Anisotropy of Solar Wind Turbulence between Ion and Electron Scales

The anisotropy of turbulence in the fast solar wind, between the ion and electron gyroscales, is directly observed using a multispacecraft analysis technique. Second order structure functions are calculated at different angles to the local magnetic field, for magnetic fluctuations both perpendicular and parallel to the mean field. In both components, the structure function value at large angles to the field $S_{\perp }$ is greater than at small angles $S_{\parallel }$: in the perpendicular component $S_{\perp }/S_{\parallel }=5\pm 1$ and in the parallel component $S_{\perp }/S_{\parallel }>3$, implying spatially anisotropic fluctuations, $k_{\perp }>k_{\parallel }$. The spectral index of the perpendicular component is $-2.6$ at large angles and $-3$ at small angles, in broad agreement with critically balanced whistler and kinetic Alfvén wave predictions. For the parallel component, however, it is shallower than $-1.9$, which is considerably less steep than predicted for a kinetic Alfvén wave cascade.

Figure 1

Magnetic field power spectrum of combined STAFF and FGM data from Cluster 3. Approximate instrument ranges are shown, as is the STAFF noise floor (green dashed line) and ion and electron gyroscales (blue dash-dotted lines). Approximate frequencies corresponding to the range of scales used are marked (red dotted lines).

Figure 2

Second order structure functions with respect to spatial separations parallel ($l_{\parallel }$) and perpendicular ($l_{\perp }$) to the local magnetic field: $\delta B_{\perp }^2$ (left) and $\delta B_{\parallel }^2$ (right).

Figure 3

Second order structure functions at different angles to the local magnetic field for the perpendicular component (upper set) and the parallel component (lower set).

Figure 4

Anisotropy of second order structure functions (upper) and spectral indices (lower). Various spectral index predictions are marked (dotted lines).