Hidden problems of thin-flux-tube approximation
Center for Plasma Astrophysics, K.U. Leuven, 3001 Heverlee, Belgium
2 IZMIRAN, Troitsk, Moscow Region, 142092, Russia
Corresponding author: Y. Zhugzhda, firstname.lastname@example.org
Accepted: 31 July 2001
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 , body waves for and surface leaky waves for . 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: Magnetohydrodynamics (MHD) / waves / Sun: atmosphere / Sun: general
© ESO, 2001