Multifractal analysis of high resolution solar wind proton density measurements

The solar wind is a highly turbulent medium, with a high level of field fluctuations throughout a broad range of scales. These include an inertial range where a turbulent cascade is assumed to be active. The solar wind cascade shows intermittency, which however may depend on the wind conditions. Recent observations have shown that ion-scale magnetic turbulence is almost self-similar, rather than intermittent. A similar result was observed for the high resolution measurements of proton density provided by the spacecraft Spektr-R. Intermittency may be interpreted as the result of the multifractal properties of the turbulent cascade. In this perspective, this paper is devoted to the description of the multifractal properties of the high resolution density measurements. In particular, we have used the standard coarse-graining technique to evaluate the generalized dimensions Dq, and from these the multifractal spectrum f(α), in two ranges of scale. A fit with the p-model for intermittency provided a quantitative measure of multifractality. Such indicator was then compared with alternative measures: the width of the multifractal spectrum, the peak of the kurtosis, and its scaling exponent. The results indicate that the small-scale fluctuations are multifractal, and suggest that different measures of intermittency are required to fully understand the small scale cascade.