Randomly driven fast waves in coronal loops II. with coupling to Alfvén waves

We study the time evolution of fast magnetosonic and Alfvén waves in a coronal loop driven by random footpoint motions. The footpoint motions are assumed to be polarized normal to the magnetic flux surfaces in linear ideal MHD. De Groof et al. (1998) (Paper I) showed that the input energy is mainly stored in the body modes when the fast waves are decoupled from the Alfvén waves. Hence driving at the loop’s feet forms a good basis for resonant absorption as heating mechanism. In order to determine the efficiency of resonant absorption, we therefore study the energy transfer from the body modes to the resonant Alfvén waves in the case of coupling. We find that the growth of Alfvén mode energy depends on several parameters. Subsequently we check whether the necessary small lengthscales are created on a realistic time scale for the coronal loop. We find that Alfvén resonances are built up at the magnetic surfaces, where local Alfvén frequencies equal the quasimodes frequencies, on time scales comparable to the lifetime of the loop. Finally we conclude that a random footpoint driving can produce enough resonances to give rise to a globally heated coronal loop.