Heating in coronal funnels by ion cyclotron waves

Plasma heating by ion cyclotron waves in rapidly expanding flow tubes in the transition region, referred to as coronal funnels, is investigated in a three-fluid plasma consisting of protons, electrons, and a-particles. Ion - cyclotron waves are able to heat the plasma from 6 × 10⁴ to 10⁶ K over a distance range of 10⁴ km by directly heating a-particles. Although only a-particles dissipate the waves, the strong Coulomb coupling between aparticles and protons and between protons and electrons makes it possible for protons and electrons to be heated also to more than 10 ⁶ K. However, owing to the extreme heating of the α-particles, the particles are not in thermal equilibrium: α-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) If spectral lines formed at T_e < 10₆6 are observed at different heights, the inferred outflow velocities may vary by a factor of 5-6. (2) 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.