Abstract
An investigation is presented theoretically for the multi- dimensional instability of dust-acoustic solitary waves in the dense Thomas-Fermi magnetoplasma. The plasma system contains classical negatively charged dust grains with degenerate electrons and ions particles. Based on the reductive perturbation approach, the Zakharov-Kuznetsov (ZK) equation has been formulated. This nonlinear ZK equation is analyzed for its solitary wave solutions. Only rarefactive solitary waves are obtained, those are influenced by the parameters such as the dust temperature and number density, the electrons, and ions Fermi temperatures, and densities. The waves growth rate of the is computed. The previous parameters’ effects on the instability are also discussed. The present results are beneficial in understanding the propagation and the instability of nonlinear aspects in dense plasma systems like white dwarfs and high-intensity laser-solid matter interaction experiments where the Thomas-Fermi dense magnetoplasma state may occur.
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References
Jung, Y.D.: Quantum-mechanical effects on electron-electron scattering in dense high-temperature plasmas. Phys. Plasmas 8(8), 3842–3844 (2001)
Markowich, P.A., Ringhofer, C.A., Schmeiser, C.: Semiconductor Equations, 1st edn. Springer, New York (1990)
Becker, K., Koutsospyros, K., Yin, S.M., et al.: Environmental and biological applications of microplasmas. Plasma Phys. Control. Fusion 47, B513–B523 (2005)
Killian, T.C.: Physics-cool vibes. Nature (London) 441, 297–298 (2006)
Malkin, V.M., Fisch, N.J., Wurtele, J.S.: Compression of powerful x-ray pulses to attosecond durations by stimulated Raman backscattering in plasmas. Phys. Rev. E 75, 026404 (2007)
Manfredi, G.: How to model quantum plasmas. Fields Inst. Commun. 46, 263–287 (2005)
Shukla, P.K., Mamun, A.A.: Introduction to Dusty Plasma Physics, 1st edn. Institute of Physics, Bristol (2002)
Fortov, V.E., Ivlev, A.V., Khrapak, S.A., Morfill, G.E.: Complex (dusty) plasmas. Phys. Rep. 421, 1–103 (2005)
Atteya, A., El-Borie, M.A., Roston, G.D., El-Helbawy, A.S., Prasad, P.K., Saha, A.: Ion-acoustic stable oscillations, solitary, periodic and shock waves in a quantum magnetize electron-positron-ion plasma. Zeitschrift für Naturforschung A 76(9), 757–768 (2021)
El-Monier, S.Y., Atteya, A.: Dust-acoustic Gardner solitons in cryogenic plasma with the effect of polarization in the presence of a quantizing magnetic field. Zeitschrift für Naturforschung A 76(2), 121–130 (2021)
Shukla, P.K., Silin, V.P.: Dust ion-acoustic wave. Phys. Scr. 45(5), 508 (1992)
Barkan, A., D’Angelo, N., Merlino, R.L.: Experiments on ion-acoustic waves in dusty plasmas. Planet. Space Sci. 44, 239–242 (1996)
Merlino, R.L., Barkan, A., Thompson, C., D’Angelo, N.: Laboratory studies of waves and instabilities in dusty plasmas. Phys. Plasmas 5, 1607–1614 (1998)
Rao, N.N., Shukla, P.K., Yu, M.Y.: Dust-acoustic waves in dusty plasmas. Planet. Space Sci. 38, 543–546 (1990)
Barkan, A., Merlino, R.L., D’Angelo, N.: Laboratory observation of the dust-acoustic wave mode. Phys. Plasmas 2, 3563–3565 (1995); Pieper, J. B.: J. Goree, Phys. Rev. Lett. 77, 3137 (1996)
Prabhakara, H.R., Tanna, V.L.: Trapping of dust and dust acoustic waves in laboratory plasmas. Phys. Plasmas 3, 3176–3181 (1996)
Banerjee, A., Harbolaa, M.K.: Hydrodynamic approach to time-dependent density functional theory; Response properties of metal clusters. J. Chem. Phys. 113, 5614–4623 (2000)
Domps, A., Reinhard, P.-G., Suraud, E.: Theoretical estimation of the importance of two-electron collisions for relaxation in metal clusters. Phys. Rev. Lett. 81, 5524–5527 (1998)
Loffredo, M., Morato, L.: On the creation of quantized vortex lines in rotating He II. Nuovo Cimento Soc. Ital. Fis., B 108, 205–215 (1993)
Feynman, R.: Statistical Mechanics. A Set of Lectures, 1st edn. Benjamin, Reading (1972)
Dubinov, A.E., Dubinova, A.A.: Nonlinear theory of ion-acoustic waves in an ideal plasma with degenerate electrons. Plasma Phys. Rep. 33, 859–870 (2007)
Abdelsalam, U.M., Moslem, W.M., Shukla, P.K.: Localized electrostatic excitations in a Thomas-Fermi plasma containing degenerate electrons. Phys. Plasmas 15, 052303 (2008)
Abdelsalam, U.M., Moslem, W.M., Shukla, P.K.: Ion-acoustic solitary waves in a dense pair-ion plasma containing degenerate electrons and positrons. Phys. Lett. A 372, 4057–4061 (2008)
Atteya, A., El-Borie, M.A., Roston, G.D., El-Helbawy, A.S.: Nonlinear dust acoustic waves in an inhomogeneous magnetized quantum dusty plasma. Waves Random Complex Media 1–16 (2021). https://doi.org/10.1080/17455030.2021.1880030
Rahim, Z., Ali, S., Qamar, A.: Dust acoustic solitary and shock excitations in a Thomas-Fermi magnetoplasma. Phys. Plasmas 21(7), 072305 (2014)
Irfan, M., Ali, S., Mirza, A.M.: Dust-acoustic solitary and rogue waves in a Thomas-Fermi degenerate dusty plasma. Astrophys Space Sci. 353(2), 515–523 (2014)
Irfan, M., Ali, S., Ata-ur-Rahman, Mirza, A.M.: Arbitrary amplitude oblique electrostatic solitary waves in a degenerate cold dusty magnetoplasma. IEEE Trans. Plasma Sci. 47(8), 4151–4158 (2019)
Abd-Elzaher, M., Atteya, A.: Obliquely overtaking collisions of electrostatic N-soliton in the Thomas-Fermi dense magnetoplasma. Waves Random Complex Media 1–21 (2021). https://doi.org/10.1080/17455030.2021.1974121
El-Taibany, W.F., Sabry, R.: Dust-acoustic solitary waves and double layers in a magnetized dusty plasma with nonthermal ions and dust charge variation. Phys. Plasmas 12, 082302 (2005)
Shukla, P.K.: Twisted dust acoustic waves in dusty plasmas. Phys. Plasmas 19, 083704 (2012)
Shukla, P.K.: Twisted electrostatic ion-cyclotron waves in dusty plasmas. Phys. Rev. E 87, 015101 (2013)
Mamun, A.A.: Instability of obliquely propagating electrostatic solitary waves in a magnetized nonthermal dusty plasma. Phys. Scr. 58, 505–509 (1998)
Mamun, A.A., Russell, S.M., Mendoza-Briceno, C.A., Alam, M.N., Datta, T.K., Das, A.K.: Multi-dimensional instability of electrostatic solitary structures in magnetized nonthermal dusty plasmas. Planet. Space Sci. 48, 163–173 (2000)
El-Taibany, W.F., El-Bedwehy, N.A., El-Shamy, E.F.: Three-dimensional stability of dust-ion acoustic solitary waves in a magnetized multicomponent dusty plasma with negative ions. Phys. Plasmas 18, 033703 (2011)
Akhter, T., Hossain, M.M., Mamun, A.A.: Multi-dimensional instability of dust-acoustic solitary waves in a magnetized plasma with opposite polarity dust. Phys. Plasmas 19, 093707 (2012)
El-Labany, S.K., El-Taibany, W.F., Behery, E.E.: Stability of three-dimensional dust acoustic waves in a dusty plasma with two opposite polarity dust species including dust size distribution. Phys. Rev. E 88, 023108 (2013)
Saini, N.S., Chahal, B.S., Bains, A.S., Bedi, C.: Zakharov-Kuznetsov equation in a magnetized plasma with two temperature superthermal electrons. Phys. Plasmas 21, 022114 (2014)
El-Labany, S.K., El-Taibany, W.F., Behery, E.E., Zedan, N.A.: Stability of three-dimensional obliquely propagating dust acoustic waves in dusty plasma including the polarization force effect. Eur. Phys. J. Plus 130, 250 (2015)
El-Taibany, W.F., Zedan, N.A., Atteya, A.: Stability of three-dimensional dust acoustic waves in a strongly coupled dusty plasma including kappa distributed superthermal ions and electrons. Eur. Phys. J. Plus 134, 479 (2019)
Zedan, N.A., Atteya, El-Taibany, W.F., El-Labany, S.K.: Stability of ion-acoustic solitons in a multi-ion degenerate plasma with the effects of trapping and polarization under the influence of quantizing magnetic field. Waves in Random and Complex Media 1–15 (2020). https://doi.org/10.1080/17455030.2020.1798560
Gao, D.-N.: Multi-dimensional instability of dust acoustic waves in magnetized quantum plasmas with positive or negative dust. Brazil. J. Phys. 51, 66–74 (2021)
Allen, M.A., Rowlands, G.: Determination of the growth rate for the linearized Zakharov-Kuznetsov equation. J. Plasma Phys. 50, 413–424 (1993)
Allen, M.A., Rowlands, G.: Stability of obliquely propagating plane solitons of the Zakharov-Kuznetsov equation. J. Plasma Phys. 53, 63–73 (1995)
Haider, M.M., Mamun, A.: Ion-acoustic solitary waves and their multi-dimensional instability in a magnetized degenerate plasma. Phys. Plasmas 19, 102105 (2012)
Jehan, N., Salahuddinin, M., Mahmood, S., Mizra, A.M.: Electrostatic solitary ion waves in dense electron-positron-ion magnetoplasma. Phys. Plasmas 16, 042313 (2009)
Chatterjee, P., Saha, T., Muniandy, S.V., ap, S.L., Wong, C.S.: Solitary waves and double layers in dense magnetoplasma. Phys. Plasmas 16, 072110 (2009)
Rahim, Z., Adnan, M., Qamar, A., Saha, A.: Nonplanar dust-acoustic waves and chaotic motions in Thomas Fermi dusty plasmas. Phys. Plasmas 25, 083706 (2018)
Roy, D., Ghosh, N., Sahu1, B.: Nonlinear modulation of quantum electron acoustic waves in a Thomas–Fermi plasma with effects of exchange-correlation. Indian J Phys. 95(11), 2479–2490 (2020)
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Atteya, A. (2022). Stability of the Dust-Acoustic Solitons in the Thomas-Fermi Dense Magnetoplasma. In: Banerjee, S., Saha, A. (eds) Nonlinear Dynamics and Applications. Springer Proceedings in Complexity. Springer, Cham. https://doi.org/10.1007/978-3-030-99792-2_16
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DOI: https://doi.org/10.1007/978-3-030-99792-2_16
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