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Nonlinear theory of non-axisymmetric resonant slow waves in straight magnetic flux tubes

Ballai, I., Erdélyi, R. and Goossens, M. (2000) Nonlinear theory of non-axisymmetric resonant slow waves in straight magnetic flux tubes. Journal of Plasma Physics, 64 (5). pp. 579-599. ISSN 0022-3778


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Nonlinear resonant slow magnetohydrodynamic (MHD) waves are studied in weakly dissipative isotropic plasmas for a cylindrical equilibrium model. The equilibrium magnetic field lines are unidirectional and parallel with the z axis. The nonlinear governing equations for resonant slow magnetoacoustic (SMA) waves are derived. Using the method of matched asymptotic expansions inside and outside the narrow dissipative layer, we generalize the connection formulae for the Eulerian perturbation of the total pressure and for the normal component of the velocity.

These nonlinear connection formulae in dissipative cylindrical MHD are an important extention of the connection formulae obtained in linear ideal MHD [Sakurai et al., Solar Phys. 133, 227 (1991)], linear dissipative MHD [Goossens et al., Solar Phys. 175, 75 (1995); Erdélyi, Solar Phys. 171, 49 (1997)] and in nonlinear dissipative MHD derived in slab geometry [Ruderman et al., Phys. Plasmas4, 75 (1997)]. These generalized connection formulae enable us to connect the solutions at both sides of the dissipative layer without solving the MHD equations in the dissipative layer. We also show that the nonlinear interaction of harmonics in the dissipative layer is responsible for generating a parallel mean flow outside the dissipative layer.

Item Type: Article
Copyright, Publisher and Additional Information: © 2000 Cambridge University Press
Institution: The University of Sheffield
Academic Units: The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield)
Depositing User: Repository Assistant
Date Deposited: 14 Sep 2006
Last Modified: 16 Nov 2015 20:52
Published Version: http://journals.cambridge.org/action/displayIssue?...
Status: Published
Publisher: Cambridge University Press
Refereed: Yes
URI: http://eprints.whiterose.ac.uk/id/eprint/1574

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