Three dimensional anisotropic k-spectra of turbulence at sub-proton scales in the solar wind
Résumé
We show the first three dimensional (3D) dispersion relations and k spectra of magnetic turbulence in the solar wind at subproton scales. We used the Cluster data with short separations and applied the k-filtering technique to the frequency range where the transition to subproton scales occurs. We show that the cascade is carried by highly oblique kinetic Alfve´n waves with !plas 0:1!ci down to k?i 2. Each k spectrum in the direction perpendicular to B0 shows two scaling ranges separated by a breakpoint (in the interval ½0:4; 1k?i): a Kolmogorov scaling k1:7 ? followed by a steeper scaling k4:5 ? . We conjecture that the turbulence undergoes a transition range, where part of the energy is dissipated into proton heating via Landau damping and the remaining energy cascades down to electron scales where electron Landau damping may predominate.