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The dispersion relation for the propagation of viscous Alfvén surface waves along viscous plasma-plasma interface has been derived. Two modes of Alfvén surface waves are found to propagate with their characteristics depend on the interface parameters like magnetic field, density ratio, viscosity….etc. The viscous damping of Alfvén surface waves has been studied in the astrophysical point of view. The damping length of Alfvén surface waves due to viscosity in the solar atmosphere has been estimated.

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