Scale-Dependent Kurtosis of Magnetic Field Fluctuations in the Solar Wind: A Multi-Scale Study With Cluster 2003–2015

During the lifetime of the Cluster mission, the inter-spacecraft distances in the solar wind have changed from the large, fluid, scales (∼10⁴ km), down to the scales of protons (∼10² km). As part of the guest investigator campaign, the mission achieved a formation where a pair of spacecraft were separated by ∼7 km. The small distances and the exceptional sensitivity of the search coil magnetometer provide an excellent data set for studying solar wind turbulence at electron scales. In this study, we investigate the intermittency of the magnetic field fluctuations in the slow solar wind. Using 20 time intervals with different constellation orientations of Cluster we cover spatial scales between 7 and 10⁴ km. We compare time-lagged increments from a single spacecraft with spatially lagged increments using multiple spacecraft. As the turbulent cascade proceeds to smaller scales in the inertial range, the deviation from Gaussian statistics is observed to increase in both temporal and spatial increments in the components transverse to the mean field direction. At ion scales, there is a maximum of kurtosis, and at sub-ion scales, the fluctuations are only weakly non-Gaussian. In the compressive component the deviation from Gaussian statistics is variable: it may increase throughout the inertial and sub-ion ranges, but also, it may have a maximum at magnetohydrodynamic scales associated with large scale magnetic holes. The observations show differences in kurtosis of time and space increments when the spacecraft pairs are transverse to the flow, indicating its spatial anisotropy.