Dissipative MHD solutions for resonant Alfven waves in 1-dimensional magnetic flux tubes

Details Dissipative MHD solutions for resonant Alfven waves in 1-dimensional magnetic flux tubes Dissipative MHD solutions for resonant Alfven waves in 1-dimensional magnetic flux tubes

Mar 1995

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995soph..157...75g&link_type=abstract

Solar Physics (ISSN 0038-0938), vol. 157, no. 1-2, p. 75-102

Physics

127

Dissipation, Magnetic Flux, Magnetohydrodynamic Waves, Magnetohydrodynamics, Mathematical Models, Resonance, Solar Physics, Linear Equations, Magnetic Field Configurations, Resonant Frequencies, Sun

Scientific paper

The present paper extends the analysis by Sakurai, Goossens, and Hollweg (1991) on resonant Alfven waves in nonuniform magnetic flux tubes. It proves that the fundamental conservation law for resonant Alfven waves found in ideal MHD by Sakurai, Goossens, and Hollweg remains valid in dissipative MHD. This guarantees that the jump conditions of Sakurai, Goossens, and Hollweg, that connect the ideal MHD solutions for xir, and P' across the dissipative layer, are correct. In addition, the present paper replaces the complicated dissipative MHD solutions obtained by Sakurai, Goossens, and Hollweg for xir, and P' in terms of double integrals of Hankel functions of complex argument of order 1/3 with compact analytical solutions that allow a straight- forward mathematical and physical interpretation. Finally, it presents an analytical dissipative MHD solution for the component of the Lagrangian displacement in the magnetic surfaces perpen- dicular to the magnetic field lines xiperpendicular which enables us to determine the dominant dynamics of resonant Alfven waves in dissipative MHD.

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