On the modeling of the three-fluid structure of the quiet solar wind

The reciprocal influence of the electrons and protons, on one side, and the -particles, on the other side in the quiet solar wind is investigated within the framework of a conductive three-fluid model (with frictional forces included). For this purpose two mathematical methods are used, namely: I. Simultaneous solution of the fluid equations for all three species; and II. Solution of two-fluid equations (for electrons and protons) followed by that of a modified one-fluid equation for the -particles (in which the two-fluid solutions are used for electrons and protons).The results of our investigation indicate the following: (a)The macroscopic -particle characteristics as obtained from the two methods of solution are almost identical. Thus, the differences between the three-fluid and two-fluid characteristics of the electrons and protons represent a second order (and negligible) effect on the -particle characteristics. In both approaches, the frictional interaction between -particles and protons raises the (lower) -particle streaming velocity to that of the protons and decreases the relative to proton density ratio to a value about 0.035, as observed at 1 AU, (b)The electron and proton characteristics obtained from three-fluid and two-fluid solutions are similar, except for the proton temperature. The two-fluid solution providesT _p-values which, though within the observational error, are larger than those obtained from the simultaneous three-fluid solution (at 1 AU, the difference amounts to about 30%). Thus, the -particles affect the temperature profile of the protons in the solar wind through heat exchange (mainly), dynamical friction, as well as through their contribution to the interplanetary electrostatic field.