Alignment of Velocity and Magnetic Fields in Fast and Slow Solar Wind

The earliest measurements of velocity and magnetic fields in the solar wind showed that the turbulence can be strongly Alfvenic in the fast wind. This property is very important as the cross-helicity, that is the correlation between velocity and magnetic field is an invariant of the ideal MHD equations and can inhibit the turbulent energy cascade if it is completely realized. It is however very important to study the local values of the cross-helicity, and in particular its probability distribution function, to determine the statistics of the local turbulent energy transfer. Indeed, even if there is no global Alfvenicity, the fluctuations of the local correlation can be very strong and, as they are related to the cosine of the angle between the velocity and the magnetic field, their distribution will depend on the dimensionality of these vector fluctuations. We have determined the probability distribution of the angle and its cosine between random vectors for different values of the cross-correlation, and we have compared these distributions with those observed at different distances by the Ulysses spacecraft in high-latitude fast solar wind, and those measured by the Helios satellite in fast and slow wind in the ecliptic. The distributions are found to always differ from the casual ones, but to be closer to two-dimensional distributions in the fast solar wind, suggesting a possible link between Alfvenicity and dimensionality of the fluctuations.