Effects of alpha particles on the angular momentum loss from the Sun
  The classic Weber-Davis model of the solar wind is reconsidered by incorporating alpha particles and by allowing the solar wind to flow out of the equatorial plane in an axisymmetrical configuration. In the ion momentum equations of the solar wind, the ion gyro-frequency is many orders of magnitude higher than any other frequency. This requires that the difference between proton and alpha velocity vectors be aligned with the background magnetic field. With the aid of this alignment condition, the governing equations of the multi-fluid solar wind are derived from the standard transport equations. The governing equations are numerically solved along a prescribed meridional magnetic field line located at colatitude $70^\circ$ at 1AU and a steady state fast solar wind solution is found. A general analysis concludes, in agreement with the Weber-Davis model, that the magnetic field helps the coronal plasma to achieve an effective corotation out to the Alfv\'enic radius, where the poloidal Alfv\'enic Mach number $M_T$ equals unity ($M_T$ is defined by equation (\ref{eq:mach})). The model computations show that, magnetic stresses predominate the angular momentum loss of the Sun. For the fast wind considered, the proton contribution to the angular momentum loss, which can be larger than the magnetic one, is almost completely canceled by the alpha particles that develop an azimuthal speed in the direction opposite to the solar rotation. The Poynting flux associated with the azimuthal components is negligible in the energy budget. However, the solar rotation can play some role in reducing the relative speed between alpha particles and protons for low latitude fast solar wind streams in interplanetary space. 
Bo Li, and Xing Li