
Published Online: 2021-03-08
Published in Print: 2021-05-26

© 2021 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. General
  3. Theoretical research of the medical U-type optical fiber sensor covered by the gold nanoparticles
  4. Machine learning studies for the effects of probes and cavity on quantum synchronization
  5. Atomic, Molecular & Chemical Physics
  6. Semiclassical study on photodetachment of hydrogen negative ion in a harmonic potential confined by a quantum well
  7. Dynamical Systems & Nonlinear Phenomena
  8. One-dimensional spherical shock waves in an interstellar dusty gas clouds
  9. Free vibrations of nanobeams under non-ideal supports based on modified couple stress theory
  10. On the evolution of acceleration discontinuities in van der Waals dusty magnetogasdynamics
  11. Head-on collision of two ion-acoustic solitons in pair-ion plasmas with nonthermal electrons featuring Tsallis distribution
  12. Arbitrary amplitude ion acoustic solitons, double layers and supersolitons in a collisionless magnetized plasma consisting of non-thermal and isothermal electrons
https://doi.org/10.1515/zna-2020-0296
Keywords for this article
ion acoustic solitary waves; non-thermal electrons; phase portraits; soliton; supersoliton

Articles in the same Issue

  1. Frontmatter
  2. General
  3. Theoretical research of the medical U-type optical fiber sensor covered by the gold nanoparticles
  4. Machine learning studies for the effects of probes and cavity on quantum synchronization
  5. Atomic, Molecular & Chemical Physics
  6. Semiclassical study on photodetachment of hydrogen negative ion in a harmonic potential confined by a quantum well
  7. Dynamical Systems & Nonlinear Phenomena
  8. One-dimensional spherical shock waves in an interstellar dusty gas clouds
  9. Free vibrations of nanobeams under non-ideal supports based on modified couple stress theory
  10. On the evolution of acceleration discontinuities in van der Waals dusty magnetogasdynamics
  11. Head-on collision of two ion-acoustic solitons in pair-ion plasmas with nonthermal electrons featuring Tsallis distribution
  12. Arbitrary amplitude ion acoustic solitons, double layers and supersolitons in a collisionless magnetized plasma consisting of non-thermal and isothermal electrons
Sign up now to receive a 20% welcome discount
Institutional Access
How does access work?
Have an idea on how to improve our website?
Please write us.
© 2025 De Gruyter Brill
Downloaded on 3.12.2025 from https://www.degruyterbrill.com/document/doi/10.1515/zna-2020-0296/html
Scroll to top button