  Here we investigate the contribution of surface Alfven wave damping to the
heating of the solar wind in minima conditions. These waves are present in
regions of strong inhomogeneities in density or magnetic field (e. g., the
border between open and closed magnetic field lines). Using a 3-dimensional
Magnetohydrodynamics (MHD) model, we calculate the surface Alfven wave damping
contribution between 1-4 solar radii, the region of interest for both
acceleration and coronal heating. We consider waves with frequencies lower than
those that are damped in the chromosphere and on the order of those dominating
the heliosphere. In the region between open and closed field lines, within a
few solar radii of the surface, no other major source of damping has been
suggested for the low frequency waves we consider here. This work is the first
to study surface Alfven waves in a 3D environment without assuming a priori a
geometry of field lines or magnetic and density profiles. We determine that
waves with frequencies >2.8x10^-4 Hz are damped between 1-4 solar radii. In
quiet sun regions, surface Alfven waves are damped at further distances
compared to active regions, thus carrying additional wave energy into the
corona. We compare the surface Alfven wave contribution to the heating by a
variable polytropic index and find that it an order of magnitude larger than
needed for quiet sun regions. For active regions the contribution to the
heating is twenty percent. As it has been argued that a variable gamma acts as
turbulence, our results indicate that surface Alfven wave damping is comparable
to turbulence in the lower corona. This damping mechanism should be included
self consistently as an energy driver for the wind in global MHD models.
