  We study the conversion of fast magneto-acoustic waves to Alfven waves by
means of 2.5D numerical simulations in a sunspot-like magnetic configuration. A
fast, essentially acoustic, wave of a given frequency and wave number is
generated below the surface and propagates upward though the Alfven/acoustic
equipartition layer where it splits into upgoing slow (acoustic) and fast
(magnetic) waves. The fast wave quickly reflects off the steep Alfven speed
gradient, but around and above this reflection height it partially converts to
Alfven waves, depending on the local relative inclinations of the background
magnetic field and the wavevector. To measure the efficiency of this conversion
to Alfven waves we calculate acoustic and magnetic energy fluxes. The
particular amplitude and phase relations between the magnetic field and
velocity oscillations help us to demonstrate that the waves produced are indeed
Alfven waves. We find that the conversion to Alfven waves is particularly
important for strongly inclined fields like those existing in sunspot
penumbrae. Equally important is the magnetic field orientation with respect to
the vertical plane of wave propagation, which we refer to as "field azimuth".
For field azimuth less than 90 degrees the generated Alfven waves continue
upwards, but above 90 degrees downgoing Alfven waves are preferentially
produced. This yields negative Alfven energy flux for azimuths between 90 and
180 degrees. Alfven energy fluxes may be comparable to or exceed acoustic
fluxes, depending upon geometry, though computational exigencies limit their
magnitude in our simulations.
