Electron scale solar wind turbulence: Cluster observations and theoretical modeling

Turbulence at MagnetoHydroDynamics (MHD) scales of the solar wind has been studied for more than three decades, using data analyzes, theoretical and numerical modeling. However smaller scales have not been explored until very recently. Here, we review recent results on the first observation of cascade and dissipation of the solar wind turbulence at the electron scales. Thanks to the high resolution magnetic and electric field data of the Cluster spacecraft, we computed the spectra of turbulence up to ∼ 100 Hz (in the spacecraft reference frame) and found two distinct breakpoints in the magnetic spectrum at 0.4 Hz 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. Solving numerically the linear Maxwell-Vlasov equations combined with recent theoretical predictions of the Gyro-Kinetic theory, we show that the present results are fully consistent with a scenario of a quasi-two-dimensional cascade into Kinetic Alfvén modes (KAW).