Evidence of a Cascade and Dissipation of Solar-Wind Turbulence at the Electron Gyroscale

We report the first direct determination of the dissipation range of magnetofluid turbulence in the solar wind at the electron scales. Combining high resolution magnetic and electric field data of the Cluster spacecraft, we computed the spectrum of turbulence and found two distinct breakpoints in the magnetic spectrum at 0.4 and 35 Hz, which correspond, respectively, to the Doppler-shifted proton and electron gyroscales, f_ρp and f_ρe. Below f_ρp, the spectrum follows a Kolmogorov scaling f^-1.62, typical of spectra observed at 1 AU. Above f_ρp, a second inertial range is formed with a scaling f^-2.3 down to f_ρe. Above f_ρe, the spectrum has a steeper power law ∼f^-4.1 down to the noise level of the instrument. We interpret this as the dissipation range and show a remarkable agreement with theoretical predictions of a quasi-two-dimensional cascade into Kinetic Alfvén Waves (KAW).