Many different types of oscillations have been observed in the Sun's atmosphere. Many of these waves are associated wiith magnetic field structures, such as coronal loops or prominences. Others are global modes which propagate over the entire disc.
Alfven waves are a type of MHD wave. Due to the long range EM presence in plasmas, they are able to support waves. MHD waves are pertubations in MHD equilibria. In MHD, the plasma is treated as a single fluid permeated by a magnetic field. The magnetic field acts on the motion of the plasma by the Lorenntz force (jXB). Thus action can be split into magnetic pressure and magnetic tension. Alfven waves are analogous to waves on a string, where they energy is carried along magnetic field lines, and the restoring force is the magnetic tension.
The observational evidence of Alfven waves is limited, but Alfven disturbances, i.e. disturbances paerpendicular to the diirection of propagation and magnetic field, have been observed in the solar wind. Indeed Alfven waves are thought to be drivers of the solar wind. Alfvenic disturbances have also been observed at lower heights in the atmosphere.
It is thought that Alfven waves of a wide range of frequencies can be generated at the surface by granular motions. These perturbations can then propagate up open magnetic field structures into the atmosphere, and deposit energy by damping.
I have been looking at a specific damping mechanism of Alfven waves in open magnetic field structures, which is related to the partially ionised photosphere and chromosphere. Using MHD simulations I have estimated the efficiency of damping for wide spectra of Alfven waves propagating upwards into the corona.