Solar wind turbulent spectrum at plasma kinetic scales

Abstract: The description of the turbulent spectrum of magnetic fluctuations in the solar wind in the kinetic range of scales is not yet completely established. Here, we perform a statistical study of 100 spectra measured by the STAFF instrument on the Cluster mission, which allows to resolve turbulent fluctuations from ion scales down to a fraction of electron scales, i.e. from $\sim 10^2$ km to $\sim 300$ m. We show that for $k_{\perp}\rho_e \in[0.03,3]$ (that corresponds approximately to the frequency in the spacecraft frame $f\in [3,300]$ Hz), all the observed spectra can be described by a general law $E(k_\perp)\propto k_\perp^{-8/3}\exp{(-k_\perp \rho_e)}$, where $k_{\perp}$ is the wave-vector component normal to the background magnetic field and $\rho_e$ the electron Larmor radius. This exponential tail found in the solar wind seems compatible with the Landau damping of magnetic fluctuations onto electrons.