Hidden problems of thin-flux-tube approximation

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 sur face waves for C-T(2)>C-Ae(2), body waves for C-Te(2)>C-T(2) and surface le aky waves for C-Te(2)<C-T(2)<C-Ae(2). The Leibovich-Roberts equation for no nlinear surface waves in a flux tube embedded in a field free plasma is gen eralized to a flux tube immersed in a magnetic plasma. The generalized Leib ovich-Roberts (GLR) equation describes the propagation of nonlinear slow su rface, body and surface leaky waves in tubes. The shortcomings of the GLR e quation are discussed. The Korteweg-de Vries equation (KdV) is generalized for surface waves. The advantage of the second order thin-flux-tube approxi mation is shown. Two scenarios for the heating of coronal loops are discuss ed. It is emphasized, that the application of the thin-flux-tube approximat ion to thin tubes of non-zero diameter has to take into account possible wa ve emission by the tube and shock front formation for amplitudes in excess of some critical value.