Rayleigh-Taylor Instability in Magnetized Plasma

Affiliation(s)

Department of Applied Mathematics and Computer Science, Faculty of Science, South Valley University, Kena, Egypt.

Department of Applied Mathematics and Computer Science, Faculty of Science, South Valley University, Kena, Egypt.

ABSTRACT

The Rayleigh-Taylor instability in stratified plasma has been
investigated in the presence of combined effect of horizontal and vertical
magnetic field. The linear growth rate has been derived for the case where
plasma with exponential density distribution is confined between two rigid
planes by solving the linear MHD equations into normal mode. Some special cases
have been particularized to explain the roles the variables of the problem play;
numerical solutions have been made and some stability diagrams are plotted and
discussed. The results show that, the growth rate depends on the horizontal and
vertical components of magnetic field and also depends on the parameter *λ*^{*}=*λ**L*_{D} (*λ* is constant and *L*_{D} is the
density-scale length). The maximum instability happens at *λ*^{*}=-0.5 and to get more stability model we select *λ*^{*} such that it is different than *λ*^{*}=-0.5. The
vertical magnetic field component have a greater effect than the horizontal
magnetic field component in the case of large wavelength, while in the case of
short wavelength, the horizontal magnetic field components have
greater effect than the vertical magnetic field component.

Cite this paper

Hoshoudy, G. (2014) Rayleigh-Taylor Instability in Magnetized Plasma.*World Journal of Mechanics*, **4**, 260-272. doi: 10.4236/wjm.2014.48027.

Hoshoudy, G. (2014) Rayleigh-Taylor Instability in Magnetized Plasma.

References

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[2] Taylor, G.I. (1950) The Instability of Liquid Surfaces When Accelerated in a Direction Perpendicular to Their Planes. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 201, 192-196.

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http://dx.doi.org/10.1103/PhysRevLett.73.2700

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http://dx.doi.org/10.1063/1.871025

[5] Cabot, W.H. and Cook, A.W. (2006) Reynolds Number Effects on Rayleigh-Taylor Instability with Possible Implications for Type-Ia Supernovae. Nature Physics, 2, 562-568.

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http://dx.doi.org/10.1086/171746

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[11] Bhatia, P.K. (1974) Rayleigh-Taylor Instability of a Viscous Compressible Plasma of Variable Density. Astrophysics and Space Science, 26, 319-325.

http://dx.doi.org/10.1007/BF00645614

[12] Shivamoggi, B.k. (1981) Rayleigh-Taylor Instability of Compressible Plasma in a Vertical Magnetic Field. Astrophysics and Space Science, 79, 3-9.

http://dx.doi.org/10.1007/BF00655900

[13] Ariel, P.D. (1991) Rayleigh-Taylor Instability of a Hall Plasma with Arbitrary Density Gradient. Astrophysics and Space Science, 184, 205-219.

[14] Ali, A. and Bhatia P.K. (1993) Rayleigh-Taylor Instability of a Stratified Hall Plasma in Two-Dimensional Horizontal Magnetic Field. Physica Scripta, 47, 567-570.

http://dx.doi.org/10.1088/0031-8949/47/4/016

[15] Khan, A. and Bhatia, P.K. (1993) Rayleigh-Taylor Instability of a Finitely Conducting Partially Ionized Hall Plasma. Physica Scripta, 48, 607-611.

http://dx.doi.org/10.1088/0031-8949/48/5/017

[16] Wu, Z., Zhang, W., Li, D. and Yang. W. (2004) Effect of Magnetic Field and Equilibrium Flow on Rayleigh-Taylor Instability. Chinese Physics Letters, 21, 2001-2004.

[17] Cao, J.T., Ren, H.J., Wu, Z.W. and Chu, P.K. (2008) Quantum Effects on Rayleigh-Taylor Instability in Magnetized Plasma. Physics of Plasmas, 15, 012110.

http://dx.doi.org/10.1063/1.2833588

[18] Hoshoudy, G.A. (2010) Quantum Effects on Rayleigh-Taylor Instability of Incompressible Plasma in a Vertical Magnetic Field. Chinese Physics Letters, 27, 125201.

http://dx.doi.org/10.1088/0256-307X/27/12/125201

[19] Hoshoudy, G.H. (2011) Rayleigh-Taylor Instability in Quantum Magnetized Viscous Plasma. Plasma Physics Reports, 37, 775-784.

http://dx.doi.org/10.1134/S1063780X11080046

[20] Yang, B.L., Wang, L.F., Ye, W.H. and Xue, C. (2011) Magnetic Field Gradient Effects on Rayleigh-Taylor Instability with Continuous Magnetic Field and Density Profiles. Physics of Plasmas, 18, 072111.

http://dx.doi.org/10.1063/1.3609773

[21] Wang, L.F., Yang, B.L., Ye, W.H. and He, X.T. (2012) Stabilization of the Rayleigh-Taylor Instability in Quantum Magnetized Plasmas. Physics of Plasmas, 19, 072704.

http://dx.doi.org/10.1063/1.4737162

[1] Rayleigh, L. (1882) Investigation of the Character of the Equilibrium of an Incompressible Heavy Fluid of Variable Density. Proceedings of the London Mathematical Society, 14, 170-177.

[2] Taylor, G.I. (1950) The Instability of Liquid Surfaces When Accelerated in a Direction Perpendicular to Their Planes. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 201, 192-196.

[3] Sanz, J. (1994) Self-Consistent Analytical Model of the Rayleigh-Taylor Instability in Inertial Confinement Fusion. Physical Review Letters, 73, 2700-2703.

http://dx.doi.org/10.1103/PhysRevLett.73.2700

[4] Lindl, J.D. (1995) Development of the Indirect-Drive Approach to Inertial Confinement Fusion and the Target Physics Basis for Ignition and Gain. Physics of Plasmas, 2, 3933.

http://dx.doi.org/10.1063/1.871025

[5] Cabot, W.H. and Cook, A.W. (2006) Reynolds Number Effects on Rayleigh-Taylor Instability with Possible Implications for Type-Ia Supernovae. Nature Physics, 2, 562-568.

[6] Timmes, F.X. and Woosley, S.E. (1992) The Conductive Propagation of Nuclear Flames. I - Degenerate C + O and O + NE + MG White Dwarfs. Astrophysical Journal, 396, 649-667.

http://dx.doi.org/10.1086/171746

[7] Blinnikov, S. and Sorokina, E. (2004) Type Ia Supernova Models: Latest Developments. Astrophysics and Space Science, 290, 13-28.

http://dx.doi.org/10.1023/B:ASTR.0000022161.03559.42

[8] Chen, F.F. (1974) Introduction to Plasma Physics. Plenum, New York.

[9] Goldston, R.J. and Rutherford, P.H. (1997) Introduction to Plasma Physics. Institute of Physics, London.

[10] Ariel, P.D. (1971) Rayleigh-Taylor Instability of Compressible Fluids in the Presence of a Vertical Magnetic Field. Applied Scientific Research, 24, 294-304.

[11] Bhatia, P.K. (1974) Rayleigh-Taylor Instability of a Viscous Compressible Plasma of Variable Density. Astrophysics and Space Science, 26, 319-325.

http://dx.doi.org/10.1007/BF00645614

[12] Shivamoggi, B.k. (1981) Rayleigh-Taylor Instability of Compressible Plasma in a Vertical Magnetic Field. Astrophysics and Space Science, 79, 3-9.

http://dx.doi.org/10.1007/BF00655900

[13] Ariel, P.D. (1991) Rayleigh-Taylor Instability of a Hall Plasma with Arbitrary Density Gradient. Astrophysics and Space Science, 184, 205-219.

[14] Ali, A. and Bhatia P.K. (1993) Rayleigh-Taylor Instability of a Stratified Hall Plasma in Two-Dimensional Horizontal Magnetic Field. Physica Scripta, 47, 567-570.

http://dx.doi.org/10.1088/0031-8949/47/4/016

[15] Khan, A. and Bhatia, P.K. (1993) Rayleigh-Taylor Instability of a Finitely Conducting Partially Ionized Hall Plasma. Physica Scripta, 48, 607-611.

http://dx.doi.org/10.1088/0031-8949/48/5/017

[16] Wu, Z., Zhang, W., Li, D. and Yang. W. (2004) Effect of Magnetic Field and Equilibrium Flow on Rayleigh-Taylor Instability. Chinese Physics Letters, 21, 2001-2004.

[17] Cao, J.T., Ren, H.J., Wu, Z.W. and Chu, P.K. (2008) Quantum Effects on Rayleigh-Taylor Instability in Magnetized Plasma. Physics of Plasmas, 15, 012110.

http://dx.doi.org/10.1063/1.2833588

[18] Hoshoudy, G.A. (2010) Quantum Effects on Rayleigh-Taylor Instability of Incompressible Plasma in a Vertical Magnetic Field. Chinese Physics Letters, 27, 125201.

http://dx.doi.org/10.1088/0256-307X/27/12/125201

[19] Hoshoudy, G.H. (2011) Rayleigh-Taylor Instability in Quantum Magnetized Viscous Plasma. Plasma Physics Reports, 37, 775-784.

http://dx.doi.org/10.1134/S1063780X11080046

[20] Yang, B.L., Wang, L.F., Ye, W.H. and Xue, C. (2011) Magnetic Field Gradient Effects on Rayleigh-Taylor Instability with Continuous Magnetic Field and Density Profiles. Physics of Plasmas, 18, 072111.

http://dx.doi.org/10.1063/1.3609773

[21] Wang, L.F., Yang, B.L., Ye, W.H. and He, X.T. (2012) Stabilization of the Rayleigh-Taylor Instability in Quantum Magnetized Plasmas. Physics of Plasmas, 19, 072704.

http://dx.doi.org/10.1063/1.4737162