Kink Oscillations of Thin Magnetic Tubes with Discontinuous Density

Abstract

We consider kink oscillations of thin magnetic tubes with the equilibrium density discontinuous in the axial direction. The aim is to find out what boundary conditions have to be used at a contact discontinuity where the equilibrium density jumps. At a contact discontinuity perturbations of all quantities but the density have to be continuous. However, in the thin-tube approximation, all these conditions cannot be satisfied simultaneously. It is shown that in the thin-tube approximation, there is a boundary layer with the thickness of the order of the tube radius that embraces the contact discontinuity. In this boundary layer the variation of the loop displacement and its axial derivative is negligible. In contrast, the total pressure variation in the boundary layer is very strong. Hence, the correct boundary conditions at a contact discontinuity in the thin-tube approximation are the continuity of the tube displacement and its axial derivative.