Nonlinear wave propagation along a magnetic flux tube

Abstract

The weakly nonlinear wave propagation of a slow sausage surface wave traveling along a magnetized slab with a thin nonuniform boundary layer is considered. The ideal incompressible MHD equations are used and the nonlinearities are assumed to be due to second harmonic generation. A nonlinear dispersion relation and the related nonlinear Schrodinger equation is derived. The existence of a continuous thin interface leads to sharply peaked field amplitudes due to resonant interaction with local Alfven waves. It is shown that the nonlinear effects from processes within the thin layer are much more important than those from the main slab. Furthermore, the nonlinear interaction with local Alfven waves yields a nonlinear damping rate of the wave that is much larger than the linear damping rate when the transition layer is sufficiently thin.