Heating in coronal funnels by ion cyclotron waves

Plasma heating by ion cyclotron waves in rapidly expanding flow tubes in the transition region, referred as coronal funnels, is investigated in a three-fluid plasma consisting of protons, electrons and alpha particles (α's). Ion cyclotron waves are able to produce a transition region and a hot corona over a distance range of 10⁴ km by directly heating alpha particles. Although only alpha particles dissipate the waves, protons and electrons can also be heated to about 10⁶ K due to Coulomb coupling. It is found that alpha particles can be much hotter and faster than protons. Beyond 1.02R_s, the particles return to thermal equilibrium when the electrons reach about 10⁶ K which is canonically defined as the base of the corona. These results lead to the following implications: (1) A transition region and corona may be energized by depositing energy to minor ions only. (2) If spectral lines formed at T_e < 10⁶ K are observed at different heights, the inferred outflow velocities may vary by a factor of 5 to 6. (3) If minor ions are indeed much faster than protons and electrons at T_e < 10⁶ K, one cannot reliably determine the bulk outflow velocity of the solar wind in that region by using minor ion outflow velocities. However, when the wave dissipation in the corona occurs much further away from the transition region, the loss of thermal equilibrium between plasma species is much less pronounced, or a transition region and a hot corona cannot be energized by the waves at all.