Dynamical response of magnetic tubes to transverse perturbations I. Thick flux tubes

By means of a 3D numerical code we investigate the response of magnetic flux tubes to transverse perturbations. Various tubes with plasma β ranging from 0.1 to 10 embedded in a uniform nonmagnetic atmosphere are considered. High spatial resolution was obtained by the application of a multiple nested grid strategy. Various kinds of internal longitudinal and transverse body waves as well as surface waves were found in addition to the external sound wave. A great advantage of our 3D treatment is that it allows to treat energy leakage and mode conversion. We investigated the efficiency of wave energy leakage from the magnetic tube to the external medium and found leakage rates ranging from 0.07 for the β = 10 tube to 0.43 for the β = 0.1 tube. This shows that leakage is an important process particularly for low β tubes and should not be ignored in studies of transverse wave propagation. As already found in 1D calculations, the purely transverse excitation generates longitudinal body waves of twice the frequency. This mode conversion process is not very efficient. A very important result of our computations, however, is the efficient generation of a non-axisymmetric longitudinal body wave which does not derive from magnetic tension forces, but is due to an inertial pile-up effect inside the tube produced by the transverse motions. Particularly in low β-tubes, the mode conversion rate for the longitudinal waves was found to be as large as 90% of the total kinetic tube energy most of it is going into the surface wave. This may be very significant for the heating of flux tubes and thus for the chromospheric and coronal heating.