NUMERICAL SIMULATIONS OF CONVERSION TO ALFVEN WAVES IN SUNSPOTS

We study the conversion of fast magnetoacoustic 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 through 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 a field azimuth less than 90 degrees the generated Alfven waves continue upward, but above 90 degrees downgoing Alfven waves are preferentially produced. This yields negative Alfven energy flux for azimuths between 90 degrees 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.