Non-linear spherical Alfvén waves

We present a one-dimensional numerical study of Alfvén waves propagating along a radial magnetic field. Neglecting losses, any spherical Alfvén wave, no matter how small its initial amplitude is, becomes non-linear at sufficiently large radii. From previous simulations of Alfvén waves in plane-parallel atmospheres we expected the waves to steepen and produce current sheets in the non-linear regime, which was confirmed by our new calculations. On the other hand we found that even the least non-linear waves were damped out almost completely before 10 R_⊙. A damping of that kind is required by models of Alfvén wave driven winds from old low-mass stars as these winds are mainly accelerated within a few stellar radii.