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The classic Weber-Davis model of the solar wind is reconsidered byincorporating alpha particles and by allowing the solar wind to flow out of theequatorial plane in an axisymmetrical configuration. In the ion momentumequations of the solar wind, the ion gyro-frequency is many orders of magnitudehigher than any other frequency. This requires that the difference betweenproton and alpha velocity vectors be aligned with the background magneticfield. With the aid of this alignment condition, the governing equations of themulti-fluid solar wind are derived from the standard transport equations. Thegoverning equations are numerically solved along a prescribed meridionalmagnetic field line located at colatitude $70^\circ$ at 1AU and a steady statefast solar wind solution is found. A general analysis concludes, in agreementwith the Weber-Davis model, that the magnetic field helps the coronal plasma toachieve an effective corotation out to the Alfv\'enic radius, where thepoloidal Alfv\'enic Mach number $M_T$ equals unity ($M_T$ is defined byequation (\ref{eq:mach})). The model computations show that, magnetic stressespredominate the angular momentum loss of the Sun. For the fast wind considered,the proton contribution to the angular momentum loss, which can be larger thanthe magnetic one, is almost completely canceled by the alpha particles thatdevelop an azimuthal speed in the direction opposite to the solar rotation. ThePoynting flux associated with the azimuthal components is negligible in theenergy budget. However, the solar rotation can play some role in reducing therelative speed between alpha particles and protons for low latitude fast solarwind streams in interplanetary space.Comment: 12 pages, 4 figures, accepted for publication in A&

Effects of α particles on the angular momentum loss from the Sun