Resonant Heating and Acceleration of Protons and Ions in Coronal Holes : Two-Proton Closure

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UVCS/SOHO has provided remarkable evidence that protons and heavy ions in coronal holes are heated by the ion-cyclotron resonance. We will review some of the basic physical principles governing the resonant interactions, emphasizing the difficulty that only about half of the protons can be in resonance with the ion-cyclotron mode. For quantitative results, we calculate the trajectories of individual protons and ions in the electric, magnetic, and gravitational fields, and we include the resonant heating and acceleration for the average particle which is diffusing in phase space. To provide closure we consider two protons, which are proxies for the resonant and non-resonant halves of the distribution. Elementary arguments show that the two protons tend to approach nearly the same radial velocity. When the waves are dispersive, this means that the resonant wavenumber, kres, increases. For a power spectrum which is a power law in wavenumber, and if the dissipation is determined only by the resonant particles, then the resonant effects become very weak as kres becomes large, and there is little heating or acceleration of the coronal plasma. On the other hand, if the dissipation is determined by a turbulent cascade, kres mainly controls the relative importance of resonant acceleration and resonant heating. Such models yield good agreement with what is known about the behavior of protons in coronal holes. We will also emphasize the importance of the UVCS/SOHO observations of Oxygen+5, whose temperature is still increasing after the proton temperature has leveled off. This provides an important constraint on the steepness of the power spectrum at the resonant wave numbers.

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