Abstract
Within the confines of a two-fluid quantum magnetohydrodynamic model, the investigation of magnetoacoustic shock and solitary waves is conducted in an electron-ion magnetoplasma that considers electrons of spin 1/2. When the plasma system is nonlinearly investigated using the reductive perturbation approach, the Korteweg de Vries-Burgers (KdVB) equation is produced. Sagdeev’s potential is created, revealing the presence of solitary solutions. However, when dissipative terms are included, intriguing physical solutions can be obtained. The KdVB equation is further investigated using the phase plane theory of a planar dynamical system to demonstrate the existence of periodic and solitary wave solutions. Predicting several classes of traveling wave solutions is advantageous due to various phase orbits, which manifest as soliton-shock waves, and oscillatory shock waves. The presence of a magnetic field, the density of electrons and ions, and the kinematic viscosity significantly alter the properties of magnetoacoustic solitary and shock waves. Additionally, electric fields have been identified. The outcomes obtained here can be applied to studying the nature of magnetoacoustic waves that are observed in compact astrophysical environments, where the influence of quantum spin phenomena remains significant, and also in controlled laboratory plasma experiments.
Funding source: Prince Sattam bin Abdulaziz University
Award Identifier / Grant number: PSAU/2024/01/78916
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Research ethics: None applicable.
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Author contributions: The authors have accepted responsibility for the entire content of this manuscript and approved its submission.
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Competing interests: The authors state no conflict of interest.
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Research funding: The authors extend their appreciation to Prince Sattam bin Abdulaziz University for funding this research work through the project number (PSAU/2024/01/78916). The authors are thankful to the Deanship of Graduate Studies and Scientific Research at University of Bisha for supporting this work through the Fast-Track Research Support Program.
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Data availability: Not applicable.
By using the transformation 2 in Eq. (1i) it becomes
Substituting (3) into (27A) and equating the coefficients of ϵ3/2 one obtains
Substitute from 4 leads to
Divide (29A) by
which lead to the linear dispersion relation.
The next higher orders of ϵ in Eq. (1) leads with the use of Eq. (4) to the second order perturbed quantities to be
Substituting (3) into (27A) and equating the coefficients of ϵ5/2 one obtains
Substitute from the first order, Eq. (4), and second order perturbed quantities, Eqs. (31B), into (32B) leads to the KdVB equation, Eq. (6).
References
[1] Y. A. Berezin, “Cylindrical waves of finite amplitude in a rarefied plasma,” J. Appl. Mech. Tech. Phys., vol. 6, pp. 78–79, 1965. https://doi.org/10.1007/bf00913391.Search in Google Scholar
[2] C. F. Kennel and R. Z. Sagdeev, “Collisionless shock waves in high β plasmas,” J. Geophys. Res., vol. 72, no. 13, pp. 3327–3341, 1967. https://doi.org/10.1029/jz072i013p03303.Search in Google Scholar
[3] A. B. Macmahon, F. Kennel, and R. Z. Sagdeev, Discussion of Paper by C, “Collisionless shock waves in high β plasmas. 2,” J. Geophys. Res., vol. 73, no. 23, pp. 7538–7539, 1968. https://doi.org/10.1029/ja073i023p07538.Search in Google Scholar
[4] R. B. Horne, R. M. Thorne, S. A. Glauert, N. P. Meredith, D. Pokhotelov, and O. Santolik, “Electron acceleration in the Van Allen radiation belts by fast magnetosonic waves,” Geophys. Res. Lett., vol. 34, no. 17, pp. 1–5, 2007. https://doi.org/10.1029/2007gl030267.Search in Google Scholar
[5] J. Li, et al.., “Interactions between magnetosonic waves and radiation belt electrons: comparisons of quasi-linear calculations with test particle simulations,” Geophys. Res. Lett., vol. 41, no. 14, pp. 4828–4834, 2014. https://doi.org/10.1002/2014gl060461.Search in Google Scholar
[6] N. P. Meredith, R. B. Horne, and R. R. Anderson, “Survey of magnetosonic waves and proton ring distributions in the Earth’s inner magnetosphere,” J. Geophys. Res., vol. 113, no. A6, pp. 1–13, 2014.10.1029/2007JA012975Search in Google Scholar
[7] O. N. Santolik, F. Gereova, K. Macusova, E. Y. de Conchy, and N. Cornilleau-Wehrlin, “Systematic analysis of equatorial noise below the lower hybrid frequency,” Ann. Geophys., vol. 22, no. 7, pp. 2587–2595, 2014. https://doi.org/10.5194/angeo-22-2587-2004.Search in Google Scholar
[8] C. T. Russell, R. E. Holzer, and E. J. Smith, “OGO 3 observations of ELF noise in the magnetosphere: 1. Spatial extent and frequency of occurrence,” J. Geophys. Res., vol. 74, no. 3, pp. 755–777, 2014. https://doi.org/10.1029/ja074i003p00755.Search in Google Scholar
[9] S. Hussain and S. Mahmood, “Propagation of nonlinear dust magnetoacoustic waves in cylindrical geometry,” Phys. Plasmas, vol. 18, no. 12, p. 022712, 2011. https://doi.org/10.1063/1.3661799.Search in Google Scholar
[10] S. Hussain, S. Mahmood, and A. ur Rehman, “Nonlinear magnetosonic waves in dense plasmas with non-relativistic and ultra-relativistic degenerate electrons,” Phys. Plasmas, vol. 21, no. 11, p. 112901, 2014. https://doi.org/10.1063/1.4901038.Search in Google Scholar
[11] G. Brodin and M. Marklund, “Spin magnetohydrodynamics,” New J. Phys., vol. 9, p. 277, 2007. https://doi.org/10.1088/1367-2630/9/8/277.Search in Google Scholar
[12] A. P. Misra and N. K. Ghosh, “Spin magnetosonic shock-like waves in quantum plasmas,” Phys. Lett. A, vol. 372, no. 42, pp. 6412–6415, 2008. https://doi.org/10.1016/j.physleta.2008.08.065.Search in Google Scholar
[13] A. Mushtaq and S. V. Vladimirov, “Arbitrary magnetosonic solitary waves in spin 1/2 degenerate quantum plasma,” Eur. Phys. J. D, vol. 64, no. 2–3, pp. 419–426, 2011. https://doi.org/10.1140/epjd/e2011-20374-x.Search in Google Scholar
[14] F. A. Asenjo, “The quantum effects of the spin and the Bohm potential in the oblique propagation of magnetosonic waves,” Phys. Lett. A, vol. 376, no. 36, pp. 2496–2500, 2012. https://doi.org/10.1016/j.physleta.2012.06.023.Search in Google Scholar
[15] B. Sahu, A. Sinha, R. Roychoudhury, and M. Khan, “Arbitrary amplitude magnetosonic solitary and shock structures in spin quantum plasma,” Phys. Plasmas, vol. 20, no. 11, p. 112303, 2013. https://doi.org/10.1063/1.4834497.Search in Google Scholar
[16] Z. Rahim, M. Adnan, and A. Qamar, “Nonlinear excitations of magnetosonic solitary waves and their chaotic behavior in spin-polarized degenerate quantum magnetoplasma,” Chaos, vol. 31, no. 2, p. 023133, 2021. https://doi.org/10.1063/5.0011622.Search in Google Scholar PubMed
[17] S. Hussain and S. Mahmood, “Density polarization effect of spin-up and spin-down electrons on magnetosonic solitons in a dense plasma with oblique magnetic field,” Phys. Scr., vol. 98, no. 4, p. 045603, 2023. https://doi.org/10.1088/1402-4896/acbe79.Search in Google Scholar
[18] Y. A. A. Hager, M. A. H. Khaled, and M. A. Shukri, “Magnetosonic waves propagation in a magnetorotating quantum plasma,” Phys. Rev. E, vol. 107, no. 5, p. 055202, 2023. https://doi.org/10.1103/physreve.107.055202.Search in Google Scholar PubMed
[19] A. Mukhopadhyay, D. Bagui, and S. Chandra, “Electrostatic shock fronts in two-component plasma and its evolution into rogue wave type solitary structures,” in The African Review of Physics, 15 Special Issue on Plasma Physics, vol. 004, 2020, p. 25.Search in Google Scholar
[20] J. Tamang, B. Pradhan, and A. Saha, “Stable oscillation and chaotic motion of the dust-acoustic waves for the KdV-burgers equation in a four-component dusty plasma,” IEEE Trans. Plasma Sci., vol. 48, no. 11, p. 3982, 2020. https://doi.org/10.1109/tps.2020.3027241.Search in Google Scholar
[21] S. Chandra, C. Das, and J. Sarkar, “Evolution of nonlinear stationary formations in a quantum plasma at finite temperature,” Z. Naturforsch. A, vol. 76, no. 4, p. 329, 2021. https://doi.org/10.1515/zna-2020-0328.Search in Google Scholar
[22] S. Raut, K. K. Mondal, P. Chatterjee, and S. Roy, “Dust ion acoustic bi-soliton, soliton, and shock waves in unmagnetized plasma with Kaniadakis-distributed electrons in planar and nonplanar geometry,” Eur. Phys. J. D, vol. 77, no. 100, pp. 1–15, 2023. https://doi.org/10.1140/epjd/s10053-023-00676-8.Search in Google Scholar
[23] R. Jahangir, S. Ali, and A. M. Mirza, “Magnetoacoustic shocks with geometrical effects in spin dense plasmas,” Phys. Plasmas, vol. 25, no. 9, p. 092102, 2018. https://doi.org/10.1063/1.5038375.Search in Google Scholar
[24] A. Saha and P. Chatterjee, “Solitonic, periodic, quasiperiodic and chaotic structures of dust ion acoustic waves in nonextensive dusty plasmas,” Eur. Phys. J. D, vol. 69, no. 9, p. 203, 2015. https://doi.org/10.1140/epjd/e2015-60115-7.Search in Google Scholar
[25] A. Saha and P. Chatterjee, “Solitonic, periodic and quasiperiodic behaviors of dust ion acoustic waves in superthermal plasmas,” Braz. J. Phys., vol. 45, no. 4, p. 419, 2015. https://doi.org/10.1007/s13538-015-0329-8.Search in Google Scholar
[26] B.-G. Zhang, W. Li, and X. Li, “Peakons and new exact solitary wave solutions of extended quantum Zakharov-Kuznetsov equation,” Phys. Plasmas, vol. 24, no. 6, pp. 1–8, 2017. https://doi.org/10.1063/1.4989707.Search in Google Scholar
[27] S. Y. El-Monier and A. Atteya, “Bifurcation analysis for dust-acoustic waves in a four-component plasma including warm ions,” IEEE Trans. Plasma Sci., vol. 46, no. 4, p. 815, 2017. https://doi.org/10.1109/tps.2017.2766097.Search in Google Scholar
[28] T. Tamang, K. Sarkar, and A. Saha, “Solitary wave solution and dynamic transition of dust ion acoustic waves in a collisional nonextensive dusty plasma with ionization effect,” Phys. A, vol. 505, no. 9, p. 18, 2018. https://doi.org/10.1016/j.physa.2018.02.213.Search in Google Scholar
[29] T. Tamang and A. Saha, “Influence of dust-neutral collisional frequency and nonextensivity on dynamic motion of dust-acoustic waves,” Waves Random Complex Media, vol. 31, no. 4, pp. 597–617, 2019. https://doi.org/10.1080/17455030.2019.1605230.Search in Google Scholar
[30] A. Abdikian and S. Sultana, “Dust-acoustic solitary and cnoidal waves in a dense magnetized dusty plasma with temperature degenerate trapped electrons and nonthermal ions,” Phys. Scr., vol. 96, no. 9, pp. 1–16, 2021.10.1088/1402-4896/ac04dbSearch in Google Scholar
[31] A. Abdikian, J. Tamang, and A. Saha, “Investigation of supernonlinear and nonlinear ion-acoustic waves in a magnetized electron-ion plasma with generalized (r, q) distributed electrons,” Waves Random Complex Media, pp. 1–22, 2021. https://doi.org/10.1080/17455030.2021.1965242.Search in Google Scholar
[32] A. Abdikian and S. V. Farahani, “The characteristics of ion-acoustic solitary waves in relativistic rotating astrophysical plasmas,” Eur. Phys. J. Plus, vol. 137, no. 652, pp. 1–16, 2022. https://doi.org/10.1140/epjp/s13360-022-02870-w.Search in Google Scholar
[33] A. Saha, B. Pradhan, and S. Banerjee, “Bifurcation analysis of quantum ion-acoustic kink, anti-kink and periodic waves of the Burgers equation in a dense quantum plasma,” Eur. Phys. J. Plus, vol. 135, no. 2, p. 216, 2020. https://doi.org/10.1140/epjp/s13360-020-00235-9.Search in Google Scholar
[34] S. Y. El-Monier and A. Atteya, “Dynamics of ion-acoustic waves in nonrelativistic magnetized multi-ion quantum plasma: the role of trapped electrons,” Waves Random Complex Media, vol. 32, no. 1, p. 299, 2022. https://doi.org/10.1080/17455030.2020.1772522.Search in Google Scholar
[35] W. F. El-Taibany, S. K. EL-Labany, A. S. El-Helbawy, and A. Atteya, “Dust-acoustic solitary and periodic waves in magnetized self-gravito-electrostatic opposite polarity dusty plasmas,” Eur. Phys. J. Plusvol. 137, p. 261, 2022. https://doi.org/10.1140/epjp/s13360-022-02461-9.Search in Google Scholar
[36] M. Akbari-Moghanjoughi and P. K. Shukla, “Theory for large-amplitude electrostatic ion shocks in quantum plasmas,” Phys. Rev. E, vol. 86, no. 6, p. 066401, 2012. https://doi.org/10.1103/physreve.86.066401.Search in Google Scholar
[37] L. Landau, “Diamagnetismus der metalle,” Z. Phys., vol. 64, no. 9–10, p. 629, 1930. https://doi.org/10.1007/bf01397213.Search in Google Scholar
[38] C. Kittel, Introduction to Solid State Physics, 8th ed. New York, John Wiley & Sons, 2005.Search in Google Scholar
[39] R. K. Pathria, Statistical Mechanics, Oxford, Butterworth-Heinemann, 1996.Search in Google Scholar
[40] H. Washimi and T. Tanuiti, “Propagation of ion-acoustic solitary waves of small amplitude,” Phys. Rev. Lett., vol. 17, no. 19, p. 996, 1966. https://doi.org/10.1103/physrevlett.17.996.Search in Google Scholar
[41] A. Abdikian, J. Tamang, and A. Saha, “Supernonlinear wave and multistability in magneto-rotating plasma with (r,q) distributed electrons,” Phys. Scr., vol. 96, no. 9, p. 595605, 2021. https://doi.org/10.1088/1402-4896/ac07b7.Search in Google Scholar
[42] S. K. EL-Labany, W. F. El-Taibany, A. E. El-Samahy, A. M. Hafez, and A. Atteya, “Higher-order corrections to nonlinear dust-ion-acoustic shock waves in a degenerate dense space plasma,” Astrophys. Space Sci., vol. 354, no. 2, p. 385, 2014. https://doi.org/10.1007/s10509-014-2096-3.Search in Google Scholar
[43] A. Atteya, E. E. Behery, and W. F. El-Taibany, “Ion acoustic shock waves in a degenerate relativistic plasma with nuclei of heavy elements,” Eur. Phys. J. Plus, vol. 132, no. 3, p. 109, 2017. https://doi.org/10.1140/epjp/i2017-11367-2.Search in Google Scholar
[44] A. Atteya, M. A. El-Borie, G. D. Roston, A. S. El-Helbawy, P. K. Prasad, and A. Saha, “Ion-acoustic stable oscillations, solitary, periodic and shock waves in a quantum magnetized electron–positron–ion plasma,” Z. Naturforsch. A, vol. 76, no. 9, p. 757, 2021. https://doi.org/10.1515/zna-2021-0060.Search in Google Scholar
[45] A. M. El-Hanbaly, M. Sallah, E. K. El-Shewy, and H. F. Darweesh, “Kinematic dust viscosity effect on linear and nonlinear dust-acoustic waves in space dusty plasmas with nonthermal ions,” J. Exp. Theor. Phys., vol. 121, no. 4, p. 669, 2015. https://doi.org/10.1134/s1063776115100179.Search in Google Scholar
[46] A. Atteya, S. Sultana, and S. Schlickeiser, “Dust-ion-acoustic solitary waves in magnetized plasmas with positive and negative ions: the role of electrons superthermality,” Chin. J. Phys., vol. 56, no. 5, p. 1931, 2018. https://doi.org/10.1016/j.cjph.2018.09.002.Search in Google Scholar
[47] J. Tamang and A. Saha, “Phase plane analysis of the dust-acoustic waves for the Burgers equation in a strongly coupled dusty plasma,” Indian J. Phys., pp. 749–757, 2020. https://doi.org/10.1007/s12648-020-01733-3.Search in Google Scholar
[48] R. Saeed and A. Shah, “Nonlinear Korteweg–de Vries–Burger equation for ion acoustic shock waves in a weakly relativistic electron-positron-ion plasma with thermal ions,” Phys. Plasmas, vol. 17, no. 3, p. 032308, 2010. https://doi.org/10.1063/1.3328805.Search in Google Scholar
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