Chromospheric damping of Alfven waves

We analytically study the damping of Alfven mode oscillations in the chromo sphere and in coronal loops. In the partially ionized chromosphere the domi nant damping process of Alfven waves is due to collisions between ions and neutrals. We calculate the damping time for Alfven waves of a given frequen cy, propagating through model chromospheres of various solar structures suc h as active region plage, quiet sun, and the penumbra and umbra of sunspots . For a given wave frequency, the maximum damping always occurs at temperat ure minimum heights and in the coldest structure(s), i.e., the umbra of sun spots. Energy dissipation due to ion-neutral damping of Alfven waves with a n energy flux of 10(7) ergs cm(-3) s(-1) can play a considerable role in th e energy balance of umbrae, quiet sun, and plage for Alfven wave periods of the order, respectively, 50, 5, and 0.5 s. We also consider Alfven waves i n coronal loops and the leakage of wave energy through the footpoints. We a ssume a three-layer model of coronal loops with constant Alfven speed upsil on (A) (and no damping) in the corona, upsilon (A) varying exponentially wi th height in the dissipative chromosphere, and upsilon (V) again constant i n the photosphere at the end of the loop. We find an exact analytical solut ion in the chromospheric part. Using these solutions, we estimate the leaka ge of wave energy from the coronal volume through the footpoint regions of the loop and find that the presence of a moderate amount of chromospheric d amping can enhance the footpoint leakage. We apply this result to determine the damping time of standing waves in coronal loops. The enhanced footpoin t leakage also has implications for theories of coronal heating based on re sonant absorption. Finally, we find exact expressions for the damping of Al fven waves launched in the photosphere and upward propagating through the c hromosphere and into the corona. The partially ionized chromosphere present s an effective barrier for upward propagating waves with periods less than a few seconds.