Turbulence at MagnetoHydroDynamics (MHD) scales in the solar wind has been studied for more than three decades, using data analysis, 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 evidence of energy dissipation around the Doppler-shifted electron gyroscale fρe. Before its dissipation, the energy is shown to undergo two cascades: a Kolmogorov-like cascade with a scaling f-1.6 above the proton gyroscale, and a new f-2.3 cascade at the sub-proton and electron gyroscales. Above fρe 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 consistent with a scenario of a quasi-two-dimensional cascade into Kinetic Alfvén modes (KAW). New analyses of other data sets, where the Cluster separation (of about ~200 km) allowed us to explore the sub-proton scales using the k-filtering technique, and to confirm the 2D nature of the turbulence at those scales. © 2010 AcadÉmie des sciences.
Sahraoui, F., Goldstein, M. L., Abdul-Kader, K., Belmont, G., Rezeau, L., Robert, P., & Canu, P. (2011). Observation and theoretical modeling of electron scale solar wind turbulence. Comptes Rendus Physique. Elsevier Masson SAS. https://doi.org/10.1016/j.crhy.2010.11.008