Journal of Nuclear Science, Engineering and Technology (JONSAT)
In cooperation with the Iranian Nuclear Society

Effect of energetic electrons on transcritical bifurcation of low-frequency electrostatic waves in plasma

Document Type : Research Paper

Author

H. Alinejad

Department of Physics, Faculty of Basic Science, Babol Noshirvani University of Technology, P.O.Box: 484, Babol - Iran

https://doi.org/10.24200/nst.2022.1472
Abstract
This paper studies the bifurcation types and phase portrait properties of ion-acoustic traveling waves in a plasma comprising warm adiabatic ions and energetic electrons with a nonthermal distribution function. A dynamical system is first derived for the evolution of the low-frequency wave, and then the bifurcation response is determined on the fixed points-energetic electron concentration plane. Our numerical results show that the motion dynamics of traveling waves undergo a transcritical bifurcation for a given value of energetic electrons. Both solitary and nonlinear periodic waves coalesce and switch their stability at the critical electron density value. Moreover, for higher values of the fast electrons density, a saddle-node bifurcation occurs, which leads to the propagation of periodic waves in plasma. The existence domain of bifurcation and transition between nonlinear modes are also determined for different values of ion temperature and energetic electrons density.

Highlights

  1. L. Stenflo, Generalized Lorenz equations for acoustic-gravity waves in the atmosphere, Phys. Scr., 53(1), 83-84 (1996).

 

  1. H. Ikezi, R. Taylor, D. Baker, Formation and Interaction of Ion-Acoustic Solitions, Phys. Rev. Lett., 25(1), 11-14 (1970).

 

  1. H. Washimi, T. Taniuti, Propagation of Ion-Acoustic Solitary Waves of Small Amplitude, Phys. Rev. Lett., 17(19), 996-998 (1966).

 

  1. R.Z. Sagdeev, Reviews of Plasma Physics, Edited by M.A. Leontovich (Consultants Bureau, New York, 1966).

 

  1. R.A. Cairns, et al, Electrostatic solitary structures in non-thermal plasmas Geophys, Res. Lett., 22(20), 2709-2712 (1995).

 

  1. G. Hairapetian, R.L. Stenzel, Expansion of a Two-Electron-Population Plasma into Vacuum, Phys. Rev. Lett., 61(14), 1607-1610 (1988).

 

  1. R. Lundin, et al, Plasma energization on auroral field lines as observed by the Viking spacecraft, Geophys. Res. Lett., 14(4), 443-446 (1987).

 

  1. D.S. Hall, Electrons in the boundary layers near the dayside magnetopause, J. Geophys. Res., 96(A5), 7869-7891 (1991).

 

  1. J.R. Asbridge, S.J. Bame, I.B. Strong, Outward flow of protons from the Earth's bow shock, J. Geophys. Res., 73(17), 5777-5782 (1968).

 

  1. R. Lundin, et al, First measurements of the ionospheric plasma escape from Mars, Nature, 341, 609–612 (1989).

 

  1. S.S. Dolginov, The magnetic field and the magnetosphere of the planet Mars, Adv. Space Res., 12(8), 187-211 (1992).

 

  1. S.R. Pillay, F. Verheest, Effect of non-thermal ion distributions on the Jeans instability in dusty plasmas, J. Plasma Phys., 71(2), 177 -184 (2005).

 

  1. F. Verheest, M.A. Hellberg, I. Kourakis, Dust-ion-acoustic supersolitons in dusty plasmas with nonthermal electrons, Phys. Rev. E, 87, 043107 (2013).

 

  1. G.M. Zaslavsky, et al., Large-scale behavior of the tokamak density fluctuations, Phys. Plasmas., 7(9), 3691-3695 (2000).

 

  1. M. Nurujjaman, R. Narayanan, A.N. Iyengar, Parametric investigation of nonlinear fluctuations in a dc glow discharge plasma, Chaos, 17(4), 043121-6 (2007).

 

  1. A.M. Wharton, et al, Theoretical and numerical modelling of chaotic electrostatic ion cyclotron (EIC) oscillations by Jerk equation, Phys. Plasmas., 21(2), 022311-6 (2014).

 

  1. P. Feng, J. Zhang, W. Wang, Spike-like solitary waves in incompressible boundary layers driven by a travelling wave, Chaos, 26(6), 063104-9 (2016).

 

  1. S. Strogatz, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering. (Perseus, Massachusetts, 1994).

 

  1. A.E. Dubinov, D.Y. Kolotov, Ion-Acoustic Super Solitary Waves in Dusty Multispecies Plasmas, IEEE Trans. Plasma Sci, 40(5), 1429-1433 (2012).

 

  1. A.E. Dubinov, D.Y. Kolotov, Ion-acoustic supersolitons in plasma, Plasma Phys. Rep., 38, 909-912 (2012).

 

  1. F. Verheest, M.A. Hellberg, I. Kourakis, On-acoustic supersolitons in plasmas with two-temperature electrons: Boltzmann and kappa distributions Phys, Plasmas, 20, 082309-12 (2013).

 

  1. G.S. Lakhina, S.V. Singh, A.P. Kakeel, Ion acoustic solitons/double layers in two-ion plasma revisited, Phys. Plasmas, 21(6), 062311-8 (2014).

 

  1. S.A.El. Wakil, E.M. Abwafa, A.A. Elhanbaly, Super-soliton dust-acoustic waves in four-component dusty plasma using non-extensive electrons and ions distributions, Phys. Plasmas, 24, 073705-06 (2017).

 

  1. H. Ikezi, Experiments on ion‐acoustic solitary waves, Phys. Fluids, 16(10), 1668-1675 (1973).

 

  1. Y. Nakamura, I. Tsukabayashi, Modified Korteweg—de Vries ion-acoustic solitons in a plasma, J. Plasma Phys, 34(3), 401-415 (1985).

 

  1. I. Cooney, M.T. Gavin, K.E. Lonngren, Radiation of ion acoustic waves in a dispersive positive ion-negative ion plasma, IEEE Trans. Plasma. Sci., 19(3), 545-547 (1991).

 

  1. W. Swider, Electron loss and the determination of electron concentrations in the D-region, Pur. Appl. Geophys., 127, 403-414 (1988).

 

  1. I.D. Kaganovich, et al, Negative Ion Density Fronts during Ignition and Extinction of Plasmas in Electronegative Gases, Phys. Rev. Lett., 84, 1918-1921 (2000).

 

  1. F.S. Mozer, et al, New Features of Time Domain Electric-Field Structures in the Auroral Acceleration Region, Phys. Rev. Lett, 79, 1281-1285 (1987).

 

  1. Q.M. Lu, D.Y. Wang, S. Wang, Generation mechanism of electrostatic solitary structures in the Earth's auroral region, J. Geophys. Res., 110, A3223-8 (2005).

 

  1. B. Kakad, A. Kakad, Y. Omura, Nonlinear evolution of ion acoustic solitary waves in space plasmas: Fluid and particle-in-cell simulations, J. Geophys. Res., 119, 5589-5599 (2014).

 

  1. A. Lotekar, A. Kakad, B. Kakad, A fluid simulation-based evidence of the soliton-type behavior of super solitary waves in plasma, Phys Plasmas, 23(10), 102108 (2016).

 

  1. A. Saha, J. Tamang, Effect of q-nonextensive hot electrons on bifurcations of nonlinear and supernonlinear ion-acoustic periodic waves, Adv. Space Res, 63(5), 1596-1606 (2019).

 

  1. J. Tamang, A. Saha, Bifurcations of small-amplitude supernonlinear waves of the mKdV and modified Gardner equations in a three-component electron-ion plasma, Phys. Plasmas, 27(1), 012105-09 (2020).

 

  1. A. Saha, P.K. Prasad, S. Banerjee, Bifurcation of ion-acoustic superperiodic waves in auroral zone of Earth’s magnetosphere, Astrophys, Space Sci., 364, 180 (2019).

 

  1. P.K. Prasad, A. Saha, Bifurcation analysis of ion-acoustic waves for Schrödinger equation in nonextensive Solar wind plasma, Adv. Space Res., 67(1), 9-19 (2021).

 

  1. T.K. Das, et al, Effect of dust ion collisional frequency on transition of dust ion acoustic waves from quasiperiodic motion to limit cycle oscillation in a magnetized dusty plasma, Phys. Plasmas, 24(7), 073707 (2017).

 

  1. S.A. Iqbal, M.G. Hafez, S.A. Karim, Bifurcation analysis with chaotic motion of oblique plane wave for describing a discrete nonlinear electrical transmission line with conformable derivative, Results in Physics, 18, 103309 (2020).

 

  1. Z. Rahim, M. Adnen, A. Qamar, Nonlinear excitations of magnetosonic solitary waves and their chaotic behavior in spin-polarized degenerate quantum magnetoplasma, Chaos, 31(2), 023133 (2021).

 

  1. H. Alinejad, Effect of dust polarity on transcritical bifurcation of dust ion-acoustic waves in a nonextensive dusty plasma, Chaos, Solitons and Fractals, 157, 111907-8 (2022).

 

  1. F.F. Chen, Introduction to Plasma Physics and Controlled Fusion, (New York: Plenum Press, 1984).

 

  1. F. Verheest, M.A. Hellberg, Compressive and rarefactive solitary waves in nonthermal two-component plasmas, Phys. Plasmas, 17(10), 102312-7 (2010).

Keywords

Bifurcation analysis
Low-frequency waves
Phase portrait
energetic electrons
  1. L. Stenflo, Generalized Lorenz equations for acoustic-gravity waves in the atmosphere, Phys. Scr., 53(1), 83-84 (1996).

 

  1. H. Ikezi, R. Taylor, D. Baker, Formation and Interaction of Ion-Acoustic Solitions, Phys. Rev. Lett., 25(1), 11-14 (1970).

 

  1. H. Washimi, T. Taniuti, Propagation of Ion-Acoustic Solitary Waves of Small Amplitude, Phys. Rev. Lett., 17(19), 996-998 (1966).

 

  1. R.Z. Sagdeev, Reviews of Plasma Physics, Edited by M.A. Leontovich (Consultants Bureau, New York, 1966).

 

  1. R.A. Cairns, et al, Electrostatic solitary structures in non-thermal plasmas Geophys, Res. Lett., 22(20), 2709-2712 (1995).

 

  1. G. Hairapetian, R.L. Stenzel, Expansion of a Two-Electron-Population Plasma into Vacuum, Phys. Rev. Lett., 61(14), 1607-1610 (1988).

 

  1. R. Lundin, et al, Plasma energization on auroral field lines as observed by the Viking spacecraft, Geophys. Res. Lett., 14(4), 443-446 (1987).

 

  1. D.S. Hall, Electrons in the boundary layers near the dayside magnetopause, J. Geophys. Res., 96(A5), 7869-7891 (1991).

 

  1. J.R. Asbridge, S.J. Bame, I.B. Strong, Outward flow of protons from the Earth's bow shock, J. Geophys. Res., 73(17), 5777-5782 (1968).

 

  1. R. Lundin, et al, First measurements of the ionospheric plasma escape from Mars, Nature, 341, 609–612 (1989).

 

  1. S.S. Dolginov, The magnetic field and the magnetosphere of the planet Mars, Adv. Space Res., 12(8), 187-211 (1992).

 

  1. S.R. Pillay, F. Verheest, Effect of non-thermal ion distributions on the Jeans instability in dusty plasmas, J. Plasma Phys., 71(2), 177 -184 (2005).

 

  1. F. Verheest, M.A. Hellberg, I. Kourakis, Dust-ion-acoustic supersolitons in dusty plasmas with nonthermal electrons, Phys. Rev. E, 87, 043107 (2013).

 

  1. G.M. Zaslavsky, et al., Large-scale behavior of the tokamak density fluctuations, Phys. Plasmas., 7(9), 3691-3695 (2000).

 

  1. M. Nurujjaman, R. Narayanan, A.N. Iyengar, Parametric investigation of nonlinear fluctuations in a dc glow discharge plasma, Chaos, 17(4), 043121-6 (2007).

 

  1. A.M. Wharton, et al, Theoretical and numerical modelling of chaotic electrostatic ion cyclotron (EIC) oscillations by Jerk equation, Phys. Plasmas., 21(2), 022311-6 (2014).

 

  1. P. Feng, J. Zhang, W. Wang, Spike-like solitary waves in incompressible boundary layers driven by a travelling wave, Chaos, 26(6), 063104-9 (2016).

 

  1. S. Strogatz, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering. (Perseus, Massachusetts, 1994).

 

  1. A.E. Dubinov, D.Y. Kolotov, Ion-Acoustic Super Solitary Waves in Dusty Multispecies Plasmas, IEEE Trans. Plasma Sci, 40(5), 1429-1433 (2012).

 

  1. A.E. Dubinov, D.Y. Kolotov, Ion-acoustic supersolitons in plasma, Plasma Phys. Rep., 38, 909-912 (2012).

 

  1. F. Verheest, M.A. Hellberg, I. Kourakis, On-acoustic supersolitons in plasmas with two-temperature electrons: Boltzmann and kappa distributions Phys, Plasmas, 20, 082309-12 (2013).

 

  1. G.S. Lakhina, S.V. Singh, A.P. Kakeel, Ion acoustic solitons/double layers in two-ion plasma revisited, Phys. Plasmas, 21(6), 062311-8 (2014).

 

  1. S.A.El. Wakil, E.M. Abwafa, A.A. Elhanbaly, Super-soliton dust-acoustic waves in four-component dusty plasma using non-extensive electrons and ions distributions, Phys. Plasmas, 24, 073705-06 (2017).

 

  1. H. Ikezi, Experiments on ion‐acoustic solitary waves, Phys. Fluids, 16(10), 1668-1675 (1973).

 

  1. Y. Nakamura, I. Tsukabayashi, Modified Korteweg—de Vries ion-acoustic solitons in a plasma, J. Plasma Phys, 34(3), 401-415 (1985).

 

  1. I. Cooney, M.T. Gavin, K.E. Lonngren, Radiation of ion acoustic waves in a dispersive positive ion-negative ion plasma, IEEE Trans. Plasma. Sci., 19(3), 545-547 (1991).

 

  1. W. Swider, Electron loss and the determination of electron concentrations in the D-region, Pur. Appl. Geophys., 127, 403-414 (1988).

 

  1. I.D. Kaganovich, et al, Negative Ion Density Fronts during Ignition and Extinction of Plasmas in Electronegative Gases, Phys. Rev. Lett., 84, 1918-1921 (2000).

 

  1. F.S. Mozer, et al, New Features of Time Domain Electric-Field Structures in the Auroral Acceleration Region, Phys. Rev. Lett, 79, 1281-1285 (1987).

 

  1. Q.M. Lu, D.Y. Wang, S. Wang, Generation mechanism of electrostatic solitary structures in the Earth's auroral region, J. Geophys. Res., 110, A3223-8 (2005).

 

  1. B. Kakad, A. Kakad, Y. Omura, Nonlinear evolution of ion acoustic solitary waves in space plasmas: Fluid and particle-in-cell simulations, J. Geophys. Res., 119, 5589-5599 (2014).

 

  1. A. Lotekar, A. Kakad, B. Kakad, A fluid simulation-based evidence of the soliton-type behavior of super solitary waves in plasma, Phys Plasmas, 23(10), 102108 (2016).

 

  1. A. Saha, J. Tamang, Effect of q-nonextensive hot electrons on bifurcations of nonlinear and supernonlinear ion-acoustic periodic waves, Adv. Space Res, 63(5), 1596-1606 (2019).

 

  1. J. Tamang, A. Saha, Bifurcations of small-amplitude supernonlinear waves of the mKdV and modified Gardner equations in a three-component electron-ion plasma, Phys. Plasmas, 27(1), 012105-09 (2020).

 

  1. A. Saha, P.K. Prasad, S. Banerjee, Bifurcation of ion-acoustic superperiodic waves in auroral zone of Earth’s magnetosphere, Astrophys, Space Sci., 364, 180 (2019).

 

  1. P.K. Prasad, A. Saha, Bifurcation analysis of ion-acoustic waves for Schrödinger equation in nonextensive Solar wind plasma, Adv. Space Res., 67(1), 9-19 (2021).

 

  1. T.K. Das, et al, Effect of dust ion collisional frequency on transition of dust ion acoustic waves from quasiperiodic motion to limit cycle oscillation in a magnetized dusty plasma, Phys. Plasmas, 24(7), 073707 (2017).

 

  1. S.A. Iqbal, M.G. Hafez, S.A. Karim, Bifurcation analysis with chaotic motion of oblique plane wave for describing a discrete nonlinear electrical transmission line with conformable derivative, Results in Physics, 18, 103309 (2020).

 

  1. Z. Rahim, M. Adnen, A. Qamar, Nonlinear excitations of magnetosonic solitary waves and their chaotic behavior in spin-polarized degenerate quantum magnetoplasma, Chaos, 31(2), 023133 (2021).

 

  1. H. Alinejad, Effect of dust polarity on transcritical bifurcation of dust ion-acoustic waves in a nonextensive dusty plasma, Chaos, Solitons and Fractals, 157, 111907-8 (2022).

 

  1. F.F. Chen, Introduction to Plasma Physics and Controlled Fusion, (New York: Plenum Press, 1984).

 

  1. F. Verheest, M.A. Hellberg, Compressive and rarefactive solitary waves in nonthermal two-component plasmas, Phys. Plasmas, 17(10), 102312-7 (2010).
Journal of Nuclear Science, Engineering and Technology (JONSAT)
Volume 43, Issue 4 - Serial Number 102
December 2022
Pages 100-108

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