  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.
