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The scattering of $f$- and $p$-modes from ensembles of thin magnetic flux tubes - An analytical approach

Motivated by the observational results of Braun (1995), we extend the model of Hanson & Cally (2014) to address the effect of multiple scattering of f and p-modes by an ensemble of thin vertical magnetic flux tubes in the surface layers of the Sun. As in observational Hankel analysis we measure the scatter and phase shift from an incident cylindrical wave in a coordinate system roughly centred in the core of the ensemble. It is demonstrated that, although thin flux tubes are unable to interact with high order fluting modes individually, they can indirectly absorb energy from these waves through the scatters of kink and sausage components. It is also shown how the distribution of absorption and phase shift across the azimuthal order m depends strongly on the tube position, as well as on the individual tube characteristics. This is the first analytical study into an ensembles multiple scattering regime, that is embedded within a stratified atmosphere.