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Effect of viscosity on propagation of MHD waves in astrophysical plasma

Published online by Cambridge University Press:  25 January 2013

ALEMAYEHU MENGESHA
Affiliation:
Department of Physics, Bule Hora University, PO Box 144, Bule Hora, Ethiopia ([email protected]) Department of Physics, Kotebe College, PO Box 31248, Addis Ababa, Ethiopia Entoto Astronomical Observatory and Space Science Research Center, PO Box 8412, Addis Ababa, Ethiopia
S. B. TESSEMA
Affiliation:
Department of Physics, Kotebe College, PO Box 31248, Addis Ababa, Ethiopia Entoto Astronomical Observatory and Space Science Research Center, PO Box 8412, Addis Ababa, Ethiopia

Abstract

We determine the general dispersion relation for the propagation of magnetohydrodynamic (MHD) waves in an astrophysical plasma by considering the effect of viscosity with an anisotropic pressure tensor. Basic MHD equations have been derived and linearized by the method of perturbation to develop the general form of the dispersion relation equation. Our result indicates that an astrophysical plasma with an anisotropic pressure tensor is stable in the presence of viscosity and a strong magnetic field at considerable wavelength.

Type
Papers
Copyright
Copyright © Cambridge University Press 2013 

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References

Abraham-Shrauner, B. 1967 Propagation of hydromagnetic waves through an anisotropic plasma. J. Plasma Phys. 1, 361378.CrossRefGoogle Scholar
Axelsson, P. 1998 Three wave coupling in a stratified MHD plasma. Nonlinear Process Geophys. 5, 105110.CrossRefGoogle Scholar
Balbus, S. A. 2004 Viscous shear instability in weakly magnetized, dilute plasmas. Astrophys. J. 616, 857864.CrossRefGoogle Scholar
Balbus, S. A. and Hawley, J. F. 1991 A powerful local shear instability in weakly magnetized discs. Astrophys. J. 376, 214226.CrossRefGoogle Scholar
Ballai, I. and Marcu, A. 2004 The effect of anisotropy on the propagation of linear compressional waves in magnetic flux tubes. Astron. Astrophys. 415, 691–703.CrossRefGoogle Scholar
Ballai, I. and Roberts, B. 2002 Ducted compressional waves in the magnetosphere in the double-polytropic approximation. Ann. Geophys. 20, 15531558.CrossRefGoogle Scholar
Brodin, G. and Stenflo, L. 1989 Three wave coupling coef- ficients for magnetized plasmas with pressure anisotropy. J. Plasma Phys. 41, 199208.CrossRefGoogle Scholar
Campos, L. M. B. C. and Mendes, P. M. V. M. 2000 On the effect of viscosity and anisotropic resistivity on the damping of Alfvén waves. Plasma Phys. 63, 221238.CrossRefGoogle Scholar
Chandra, S. and Kumthekar, B. K. 2010 Propagation of MHD waves in homogeneous plasma. Open Astron. J. 3, 711.CrossRefGoogle Scholar
Erdelyi, R. and Goossens, M. 1994 Viscous computations of resonant absorption of MHD waves in flux tubes by FEM. Astron. Astrophys. 213, 273298.Google Scholar
Erdelyi, R. and Goossens, M. 1995 Resonant absorption of Alfvén waves in coronal loops i visco-resistive MHD. Astron. Astrophys. 294, 575586.Google Scholar
Kumar, N. and Singh, S. 2006 Coronal heating by MHD waves. J. Astron. Astrophys. 453, 10671078.CrossRefGoogle Scholar
Mikhailovskii, A. B. and Lominadze, J. G. 2008 Magnetic instabilities in collisionless astrophysical rotating plasma with an isotropic pressure. J. Phys. Plasmas 15, 062904.CrossRefGoogle Scholar
Ofman, L. and Steinolfson, R. S. 1994 Coronal heating by the resonant absorption of Alfvén waves: the effect of viscous stress tensor. Astrophys. J. 421, 360371.CrossRefGoogle Scholar
Pandey, V. S. and Dwivedi, B. N. 2007 Dispersion relation for MHD waves in homogeneous plasma. Phil. Trans. R. Soc. Lond. 338, 325357.Google Scholar
Pinter, B. and Erdelyi, R. 1996 The linear spectrum of twisted magnetic flux tubes in viscous MHD. Astrophys. Lett. Commun. 34, 169174.Google Scholar
Porter, L. J. and Sturrock, A. 1994 The possible role of MHD waves in heating the solar corona. Astrophys. J. 435, 482501.CrossRefGoogle Scholar
Ren, H., Cao, J., Wu, Z. and Chu, P. K. 2011 Magnetorotational instability in a collisionless plasma with heat flux vector and an isotropic plasma with self-gravitational effect. J. Phys. Plasmas 18, 092117.CrossRefGoogle Scholar
Roberts, B. 1981a Wave propagation in a magnetically structured atmosphere. Sol. Phys. 69, 2738.CrossRefGoogle Scholar
Roberts, B. 1981b Wave propagation in a magnetically structured atmosphere. Sol. Phys. 69, 3956.CrossRefGoogle Scholar
Rosin, M. S. and Schekochihin, A. A. 2011 A non-linear theory of the parallel firehose and gyrothermal instabilities in a weakly collisional plasma. Mon. Not. R. Astron. Soc. 413, 13652966.CrossRefGoogle Scholar
Ruderman, M. S. and Goossens, M. 1996 Dissipative instability of the MHD tangential discontinuity in magnetised plasmas with anisotropic viscosity and thermal conductivity. Plasma Phys. 56, 285306.CrossRefGoogle Scholar
Runderman, M. S. and Oliver, R. 2000 Slow surface wave damping in plasmas with anisotropic viscosity and thermal conductivity. Astron. Astrophys. 354, 261276.Google Scholar
Schoeffler, K. M., Drake, J. F. and Swisdak, M. 2011 The effects of plasma beta and anisotropy instabilities on the dynamics of reconnecting magnetic fields in the heliosheath. Astrophys. J. 743, 7077.CrossRefGoogle Scholar
Tessema, S. B. 2011 Accretion Discs around Magnetized Stars, in Particular Neutron Stars. Germany: Lap Lambert Academic Publishing, p. 13.Google Scholar
Tessema, S. B. and Torkelsson, U. 2010 The structure of thin accretion discs around magnetized stars. J. Astron. Astrophys. 509, A45.CrossRefGoogle Scholar