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tokens: anti-correlation between the expansion factor and the wind speed, which is in agreement with observations (see Wang Sheeley 1990 ; Wang 2016 ). At the source surface, the global anti-correlation is shown with a brownish line, and no correlation can be extracted for the point near minimum alone. Figure 9. Correlation between the wind speed and the expansion factor at three different heights in the corona: at the optimal source surface radius (on the left panel), at the sonic point (middle panel) and at (where the wind speed is computed for all panels). The colors indicate the parameter , so that orange colors indicate a very weak dipolar component (near maximum) and black colors indicate a strong dipolar component (near minimum). We see that the correlation changes with the cycle phase. The positive correlation between and the wind speed is the strongest at large heights, due to expansion beyond the sonic point. Nevertheless, higher in the corona, we can obtain two different regressions, for simulations whose parameter is over or below 50% of the maximum value () for the period considered. For near minimum cases, we get a positive correlation (shown by a black line) between the wind speed and the expansion factor starting at the sonic point. This correlation gets better as we go up in height at . Hence, for a simple, near-dipolar configuration of the solar magnetic field, where most of the open field lines come from the large polar coronal holes, the expansion around and beyond the sonic point operates a significant reorganization. Of course, beyond the source surface, the total area is conserved and both super and under radial expansion must compensate. As such, super (under) radial expansion increases (decreases) the wind speed, and the correlation between the terminal speed and the total expansion factor is reversed (see also Pinto Rouillard 2017 ). The additional acceleration provided only by the super radial expansion is maximum on field lines that cross local maxima of . This process must influence the acceleration of the fast solar wind, which is thought to occur at large distances from the Sun, where Alfvén waves dissipate. The correlation (shown by the orange line) stays globally negative for points near maximum of activity everywhere in the corona. In Figure 10 , we show the mass flux as a function of the expansion factor at the source surface ) at different heights in the corona. As shown by the blue dots, a large expansion below the source surface (associated with slow streams) increases the mass flux at the coronal base, through the velocity that is left free in the boundary. The mass flux at the surface spans over an order of magnitude, and the mass loading diminishes the energy per particle and the terminal speed. This explains the good correlation between the wind speed and the expansion factor at the source surface. However, near the source surface, the mass flux/expansion correlation is reversed with faster wind (low )