Home Role of entropy in ηi-mode driven nonlinear structures obtained by homotopy perturbation method in electron–positron–ion plasma
Article
Licensed
Unlicensed Requires Authentication

Role of entropy in ηi-mode driven nonlinear structures obtained by homotopy perturbation method in electron–positron–ion plasma

  • Aziz Khan , U. Zakir EMAIL logo , Qamar ul Haque and Anisa Qamar
Published/Copyright: June 9, 2021
Zeitschrift für Naturforschung A
From the journal Zeitschrift für Naturforschung A Volume 76 Issue 8

Abstract

We present an analysis of the effect of entropy on ion temperature gradient ηi-mode driven solitary and shock waves in electron–positron–ion plasma having density and temperature inhomogeneities. Linear and nonlinear analysis having solutions in form of solitons and shocks shows that entropy influence changes the drift mode instability. Different limiting cases when (i) temperature fluctuations due to E × B only (ηi ≫ 2/3), (ii) in the absence of entropy and (iii) neglecting positron effect (β = 1) are discussed. The homotophy perturbation method (HPM) is applied on the derived Korteweg–de-Vries (KdV) and KdV–Burger equations under small time approximation. It is found that both results, those obtained analytically and by the HPM technique, strongly agree with each other. These investigations may be useful to study low frequency electrostatic modes in magnetized electron–positron–ion plasma. For illustration, the model has been applied to the nonlinear electrostatic excitations in interstellar medium and tokamak plasma.

Keywords: drift waves; electron–positron–ion plasma; entropy; homotopy perturbation method; nonlinear structures
Corresponding author: U. Zakir, Department of Physics, University of Malakand, 18800, Dir(L), Khyber Pakhtunkhwa, Pakistan, E-mail:

  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] F. Verheest, M. A. Hellberg, G. J. Gray, and R. L. Mace, “Electrostatic solitons in multispecies electron-positron plasmas,” Astrophys. Space Sci., vol. 239, p. 125, 1996. https://doi.org/10.1007/bf00653773.Search in Google Scholar

[2] A. Mushtaq and H. A. Shah, “Nonlinear Zakharov–Kuznetsov equation for obliquely propagating two-dimensional ion-acoustic solitary waves in a relativistic, rotating magnetized electron-positron-ion plasma,” Phys. Plasma., vol. 12, p. 072306, 2005. https://doi.org/10.1063/1.1946729.Search in Google Scholar

[3] I. Kourakis, F. Verheest, and N. F. Cramer, “Nonlinear perpendicular propagation of ordinary mode electromagnetic wave packets in pair plasmas and electron-positron-ion plasmas,” Phys. Plasma., vol. 14, p. 02230, 2007. https://doi.org/10.1063/1.2446373.Search in Google Scholar

[4] S. I. Popel, S. V. Vladimirov, and P. K. Shukla, “Ion-acoustic solitons in electron–positron–ion plasmas,” Phys. Plasmas, vol. 2, p. 716, 1995. https://doi.org/10.1063/1.871422.Search in Google Scholar

[5] F. B. Rizzato, “Weak nonlinear electromagnetic waves and low-frequency magnetic-field generation in electron-positron-ion plasmas,” J. Plasma Phys., vol. 40, p. 289, 1988. https://doi.org/10.1017/s0022377800013283.Search in Google Scholar

[6] V. I. Berezihiani, L. N. Tsintsadze, and P. K. Shukla, “ion-acoustic structures in dusty plasma,” J. Plasma Phys., vol. 48, p. 139, 1992.10.1017/S0022377800016421Search in Google Scholar

[7] V. I. Berezihiani and S. M. Mahajan, “ion-acoustic structures in dusty plasma with superthermal electrons and positrons,” Phys. Rev. Lett., vol. 73, p. 1110, 1994.Search in Google Scholar

[8] N. A. EL-Bedwehy and W. M. Moslem, “Nonlinear ion-acoustic structures in dusty plasma with superthermal electrons and positrons,” Astrophys. Space Sci., vol. 335, pp. 435–442, 2011. https://doi.org/10.1007/s10509-011-0742-6.Search in Google Scholar

[9] M. C. Begelman, R. D. Blandford, and M. J. Rees, “Theory of extragalactic radio sources,” Rev. Mod. Phys., vol. 56, p. 255, 1984. https://doi.org/10.1103/revmodphys.56.255.Search in Google Scholar

[10] 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

[11] M. L. Burns, A. K. Harding, and R. Ramaty, Positron-Electron Pairs in Astrophysics, vol. 6, New York, AIP, 1983, p. 2289.Search in Google Scholar

[12] W. Minser, K. S. Throne, and J. A. Wheeler, Gravitation, San Francisco, Freeman, 1973.Search in Google Scholar

[13] C. Gahn, “Generating positrons with femtosecond-laser pulses,” Appl. Phys. Lett., vol. 77, p. 2662, 2000. https://doi.org/10.1063/1.1319526.Search in Google Scholar

[14] N. B. Narozhny, “Pair production by a focused laser pulse in vacuum,” JETP Lett., vol. 80, p. 382, 2004. https://doi.org/10.1134/1.1830652.Search in Google Scholar

[15] S. Miglinolo, “A comparative study of transport in stellarators and tokamaks,” Nucl. Fusion, vol. 32, p. 8, 1992.10.1088/0029-5515/32/1/414Search in Google Scholar

[16] R. Hirota, The Direct Method in Soliton Theory, Cambridge, Cambridge University Press, 2004.10.1017/CBO9780511543043Search in Google Scholar

[17] A. M. Wazwaz, Partial Differential Equations of Solitary Waves Theory, Beijing, Higher Education Press, 2009.10.1007/978-3-642-00251-9Search in Google Scholar

[18] P. K. Shukla and A. A. Mamun, “Solitons, shocks and vortices in dusty plasmas,” New J. Phys., vol. 5, p. 17, 2003. https://doi.org/10.1088/1367-2630/5/1/317.Search in Google Scholar

[19] W. Rudolf, W. Baumjohann, and A. Treumann, Basic Space Plasma Physics, vol. 4, London, ICP, 1997, p. 176.10.1142/p015Search in Google Scholar

[20] M. Hoshino, J. Arons, Y. Gallant, and A. B. Langdon, “Relativistic magnetosonic shock waves in synchrotron sources: shock structure and nonthermal acceleration of positrons,” Astrophys. J., vol. 390, p. 454, 1992. https://doi.org/10.1086/171296.Search in Google Scholar

[21] H. R. Pakzad, “Ion acoustic solitary waves in plasma with nonthermal electron and positron,” Phys. Lett., vol. 373, pp. 847–850, 2009. https://doi.org/10.1016/j.physleta.2008.12.066.Search in Google Scholar

[22] N. Jehan, M. Slahuddin, and A. M. Mirza, “Oblique modulation of ion-acoustic waves and envelope solitons in electron-positron-ion plasma,” Phys. Plasmas, vol. 16, p. 062305, 2009. https://doi.org/10.1063/1.3142473.Search in Google Scholar

[23] A. Esfandyari-Kalejahi, I. Kourakis, M. Mehdipoor, and P. K. Shukla, “Electrostatic mode envelope excitations in e-p-i plasmas - application in warm pair ion plasmas with a small fraction of stationary ions,” J. Phys. Gen. Phys., vol. 39, p. 052117, 2006. https://doi.org/10.1088/0305-4470/39/44/014.Search in Google Scholar

[24] M. G. Shah, M. R. Hossen, and A. A. Mamun, “Nonlinear propagation of positron-acoustic waves in a four component space plasma,” J. Plasma Phys., vol. 81, p. 0905810517, 2015. https://doi.org/10.1017/s0022377815001014.Search in Google Scholar

[25] M. A. Hossen, M. G. Shah, M. R. Hossen, and A. A. Mamun, “Instability analysis of positron-acoustic waves in a magnetized multi-species plasma,” Commun. Theor. Phys., vol. 67, p. 458, 2017. https://doi.org/10.1088/0253-6102/67/4/458.Search in Google Scholar

[26] W. Horton, “Drift waves and transport,” Rev. Mod. Phys., vol. 71, p. 735, 1999. https://doi.org/10.1103/revmodphys.71.735.Search in Google Scholar

[27] J. Weiland, “Current topics,” Phys. Fluids, vol. 1, p. 439, 1994.Search in Google Scholar

[28] V. Pavlenko and J. Weiland, “Transport due to ion temperature gradient mode vortex turbulence”,” Phys. Scripta, vol. 47, no. 1, pp. 96–98, 1993. https://doi.org/10.1088/0031-8949/47/1/017.Search in Google Scholar

[29] Y. Q. Zhang, A. W. DeSilva, and A. N. Mostovych, “Density fluctuation spectra of a collision-dominated plasma measured by light scattering,” Phys. Rev. Lett., vol. 62, p. 1848, 1989. https://doi.org/10.1103/physrevlett.62.1848.Search in Google Scholar

[30] A. I. Dyachenko, S. V. Nazarenko, and V. E. Zakharov, “Wave-vortex dynamics in drift and β-plane turbulence,” Phys. Lett., vol. 165, p. 330, 1992. https://doi.org/10.1016/0375-9601(92)90503-e.Search in Google Scholar

[31] H. Eubank, R. J. Goldston, V. Arunasalam, et al.., Proceedings of the 7th International Conference on Plasma Physics and Controlled Nuclear Fusion Research, Innsbruck, Austria, vol. 1, Vienna, Austria, International Atomic Energy Agency, 1979, p. 167.Search in Google Scholar

[32] A. Jerman, D. Anderson, and J. Weiland, “Chemiluminescent determination of adenosine, inosine, and hypoxanthine/xanthine,” Nucl. Fusion. vol. 27, p. 6, 1987.Search in Google Scholar

[33] J. Weiland, Collective Modes in Inhomogenous Media, Kinetic and Advance Fluid Theory, Bristol, IOP, 2000.Search in Google Scholar

[34] L. I. Rudakov and R. Z. Sagdeev, “The stability of a spatially inhomogeneous plasma in a magnetic field,” Sov. Phys. Dokl., vol. 6, p. 415, 1963.Search in Google Scholar

[35] B. Coppi, M. N. Rosenbluth, and R. Z. Sagdeev, “Instabilities due to temperature gradients in complex magnetic field configurations,” Phys. Fluids, vol. 10, p. 582, 1967. https://doi.org/10.1063/1.1762151.Search in Google Scholar

[36] P. K. Shukla and J. Weiland, “Tripolar vortices and vortex chains in dusty plasma,” Phys. Lett. A, vol. 136, p. 59, 1999.10.1016/0375-9601(89)90677-4Search in Google Scholar

[37] P. K. Shukla and L. Stenflo, “Zonal flow excitation in plasmas by electron-temperature-gradient modes,” J. Plasma Phys., vol. 70, pp. 41–46, 2004. https://doi.org/10.1017/s0022377803002484.Search in Google Scholar

[38] G. M. Staebler and R. R. Dominguez, “Electric field effects on ion temperature gradient modes in a sheared slab,” Nucl. Fusion, vol. 31, p. 10, 1991. https://doi.org/10.1088/0029-5515/31/10/007.Search in Google Scholar

[39] N. Batool, W. Masood, and A. M. Mirza, “The effects of nonthermal electron distributions on ion-temperature-gradient driven drift-wave instabilities in electron-ion plasma,” Phys. Plasma., vol. 19, p. 082111, 2012. https://doi.org/10.1063/1.4742990.Search in Google Scholar

[40] D. D. Ganji and M. Rafei, “Solitary wave solutions for a generalized Hirota-Satsuma coupled KdV equation by homotopy perturbation method,” Phys. Lett., vol. 356, pp. 131–137, 2006. https://doi.org/10.1016/j.physleta.2006.03.039.Search in Google Scholar

[41] J. H. He, “On the exact solution of Newell-Whitehead-Segel equation using the homotopy perturbation method,” Comput. Methods Appl. Mech. Eng., vol. 178, p. 257, 1999. https://doi.org/10.1016/s0045-7825(99)00018-3.Search in Google Scholar

[42] J. H. He, “Variational approach to the Lane-Emden equation,” Appl. Math. Comput., vol. 135, p. 73, 2003.10.1016/S0096-3003(02)00382-XSearch in Google Scholar

[43] T. Ozis and A. Yildirim, “Solution of a partial differential equation subject to temperature overspecification by He’s homotopy perturbation method,” Int. J. Nonlinear Sci. Numer. Stimul., vol. 8, p. 243, 2007.Search in Google Scholar

[44] M. M. Mousa and S. F. Ragab, “Application of the homotopy perturbation method to linear and nonlinear Schrödinger equations,” Z. Naturforsch., A: Phys. Sci., vol. 63, p. 140, 2008.10.1515/zna-2008-3-404Search in Google Scholar

[45] M. M. Mousa and A. Kaltayev, “Homotopy perturbation Padé technique for constructing approximate and exact solutions of Boussinesq equations,” Appl. Math. Sci., vol. 3, p. 1061, 2009.Search in Google Scholar

[46] M. Dehghan and F. Shakeri, “Solution of a partial differential equation subject to temperature overspecification by He’s homotopy perturbation method,” Phys. Scripta, vol. 75, p. 778, 2007. https://doi.org/10.1088/0031-8949/75/6/007.Search in Google Scholar

[47] M. Dehghan and F. Shakeri, “Approximate solution of a differential equation arising in astrophysics using the variational iteration method,” Prog. Electromagn. Res., vol. 78, p. 361, 2008. https://doi.org/10.2528/pier07090403.Search in Google Scholar

[48] M. Dehghan and F. Shakeri, “Solution of delay differential equations via a homotopy perturbation method,” J. Porous Media, vol. 11, p. 765, 2008. https://doi.org/10.1615/jpormedia.v11.i8.50.Search in Google Scholar

[49] M. Dehghan and F. Shakeri, “The numerical solution of the second Painlevé equation,” Numer. Methods Part. Differ. Equ., vol. 25, p. 1238, 2009. https://doi.org/10.1002/num.20416.Search in Google Scholar

[50] M. Dehghan and J. Manafian, “Homotopy perturbation method for one-dimensional hyperbolic equation with integral conditions,” Z. Naturforsch., A: Phys. Sci., vol. 64, p. 411, 2009.Search in Google Scholar

[51] U. Zakir, M. Adnan, Q. Haque, Q. Anisa, and A. M. Mirza, “Ion temperature gradient mode driven solitary and shock waves,” Phys. Plasmas, vol. 23, p. 042104, 2016. https://doi.org/10.1063/1.4945632.Search in Google Scholar

[52] K. Aziz, U. Zakir, and Q. Haque, “Ion temperature gradient mode driven solitary and shock waves in electron-positron-ion magnetized plasma,” Braz. J. Phys., vol. 50, p. 430, 2020.10.1007/s13538-020-00752-zSearch in Google Scholar

Received: 2021-02-08
Revised: 2021-05-10
Accepted: 2021-05-17
Published Online: 2021-06-09
Published in Print: 2021-08-26

© 2021 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. General
  3. Temperature-insensitive intensity-modulation liquid refractive index sensor based on fiber-optic Michelson probe structure
  4. Dynamical Systems & Nonlinear Phenomena
  5. Impact of non-thermal electrons on spatial damping: a kinetic model for the parallel propagating modes
  6. Role of entropy in ηi-mode driven nonlinear structures obtained by homotopy perturbation method in electron–positron–ion plasma
  7. Study of ferrofluid flow and heat transfer between cone and disk
  8. Solid State Physics & Materials Science
  9. Structural, electronic, magnetic and mechanical properties of the full-Heusler compounds Ni2Mn(Ge,Sn) and Mn2NiGe
  10. Exothermic behaviour of aluminium and graphene as a fuel in Fe2O3 based nanothermite
  11. Surface levels of organic conductors in a tilted in-plane magnetic field
  12. Thermodynamics & Statistical Physics
  13. Adiabatic compressibility of biphasic salt melts
  14. Stochastic thermodynamics of a finite quantum system coupled to a heat bath
https://doi.org/10.1515/zna-2021-0031
Keywords for this article
drift waves; electron–positron–ion plasma; entropy; homotopy perturbation method; nonlinear structures

Articles in the same Issue

  1. Frontmatter
  2. General
  3. Temperature-insensitive intensity-modulation liquid refractive index sensor based on fiber-optic Michelson probe structure
  4. Dynamical Systems & Nonlinear Phenomena
  5. Impact of non-thermal electrons on spatial damping: a kinetic model for the parallel propagating modes
  6. Role of entropy in ηi-mode driven nonlinear structures obtained by homotopy perturbation method in electron–positron–ion plasma
  7. Study of ferrofluid flow and heat transfer between cone and disk
  8. Solid State Physics & Materials Science
  9. Structural, electronic, magnetic and mechanical properties of the full-Heusler compounds Ni2Mn(Ge,Sn) and Mn2NiGe
  10. Exothermic behaviour of aluminium and graphene as a fuel in Fe2O3 based nanothermite
  11. Surface levels of organic conductors in a tilted in-plane magnetic field
  12. Thermodynamics & Statistical Physics
  13. Adiabatic compressibility of biphasic salt melts
  14. Stochastic thermodynamics of a finite quantum system coupled to a heat bath
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-2021-0031/html
Scroll to top button