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Nonlinear excitations and dynamic features of dust ion-acoustic waves in a magnetized electron–positron–ion plasma

Rabindranath Maity and Biswajit Sahu ORCID logo

Abstract

A wide class of nonlinear excitations and the dynamics of wave groups of finite amplitude ion-acoustic waves are investigated in multicomponent magnetized plasma system comprising warm ions, and superthermal electrons as well as positrons in presence of negatively charged impurities or dust particles. Employing the reductive perturbation technique (RPT), the Korteweg–de-Vries (KdV) equation, and extended KdV equation are derived. The presence of excess superthermal electrons as well as positrons and other plasma parameters are shown to influence the characteristics of both compressive and rarefactive solitons as well as double layers (DLs). Also, we extend our investigation by deriving the nonlinear Schrödinger equation from the extended KdV equation employing a suitable transformation to study the wave group dynamics for long waves. The analytical and numerical simulation results demonstrate that nonlinear wave predicts solitons, “table-top” solitons, DLs, bipolar structure, rogue waves, and breather structures. Moreover, implementing the concept of dynamical systems, phase portraits of nonlinear periodic, homoclinic trajectories, and supernonlinear periodic trajectories are presented through numerical simulation.


Corresponding author: Biswajit Sahu, Department of Mathematics, West Bengal State University, Barasat, Kolkata700126, India, E-mail:

Acknowledgments

The authors are grateful to anonymous reviewers for their valuable comments which lead to the improvement of the quality of the manuscript.

  1. Author contribution: 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. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation, San Francisco, Freeman, 1973, p. 763. Search in Google Scholar

[2] F. C. Michel, “Theory of pulsar magnetospheres,” Rev. Mod. Phys., vol. 54, p. 1, 1982. https://doi.org/10.1103/revmodphys.54.1. Search in Google Scholar

[3] M. J. Rees, “Very early universe,” in The Very Early Universe, G. W. Gibbons, S. W. Hawking, and S. Siklas, Eds., Cambridge, Cambridge University Press, 1983. Search in Google Scholar

[4] F. C. Miller and P. J. Wiita, Active Galactic Nuclei, Berlin, Springer, 1987, p. 202. Search in Google Scholar

[5] E. P. Liang, S. C. Wilks, and M. Tabak, “Pair production by ultraintense lasers,” Phys. Rev. Lett., vol. 81, p. 4887, 1998. https://doi.org/10.1103/physrevlett.81.4887. Search in Google Scholar

[6] X. Wang, P. Muggli, T. Katsouleas, et al.., “Optimization of positron trapping and acceleration in an electron-beam-driven plasma wakefield accelerator,” Phys. Rev. Accel. Beams, vol. 12, p. 051303, 2009. https://doi.org/10.1103/physrevstab.12.051303. Search in Google Scholar

[7] A. A. Gusev, U. B. Jayanthi, I. M. Martin, G. I. Pugacheva, and W. N. Spjeldvik, “Nuclear reactions in the uppermost Earth atmosphere as a source of the magnetospheric positron radiation belt,” J. Geophys. Res., vol. 106, p. 26111, 2001. https://doi.org/10.1029/1999ja000443. Search in Google Scholar

[8] P. Debu, “GBAR: Gravitational behavior of antihydrogen at rest,” Hyperfine Interact., vol. 212, p. 51, 2011. https://doi.org/10.1007/s10751-011-0379-4. Search in Google Scholar

[9] R. Bharuthram, “Arbitrary amplitude double layers in a multi-species electron-positron plasma,” Astrophys. Space Sci., vol. 189, p. 213, 1992. https://doi.org/10.1007/bf00643126. Search in Google Scholar

[10] M. Ferdousi, S. Sultana, and A. A. Mamun, “Oblique propagation of ion-acoustic solitary waves in a magnetized electron-positron-ion plasma,” Phys. Plasmas, vol. 22, p. 032117, 2015. https://doi.org/10.1063/1.4916038. Search in Google Scholar

[11] M. M. Haider, “Soliton and shock profiles in electron-positron-ion degenerate plasmas for both nonrelativistic and ultra-relativistic limits,” Z. Naturforsch., vol. 71, p. 1131, 2016. https://doi.org/10.1515/zna-2016-0280. Search in Google Scholar

[12] N. S. Saini and K. Singh, “Head-on collision of two dust ion acoustic solitary waves in a weakly relativistic multicomponent superthermal plasma,” Phys. Plasmas, vol. 23, p. 103701, 2016. https://doi.org/10.1063/1.4963774. Search in Google Scholar

[13] I. B. Zel’dovich and I. D. Novikov, “Relativistic Astrophysics, 2,” in The Structure and Evolution of the Universe, vol. 2, Chicago, University of Chicago Press, 1971. Search in Google Scholar

[14] T. Tajima and K. Shibata, Plasma Astrophysics, New York, Addison-Wesley, 1997. Search in Google Scholar

[15] P. K. Shukla and M. Marklund, “Dust acoustic wave in a strongly magnetized pair-dust plasma,” Phys. Scripta, vol. T113, p. 36, 2004. https://doi.org/10.1238/physica.topical.113a00036. Search in Google Scholar

[16] W. H. Zurek, “Annihilation radiation from the galactic center - positrons in dust?” APJ (Acta Pathol. Jpn.), vol. 289, p. 603, 1985. https://doi.org/10.1086/162921. Search in Google Scholar

[17] J. C. Higdon, R. E. Lingenfelter, and R. E. Rothschild, “The galactic positron annihilation radiation and the propagation of positrons in the interstellar medium,” APJ (Acta Pathol. Jpn.), vol. 698, p. 350, 2009. https://doi.org/10.1088/0004-637x/698/1/350. Search in Google Scholar

[18] A. Evans, The Dusty Universe, New York, John Wiley & Sons, 1994. Search in Google Scholar

[19] J. Miller and D. A. Williams, Dust and Chemistry in Astronomy, Bristol, Institute of Physics, 1993. Search in Google Scholar

[20] M. Horányi, T. W. Hartquist, O. Havnes, D. A. Mendis, and G. E. Morfill, “Dusty plasma effects in Saturn’s magnetosphere,” Rev. Geophys., vol. 42, no. 4, p. RG4002, 2004. Search in Google Scholar

[21] R. L. Merlino, “Dusty plasmas and applications in space and industry,” Plasma Phys. Appl., vol. 81, p. 73, 2006. Search in Google Scholar

[22] F. Verheest, Waves in Dusty Space Plasmas, Dordrecht, Kluwer Academic, 2000. Search in Google Scholar

[23] S. Ghosh and R. Bharuthram, “Ion acoustic solitons and double layers in electron-positron-ion plasmas with dust particulates,” Astrophys. Space Sci., vol. 314, p. 121, 2008. https://doi.org/10.1007/s10509-008-9748-0. Search in Google Scholar

[24] S. A. El-Tantawy, N. A. El-Bedwehy, and W. M. Moslem, “Nonlinear ion-acoustic structures in dusty plasma with superthermal electrons and positrons,” Phys. Plasmas, vol. 18, p. 052113, 2011. https://doi.org/10.1063/1.3592255. Search in Google Scholar

[25] A. Paul and A. Bandyopadhyay, “Dust ion acoustic solitary structures in presence of nonthermal electrons and isothermal positrons,” Astrophys. Space Sci., vol. 361, p. 172, 2016. https://doi.org/10.1007/s10509-016-2758-4. Search in Google Scholar

[26] V. M. Vasyliunas, “A survey of low-energy electrons in the evening sector of the magnetosphere with OGO 1 and OGO 3,” J. Geophys. Res., vol. 73, p. 2839, 1968. https://doi.org/10.1029/ja073i009p02839. Search in Google Scholar

[27] S. P. Christon, D. G. Mitchell, D. J. Williams, L. A. Frank, C. Y. Huang, and T. E. Eastman, “Energy spectra of plasma sheet ions and electrons from ∼50 eV/e to ∼1 MeV during plasma temperature transitions,” J. Geophys. Res., vol. 93, p. 2562, 1988. https://doi.org/10.1029/ja093ia04p02562. Search in Google Scholar

[28] M. Maksimovic, V. Pierrard, and P. Riley, “Ulysses electron distributions fitted with Kappa functions,” Geophys. Res. Lett., vol. 24, p. 1151, 1997. https://doi.org/10.1029/97gl00992. Search in Google Scholar

[29] T. S. Gill, C. Bedi, and A. S. Bains, “Envelope excitations of ion acoustic solitary waves in a plasma with superthermal electrons and positrons,” Phys. Scripta, vol. 81, p. 055503, 2010. https://doi.org/10.1088/0031-8949/81/05/055503. Search in Google Scholar

[30] P. Chatterjee, R. Ali, and A. Saha, “Analytical solitary wave solution of the dust ion acoustic waves for the damped forced Korteweg-de Vries equation in superthermal plasmas,” Z. Naturforsch., vol. 73, p. 151, 2018. https://doi.org/10.1515/zna-2017-0358. Search in Google Scholar

[31] M. Mehdipoor, “Dissipative ion-acoustic waves in collisional electron-positron-ion plasmas with Kappa distribution,” Contrib. Plasma Phys., vol. 59, p. e201900006, 2019. https://doi.org/10.1002/ctpp.201900006. Search in Google Scholar

[32] R. Ali and P. Chatterjee, “Three-soliton interaction and soliton turbulence in superthermal dusty plasmas,” Z. Naturforsch., vol. 74, p. 757, 2019. https://doi.org/10.1515/zna-2018-0452. Search in Google Scholar

[33] M. Berthomier, R. Pottelette, and M. Malingre, “Solitary waves and weak double layers in a two-electron temperature auroral plasma,” J. Geophys. Res., vol. 103, no. A3, p. 4261, 1998. https://doi.org/10.1029/97ja00338. Search in Google Scholar

[34] C. Cattell, J. Crumley, J. Dombeck, et al.., “Polar observations of solitary waves at high and low altitudes and comparison to theory,” Adv. Space Res., vol. 28, p. 1631, 2001. https://doi.org/10.1016/s0273-1177(01)00478-1. Search in Google Scholar

[35] J. D. Williams, L.-J. Chen, W. S. Kurth, D. A. Gurnett, and M. K. Dougherty, “Electrostatic solitary structures observed at Saturn,” Geophys. Res. Lett., vol. 33, p. L06103, 2006. https://doi.org/10.1029/2005gl024532. Search in Google Scholar

[36] C. Norgren, M. André, A. Vaivads, and Y. V. Khotyaintsev, “Slow electron phase space holes: magnetotail observations,” Geophys. Res. Lett., vol. 42, p. 1654, 2015. https://doi.org/10.1002/2015gl063218. Search in Google Scholar

[37] A. Kakad, B. Kakad, C. Anekallu, G. Lakhina, Y. Omura, and A. Fazakerley, “Slow electrostatic solitary waves in Earth’s plasma sheet boundary layer,” J. Geophys. Res.: Space Phys., vol. 121, p. 4452, 2016. https://doi.org/10.1002/2016ja022365. Search in Google Scholar

[38] H. Alfvén, “On the theory of magnetic storms and aurorae,” Tellus, vol. 10, p. 104, 1958. https://doi.org/10.3402/tellusa.v10i1.9213. Search in Google Scholar

[39] R. E. Ergun, L. Andersson, D. Main, et al.., “Parallel electric fields in the upward current region of the aurora: numerical solutions,” Phys. Plasmas, vol. 9, p. 3695, 2002. https://doi.org/10.1063/1.1499121. Search in Google Scholar

[40] M. K. Mishra, R. S. Tiwari, and S. K. Jain, “Small amplitude ion-acoustic double layers in multicomponent plasma with positrons,” Phys. Rev. E, vol. 76, p. 03640, 2007. https://doi.org/10.1103/physreve.76.036401. Search in Google Scholar

[41] N. Boubakour, M. Tribeche, and K. Aoutou, “Ion acoustic solitary waves in a plasma with superthermal electrons and positrons,” Phys. Scripta, vol. 79, p. 065503, 2009. https://doi.org/10.1088/0031-8949/79/06/065503. Search in Google Scholar

[42] S. Ali Shan and N. Imtiaz, “Double layers and solitary structures in electron-positron-ion plasma with Kappa distributed trapped electrons,” Phys. Plasmas, vol. 24, p. 102109, 2017. https://doi.org/10.1063/1.4986990. Search in Google Scholar

[43] R. Grimshaw, D. Pelinovsky, E. Pelinovsky, and A. Slunyaev, “Generation of large-amplitude solitons in the extended Korteweg-de Vries equation,” Chaos, vol. 12, p. 1070, 2002. https://doi.org/10.1063/1.1521391. Search in Google Scholar

[44] R. Grimshaw, A. Slunyaev, and E. Pelinovsky, “Generation of solitons and breathers in the extended Korteweg-de Vries equation with positive cubic nonlinearity,” Chaos, vol. 20, p. 013102, 2010. https://doi.org/10.1063/1.3279480. Search in Google Scholar

[45] M. S. Ruderman, T. Talipova, and E. Pelinovsky, “Dynamics of modulationally unstable ion-acoustic wavepackets in plasmas with negative ions,” J. Plasma Phys., vol. 74, p. 639, 2008. https://doi.org/10.1017/s0022377808007150. Search in Google Scholar

[46] S. Ghosh, “Nonlinear ion acoustic wave and group dynamics near critical density in a plasma with negative ion,” J. Phys. Soc. Jpn., vol. 88, p. 074501, 2019. https://doi.org/10.7566/jpsj.88.074501. Search in Google Scholar

[47] W. M. Moslem, R. Sabry, S. K. El-Labany, and P. K. Shukla, “Dust-acoustic rogue waves in a nonextensive plasma,” Phys. Rev. E, vol. 84, p. 066402, 2011. https://doi.org/10.1103/physreve.84.066402. Search in Google Scholar

[48] H. Bailung, S. K. Sharma, and Y. Nakamura, “Observation of peregrine solitons in a multicomponent plasma with negative ions,” Phys. Rev. Lett., vol. 107, p. 255005, 2011. https://doi.org/10.1103/physrevlett.107.255005. Search in Google Scholar

[49] S. A. El-Tantawy, N. A. El-Bedwehy, and S. K. El-Labany, “Ion-acoustic super rogue waves in ultracold neutral plasmas with nonthermal electrons,” Phys. Plasmas, vol. 20, p. 072102, 2013. https://doi.org/10.1063/1.4812630. Search in Google Scholar

[50] T. K. Baluku, M. A. Hellberg, and F. Verheest, “New light on ion acoustic solitary waves in a plasma with two-temperature electrons,” EPL, vol. 91, p. 15001, 2010. https://doi.org/10.1209/0295-5075/91/15001. Search in Google Scholar

[51] 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

[52] A. E. Dubinov, D. Y. Kolotkov, and M. A. Sazonkin, “Supernonlinear waves in plasma,” Plasma Phys. Rep., vol. 38, p. 833, 2012. https://doi.org/10.1134/s1063780x12090036. Search in Google Scholar

[53] D. P. Chapagai, J. Tamang, and A. Saha, “Bifurcation analysis for small-amplitude nonlinear and supernonlinear ion-acoustic waves in a superthermal plasma,” Z. Naturforsch., vol. 75, p. 183, 2020. https://doi.org/10.1515/zna-2019-0210. Search in Google Scholar

[54] 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

[55] S. Sultana, I. Kourakis, N. S. Saini, and M. A. Hellberg, “Oblique electrostatic excitations in a magnetized plasma in the presence of excess superthermal electrons,” Phys. Plasmas, vol. 17, p. 032310, 2010. https://doi.org/10.1063/1.3322895. Search in Google Scholar

[56] H. Alinejad, “Effect of nonthermal electrons on oblique electrostatic excitations in a magnetized electron-positron-ion plasma,” Phys. Plasmas, vol. 19, p. 052302, 2012. https://doi.org/10.1063/1.4714609. Search in Google Scholar

[57] M. Sharifi and A. Parvazian, “Electrostatic waves in a magnetized plasma with nonextensive distribution,” Phys. Stat. Mech. Appl., vol. 393, p. 489, 2014. https://doi.org/10.1016/j.physa.2013.09.024. Search in Google Scholar

[58] M. Sarker, M. R. Hossen, M. G. Shah, B. Hosen, and A. A. Mamun, “Oblique propagation of electrostatic waves in a magnetized electron-positron-ion plasma in the presence of heavy particles,” Z. Naturforsch., vol. 73, p. 501, 2018. https://doi.org/10.1515/zna-2017-0419. Search in Google Scholar

[59] R. Z. Sagdeev, in Reviews of Plasma Physics, M. A. Leontovich, Ed., New York, Consultants Bureau, 1966, p. 23. Search in Google Scholar

[60] M. Saito, S. Watanabe, and H. Tanaca, “Modulational instability of ion wave in plasma with negative ion,” J. Phys. Soc. Jpn., vol. 53, p. 2304, 1984. https://doi.org/10.1143/jpsj.53.2304. Search in Google Scholar

[61] R. Grimshaw, D. Pelinovsky, E. Pelinovsky, and T. Talipova, “Wave group dynamics in weakly nonlinear long-wave models,” Phys. Nonlinear Phenom., vol. 159, p. 35, 2001. https://doi.org/10.1016/s0167-2789(01)00333-5. Search in Google Scholar

[62] T. Taniuti and N. Yajima, “Perturbation method for a nonlinear wave modulation. I,” J. Math. Phys., vol. 10, p. 1369, 1969. https://doi.org/10.1063/1.1664975. Search in Google Scholar

[63] W.-P. Zhong, M. R. Belic, and T. Huang, “Rogue wave solutions to the generalized nonlinear Schrödinger equation with variable coefficients,” Phys. Rev. E, vol. 87, p. 065201, 2013. https://doi.org/10.1103/physreve.87.065201. Search in Google Scholar

[64] D. H. Peregrine, “Water waves, nonlinear Schrödinger equations and their solutions,” J. Aust. Math. Soc. Series B, Appl. Math., vol. 25, p. 16, 1983. https://doi.org/10.1017/s0334270000003891. Search in Google Scholar

[65] N. Akhmediev, A. Ankiewicz, and M. Taki, “Waves that appear from nowhere and disappear without a trace,” Phys. Lett., vol. 373, p. 675, 2009. https://doi.org/10.1016/j.physleta.2008.12.036. Search in Google Scholar

Received: 2021-06-14
Accepted: 2021-08-26
Published Online: 2021-09-14

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