External Magnetic Field Effects on the Rayleigh-Taylor Instability in an Inhomogeneous Rotating Quantum Plasma
Author(s)
G. A. Hoshoudy*
Affiliation(s)
Department of Applied Mathematics, Faculty of Science, South Valley University, Qena, Egypt.
Department of Applied Mathematics, Faculty of Science, South Valley University, Qena, Egypt.
ABSTRACT
The effects of external magnetic field effects on the Rayleigh-Taylor instability in an inhomogeneous stratified quantum plasma rotating uniformly are investigated. The external magnetic field is considered in both horizontal and vertical direction. The linear growth rate is derived for the case where a plasma with exponential density distribution is confined between two rigid planes at z=0 and z=h, by solving the linear QMHD equations into normal mode. Some special cases are particularized to explain the roles that play the variables of the problem. The results show that, the presence of both external horizontal and vertical magnetic field beside the quantum effect will bring about more stability on the growth rate of unstable configuration. The maximum stability will happen in the case of wave number parallels to or in the same direction of external horizontal magnetic field.
The effects of external magnetic field effects on the Rayleigh-Taylor instability in an inhomogeneous stratified quantum plasma rotating uniformly are investigated. The external magnetic field is considered in both horizontal and vertical direction. The linear growth rate is derived for the case where a plasma with exponential density distribution is confined between two rigid planes at z=0 and z=h, by solving the linear QMHD equations into normal mode. Some special cases are particularized to explain the roles that play the variables of the problem. The results show that, the presence of both external horizontal and vertical magnetic field beside the quantum effect will bring about more stability on the growth rate of unstable configuration. The maximum stability will happen in the case of wave number parallels to or in the same direction of external horizontal magnetic field.
Cite this paper
G. Hoshoudy, "External Magnetic Field Effects on the Rayleigh-Taylor Instability in an Inhomogeneous Rotating Quantum Plasma," Journal of Modern Physics, Vol. 3 No. 11, 2012, pp. 1792-1801. doi: 10.4236/jmp.2012.311224.
G. Hoshoudy, "External Magnetic Field Effects on the Rayleigh-Taylor Instability in an Inhomogeneous Rotating Quantum Plasma," Journal of Modern Physics, Vol. 3 No. 11, 2012, pp. 1792-1801. doi: 10.4236/jmp.2012.311224.
References
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A. Hoshoudy, “Quantum Effects on Rayleigh-Taylor Instability in a Horizontal Inhomogeneous Rotating Plasma,” Physics of Plasmas, Vol. 16, No. 6, 2009, Article ID: 064501, p 4. [27] M. Modestov, V. Bychkov and M. Marklund, “The Rayleigh-Taylor Instability in Quantum Magnetized Plasma with Para- and Ferromagnetic Properties,” Physics of Plasmas, Vol. 16, No. 3, 2009, Article ID: 032106, p 12. doi:10.1063/1.3085796 [28] G. A. Hoshoudy, “Quantum Effects on the Rayleigh-Taylor Instability of Stratified Fluid/Plasma through Porous Media,” Physics Letters A, Vol. 373, No. 30, 2009, pp. 2560-2567. [29] G. A. Hoshoudy, “Quantum Effects on the Rayleigh- Taylor Instability of Stratified Fluid/Plasma through Brinkman Porous Media,” Journal of Porous Media, Vol. 15, No. 4, 2012, pp. 373-381. doi:10.1615/JPorMedia.v15.i4.50 [30] S. Ali, Z. Ahmed, M. Arshad Mirza and I. Ahmad, “Rayleigh-Taylor/Gravitational Instability in Dense Magnetoplasmas,” Physics Letters A, Vol. 373, No. 33, 2009, pp. 2940-2946. doi:10.1016/j.physleta.2009.06.021
[1] L. C. Gardner, “The Quantum Hydrodynamic Model for Semiconductor Devices,” SIAM Journal on Applied Mathematics, Vol. 54, No. 2, 1994, pp. 409-427. doi:10.1137/S0036139992240425 [2] F. Haas “A Magnetohydrodynamic Model for Quantum Plasmas,” Physics of Plasmas, Vol. 12, No. 6, 2005, Article ID: 062117, p 9. doi:10.1063/1.1939947 [3] L. Rayleigh, “Investigation of the Character of the Equilibrium of an Incompressible Heavy Fluid of Variable Density,” Proceedings London Mathematical Society, Vol. 14, No. 1, 1882, pp. 170-177. doi:10.1112/plms/s1-14.1.170 [4] G. I. Taylor, “The Instability of Liquid Surfaces when Accelerated in a Direction Perpendicular to Their Planes,” Proceedings of the Royal Society of London. Series A, vol. 201, No. 1065, 1950, pp. 192-196. doi:10.1098/rspa.1950.0052 [5] k. Bhimsen Shivamoggi, “Rayleigh-Taylor Instability of Compressible Plasma in a Vertical Magnetic Field,” Astrophysics and Space Science, vol. 79, No. 1, 1981, pp. 3-9. doi:10.1007/BF00655900 [6] S. Liberatore, S. Jaoue, E. Tabakhoff and B. Canaud, “Compressible Magnetic Rayleigh-Taylor Instability in Stratified Plasmas: Comparison of Analytical and Numerical Results in the Linear Regime,” Physics of Plasmas, Vol. 16, No. 4, 2009, Article ID: 044502, p 4. doi:10.1063/1.3109664 [7] R. J. Goldston and P. H. Rutherford, “Introduction to Plasma Physics Institute of Physics,” Taylor & Francis, London, 1997. doi:10.1201/9781439822074 [8] Z. Wu, W. Zhang, D. Li and W. Yang, “Effect of Magnetic Field and Equilibrium Flow on Rayleigh-Taylor Instability,” Chinese Physics Letters, Vol. 21, No. 10, 2004, pp. 2001-2004. doi:10.1088/0256-307X/21/10/038 [9] P. A. Markowic, C. A. Ringhofer and C. Schmeiser, “Semiconductor Equations,” Springer-Verlag, New York, 1990. doi:10.1007/978-3-7091-6961-2 [10] M. Opher, L. O. Silva, D. E. Dauger, V. K. Decyk and J. M. Dawson, “Nuclear Reaction Rates and Energy in Stellar Plasmas: The Effect of Highly Damped Modes,” Physics of Plasmas, Vol. 8, No. 5, 2001, pp. 2454-2460. doi:10.1063/1.1362533 [11] Y. D. Jung, “Quantum-Mechanical Effects on Electron-Electron Scattering in Dense High-Temperature Plasmas,” Physics of Plasmas, Vol. 8, 2001, p. 83842. [12] D. Kremp, Th. Bornath, M. Bonitz and M. Schlanges, “Quantum Kinetic Theory of Plasmas in Strong Laser Fields,” Physical Review E, Vol. 60, No. 4, 1999, pp. 4725-4732. doi:10.1103/PhysRevE.60.4725 [13] M. Leontovich, “On a Method for Solving the Problem of Electromagnetic Wave Propagation along the Earth Surface,” Lzv. Akad. Nauk SSSR. Ser. Fiz, Vol. 8, 1994, pp. 16-22. [14] G. Agrawal, “Nonlinear Fiber Optics,” Academic Press, San Diego, 1995. [15] G. Manfredi and F. Haas, “Self-Consistent Fluid Model for a Quantum Electron Gas,” Physical Review B, Vol. 64, No. 7, 2001, Article ID: 075316, p 7. doi:10.1103/PhysRevB.64.075316 [16] G. Manfredi, “How to Model Quantum Plasmas,” Fields Institute Communications Series, Vol. 46, 2005, pp. 263-287. [17] G. Gardner, “The Quantum Hydrodynamic Model for Semiconductor Devices,” SIAM Journal on Applied Mathematics, Vol. 54, No. 2, 1994, pp. 409-427. doi:10.1137/S0036139992240425 [18] F.Haas, G. Manfredi and M. Feix, “Multistream Model for Quantum Plasmas,” Physical Review E, Vol. 62, No. 2, 2000, pp. 2763-2772. doi:10.1103/PhysRevE.62.2763 [19] B. Eliasson and P. K. Shukla, “Dispersion Properties of Electrostatic Oscillations in Quantum Plasmas,” Journal of Plasma Physics, Vol. 76, No. 1, 2010, pp. 7-17. doi:10.1017/S0022377809990316 [20] J. H. Jeans, “Astronomy and Cosmogony,” Cambridge University Press, Cambridge, 2009. [21] B. Vitaly, M. Marklund and M. Modestov, “The Rayleigh-Taylor Instability and Internal Waves in Quantum Plasmas,” Physics Letters A, Vol. 372, No. 17, 2008, pp. 3042-3045. doi:10.1016/j.physleta.2007.12.065 [22] J. T. Cao, H. J. Ren, Z. W. Wu and P. K. Chu, “Quantum Effects on Rayleigh-Taylor Instability in Magnetized Plasma,” Physics of Plasmas, Vol. 15, No. 1, 2008, Article ID: 012110. doi:10.1063/1.2833588 [23] G. A. Hoshoudy, “Quantum Effects on Rayleigh-Taylor Instability of Incompressible Plasma in a Vertical Magnetic Field,” Chinese Physics Letters, Vol. 27, No. 12, 2010, Article ID: 125201. doi:10.1088/0256-307X/27/12/125201 [24] G. A. Hoshoudy, “Rayleigh-Taylor Instability in Quantum Magnetized Viscous Plasma,” Plasma Physics Reports, Vol. 37, No. 9, 2011, pp. 775-784. doi:10.1134/S1063780X11080046 [25] G. A. Hoshoudy, “Quantum Effects on Rayleigh-Taylor Instability in a Vertical Inhomogeneous Rotating Plasma,” Physics of Plasmas, Vol. 16, No. 2, 2009, Article ID: 024501, p 4. doi:10.1063/1.3080202 [26] G. A. Hoshoudy, “Quantum Effects on Rayleigh-Taylor Instability in a Horizontal Inhomogeneous Rotating Plasma,” Physics of Plasmas, Vol. 16, No. 6, 2009, Article ID: 064501, p 4. [27] M. Modestov, V. Bychkov and M. Marklund, “The Rayleigh-Taylor Instability in Quantum Magnetized Plasma with Para- and Ferromagnetic Properties,” Physics of Plasmas, Vol. 16, No. 3, 2009, Article ID: 032106, p 12. doi:10.1063/1.3085796 [28] G. A. Hoshoudy, “Quantum Effects on the Rayleigh-Taylor Instability of Stratified Fluid/Plasma through Porous Media,” Physics Letters A, Vol. 373, No. 30, 2009, pp. 2560-2567. [29] G. A. Hoshoudy, “Quantum Effects on the Rayleigh- Taylor Instability of Stratified Fluid/Plasma through Brinkman Porous Media,” Journal of Porous Media, Vol. 15, No. 4, 2012, pp. 373-381. doi:10.1615/JPorMedia.v15.i4.50 [30] S. Ali, Z. Ahmed, M. Arshad Mirza and I. Ahmad, “Rayleigh-Taylor/Gravitational Instability in Dense Magnetoplasmas,” Physics Letters A, Vol. 373, No. 33, 2009, pp. 2940-2946. doi:10.1016/j.physleta.2009.06.021