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 Alfvén waves with ${\omega }_{\mathrm{plas}}\le 0.1{\omega }_{\mathrm{ci}}$ down to $k_{\perp }{\rho }_i\sim 2$. Each $k$ spectrum in the direction perpendicular to ${\mathbf{B}}_0$ shows two scaling ranges separated by a breakpoint (in the interval $[0.4,1]k_{\perp }{\rho }_i$): a Kolmogorov scaling $k_{\perp }^{-1.7}$ followed by a steeper scaling $\sim k_{\perp }^{-4.5}$. 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.

• Received 14 May 2010
• Publisher error corrected 27 September 2010

DOI:https://doi.org/10.1103/PhysRevLett.105.131101