Potential wells, the cyclotron resonance, and ion heating in coronal holes

We consider the motions of protons and O5+ ions in coronal holes. We first consider the effects of a potential well, which arises from the combination of gravity, the electrostatic electric field, and the mirror force. We show that if the potential well is time dependent, then ions which are initially trapped will undergo a time-averaged energy gain. They can eventually gain enough energy to escape out of the potential well and be ejected out of the corona. The process is analogous to Fermi acceleration of cosmic rays by reflections off of moving magnetic clouds, except here the trapped ions can be regarded as reflecting off of moving walls. There is evidence that the trajectories of the particles are chaotic. However, the timescales are long, the potential wells are not very deep, and the; process is probably not important for coronal heating. We also point out that the potential wells can provide a population of particles which are moving inward relative to waves which are propagating outward from the Sun. These particles are the ones which can interact most strongly with ion cyclotron waves, since they resonate with the lowest frequency waves which have the highest phase speeds and presumably the most power. We present some simple arguments, invoking energy-conserving pitch angle scattering in the wave frame, which show how O5+ ions can in principle acquire perpendicular temperatures which are more than mass-proportionally hotter than the protons. The basic principles are demonstrated by calculating trajectories for average particles interacting with dispersive ion cyclotron waves. We also present a strongly driven case which gives perpendicular energies and parallel flow speeds qualitatively resembling those believed to exist in coronal holes, but there are significant differences between the model results and the SOHO/UVCS data. In this case the particles are not trapped in a potential well.