Heating of solar coronal holes by reflected Alfven waves

As a continuation of the work of Moore et al. (1991), who found evidence that coronal holes are heated by Alfven waves that are reflected back down within the coronal holes, this paper shows that to demonstrate this evidence, it is only necessary to consider a subset of the Moore et al. models, namely, those having radial magnetic field. Using these models, it is shown that the Alfven velocity is not constant in the atmosphere of coronal holes, but changes with height (or radius), causing downward reflection of all upward Alfven waves of sufficiently long wavelength (or period).