Heating of coronal holes by phase mixing.

A two-dimensional, analytical, self-similar solution to the Alfven wave phase mixing equations is presented for a coronal hole model. The solution shows clearly that the damping of the waves with height follows the scaling predicted by Heyvaerts & Priest 1983 at low heights, before switching to an algebraic decay at large heights. The ohmic dissipation is calculated and it is shown that the maximum dissipation occurs at a height that scales with eta(1/3). However, the total Ohmic dissipation is, of course, independent of the resistivity. Using realistic solar parameters it appears that phase mixing is a viable mechanism for heating the lower corona provided either the frequency of photospheric motions is sufficiently large or the background Alfven velocity is sufficiently small.