We present a measurement of the energy carried and dissipated by Alfven waves in a polar coronal hole. Alfven waves have been proposed as the energy source that heats the corona and drives the solar wind. Previous work has shown that line widths decrease with height in coronal holes, which is a signature of wave damping, but have been unable to quantify the energy lost by the waves. This is because line widths depend on both the non-thermal velocity v_nt and the ion temperature T_i. We have implemented a means to separate the T_i and v_nt contributions using the observation that at low heights the waves are undamped and the ion temperatures do not change with height. This enables us to determine the amount of energy carried by the waves at low heights, which is proportional to v_nt. We find the initial energy flux density present was 6.7 +/- 0.7 x 10^5 erg cm^-2 s^-1, which is sufficient to heat the coronal hole and acccelerate the solar wind during the 2007 - 2009 solar minimum. Additionally, we find that about 85% of this energy is dissipated below 1.5 R_sun, sufficiently low that thermal conduction can transport the energy throughout the coronal hole, heating it and driving the fast solar wind. The remaining energy is roughly consistent with what models show is needed to provide the extended heating above the sonic point for the fast solar wind. We have also studied T_i, which we found to be in the range of 1 - 2 MK, depending on the ion species.
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