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 sho w that if the potential well is time dependent, then ions which are initial ly trapped will undergo a time-averaged energy gain. They can eventually ga in 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 b y reflections off of moving magnetic clouds, except here the trapped ions c an be regarded as reflecting off of moving walls. There is evidence that th e trajectories of the particles are chaotic. However, the timescales are lo ng, 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 w aves which are propagating outward from the Sun. These particles are the on es which can interact most strongly with ion cyclotron waves, since they re sonate with the lowest frequency waves which have the highest phase speeds and presumably the most power. We present some simple arguments, invoking e nergy-conserving pitch angle scattering in the wave frame, which show how O 5+ 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 signific ant differences between the model results and the SOHO/UVCS data. In this c ase the particles are not trapped in a potential well.