Fluid-like dissipation of magnetic turbulence at electron scales in the solar wind

The turbulent spectrum of magnetic fluctuations in the solar wind displays a spectral break at ion characteristic scales. At electron scales the spectral shape is not yet completely established. Here, we perform a statistical study of 102 spectra at plasma kinetic scales, measured by the Cluster/STAFF instrument in the free solar wind. We show that the magnetic spectrum in the high frequency range, [1,400] Hz, has a form similar to what is found in hydrodynamics in the dissipation range ~Ak^(-\alpha)exp(-kl_d). The dissipation scale l_d is found to be correlated with the electron Larmor radius \rho_e. The spectral index \alpha varies in the range [2.2,2.9] and is anti-correlated with l_d, as expected in the case of the balance between the energy injection and the energy dissipation. The coefficient A is found to be proportional to the ion temperature anisotropy, suggesting that local ion instabilities may play some role for the solar wind turbulence at plasma kinetic scales. The exponential spectral shape found here indicates that the effective dissipation of magnetic fluctuations in the solar wind has a wave number dependence similar to that of the resistive term in collisional fluids ~k^2\delta B.