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Issue A&A
Volume 377, Number 1, October I 2001
Page(s) 330 - 342
Section The Sun
DOI http://dx.doi.org/10.1051/0004-6361:20011094



A&A 377, 330-342 (2001)
DOI: 10.1051/0004-6361:20011094

Hidden problems of thin-flux-tube approximation

Y. D. Zhugzhda1, 2 and M. Goossens1

1  Center for Plasma Astrophysics, K.U. Leuven, 3001 Heverlee, Belgium
2  IZMIRAN, Troitsk, Moscow Region, 142092, Russia

(Received 9 November 2000 / Accepted 31 July 2001)

Abstract
This paper scrutinizes the validity of the thin-flux-tube approximation for magnetic flux tubes embedded in a surrounding magnetic plasma. It is shown that the thin-flux-tube approximation gives an accurate description of surface waves for $C_{\rm T}^2> C_{\rm Ae}^2$, body waves for $C_{\rm Te}^2> C_{\rm T}^2$ and surface leaky waves for $C_{\rm Te}^2< C_{\rm T}^2 < C_{\rm Ae}^2$. The Leibovich-Roberts equation for nonlinear surface waves in a flux tube embedded in a field free plasma is generalized to a flux tube immersed in a magnetic plasma. The generalized Leibovich-Roberts (GLR) equation describes the propagation of nonlinear slow surface, body and surface leaky waves in tubes. The shortcomings of the GLR equation are discussed. The Korteweg-de Vries equation (KdV) is generalized for surface waves. The advantage of the second order thin-flux-tube approximation is shown. Two scenarios for the heating of coronal loops are discussed. It is emphasized, that the application of the thin-flux-tube approximation to thin tubes of non-zero diameter has to take into account possible wave emission by the tube and shock front formation for amplitudes in excess of some critical value.


Key words: agnetohydrodynamics (MHD) -- waves -- Sun: corona -- oscillations

Offprint request: Y. Zhugzhda, yvzef@coot.kis.uni-freiburg.de




© ESO 2001


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