Heating of coronal loops by phase-mixid shear Alfven waves

The dissipation of shear Alfven waves in a coronal loop driven externally by an incident wave in the subcoronal region is investigated. The phase mixing of these incident shear Alfven waves serves as the dissipation mechanism in the corona. The wave solution found by Heyvaerts and Priest (1983) for coronal holes is used to compute the total energy deposited in a loop. The energy deposited is shown to depend upon the magnetic diffusivity nu(m) and viscosity nu(v), contrary to the conclusion of authors who assumed that coronal loops are perfect resonators. The energy deposited in a three-layer model is computed for incident waves with periods of five minutes or five seconds. For a five-minute period, almost no energy is deposited, especially for small loops. For a five-second period, a substantial amount of energy is deposited in the loop, but not enough to account for the heating of small loops.