Three Dimensional Anisotropic k Spectra of Turbulence at Subproton Scales in the Solar Wind

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 Alfven waves with omega(plas) <= 0.1 omega(ci) down to k(perpendicular to)rho(i) similar to 2. Each k spectrum in the direction perpendicular to B-0 shows two scaling ranges separated by a breakpoint (in the interval [0.4, 1]k(perpendicular to)rho(i)): a Kolmogorov scaling k(perpendicular to)(-1.7) followed by a steeper scaling similar to k(perpendicular to)(-4.5). 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.