Anisotropy of the Spectral Index in Ion Scale Compressible Turbulence: MMS Observations in the Magnetosheath

Turbulence in the Earth's magnetosheath at ion kinetic scales is investigated with the Magnetospheric MultiScale (MMS) spacecraft. The multi-point measurements allow the three dimensional power spectra in wave-vector space to be determined. Previously the three dimensional structure of fluctuations in the magnetic field and density (using spacecraft potential as a proxy) were possible with Cluster. However, using the excellent time resolution data set provided from both the Fluxgate Magnetometer (FGM) and the Fast Plasma Investigation (FPI) on MMS the spectra can be determined for a number of different parameters such as ion velocity, and ion temperatures parallel and perpendicular to the mean magnetic field directions. The spectra for different fluctuations show similar features to one another such as a strong power anisotropy with respect to the mean magnetic field direction, such that the energy decays faster in the direction parallel to the mean magnetic field than the perpendicular direction. A weak non-gyrotropy is also seen in the direction of the bulk velocity similar to what has been seen in magnetic field fluctuations with Cluster at ion kinetic scales in the solar wind. Velocity fluctuations are shown to be the most anisotropic. The density and temperature fluctuations exhibit similar anisotropies but are much weaker in comparison.