The phase mixing of Alfven waves, coordinated modes, and coronal heating

Phase mixing has been a popular theoretical mechanism invoked to dissipate the photospheric plane shear Alfven waves hypothesized to penetrate up into the coronal hole and solar wind, thereby maintaining the expanding coronal gas at 1.5 million K and serving as the principal energy source for the solar wind. However, phase mixing requires an ignorable coordinate, which is not available in the presumably filamentary coronal hole. The filamentary density and temperature of the coronal hole couple the waves into a coordinated mode with a unique phase velocity omega/k, which provides the other popular theoretical mechanism, viz, resonant absorption where the local Alfven speed C is equal to omega/k. This provides coronal heating at radial distances O(10 solar radii), where it serves to accelerate the solar wind to high velocity. But it does not provide the principal heat input in the first 1-2 solar radii, required by Withbroe's (1988) analysis of the observed structure of the coronal hole.