A two-fluid model for the solar wind

We present a two-fluid model of the solar wind, treating, under stationary conditions, the wind acceleration and the coronal heating simultaneously as a single problem. Our aim is to construct a scheme for the solution of the wind equations that can be readily adapted to different boundary conditions and also different heating and acceleration mechanisms. The method developed is applied to the case of heating by dissipation of Alfven waves, limiting the analysis to the range 1-10 solar radii. We include in the analysis thermal conduction, radiative losses and momentum, and energy deposition by dissipation of MHD waves. Energy exchange by Coulomb collisions between electrons and protons is taken into account. We discuss how critical solutions of the wind equations can be successfully achieved adopting a relaxation method, which allows us to explore the range of given parameters and boundary conditions. The analysis shows that the proton-electron coupling becomes weaker well below 2 solar radii, as assumed in the literature; electrons require extra heating in order to reach temperatures above two millions degrees, as implied by observations.