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 \sim Ak ^ { - \alpha } \exp { ( - k \ell _ { d } ) } .
The dissipation scale \ell _ { 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 \ell _ { 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 rôle 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 \sim \triangle \delta B \sim k ^ { 2 } \delta B .