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This paper considers turbulent damping of Alfven waves in magnetized plasmas.We identify two cases of damping, one related to damping of cosmic raysstreaming instability, the other related to damping of Alfven waves emitted bya macroscopic wave source, e.g. stellar atmosphere. The physical differencebetween the two cases is that in the former case the generated waves areemitted in respect to the local direction of magnetic field, in the latter inrespect to the mean field. The scaling of damping is different in the twocases. We the regimes of turbulence ranging from subAlfvenic to superAlfvenicwe obtain analytical expressions for the damping rates and define the ranges ofapplicability of these expressions. Describing the damping of the streaminginstability, we find that for subAlfvenic turbulence the range of cosmic rayenergies influenced by weak turbulence is unproportionally large compared tothe range of scales that the weak turbulence is present. On the contrary, therange of cosmic ray energies affected by strong Alfvenic turbulence is ratherlimited. A number of astrophysical applications of the process ranging fromlaunching of stellar and galactic winds to propagation of cosmic rays ingalaxies and clusters of galaxies is considered. In particular, we discuss howto reconcile the process of turbulent damping with the observed isotropy of theMilky Way cosmic rays.

Damping of Alfven waves by Turbulence and its Consequences: from Cosmic-Rays Streaming to Launching Winds