The rotation angle distribution underlying magnetic field fluctuations in the 1/ f range of solar wind turbulent spectra

We discuss properties of large amplitude magnetic field fluctuations during fast Alfvenic solar wind streams, focussing on the statistics of the rotation angle between consecutive magnetic field vector measurements for different scales in the plasma. Since in the fast solar wind fluctuations preserve the modulus of the magnetic field to a good approximation, the tip of the magnetic field vector is observed to move on a sphere of approximately constant radius |B|. We then compare statistics of solar wind measurements with that of a simple model of a random walk bounded on a spherical surface. The analogy consists in the fact that in both systems the geometrical constraint imposes a limiting amplitude at large separations and thus introduces a break scale in the power spectrum of the fluctuations, leading to a shallower slope for scales where the fluctuations amplitude becomes scale-independent. However, while in the case of the random walk the saturation of the fluctuations occurs when the pattern becomes uniform on the sphere (flat distribution of the cosine of the rotation angle), transitioning then to a white noise regime, in the solar wind magnetic field fluctuations saturate in amplitude maintaining a preferential direction. We suggest that this behaviour is due to the presence of the background interplanetary magnetic field, which keeps some long-range memory in the system also when the fluctuations becomes independent of the scale. This long-range correlation is a necessary ingredient in order to produce the 1/f spectrum observed at large scales in the solar wind.