Spectrum of Kinetic Alfven Turbulence

A model for strong kinetic Alfv\'en plasma turbulence at scales smaller than the ion gyroscale is proposed. It is argued that magnetic and density fluctuations are concentrated mostly at two-dimensional structures, which leads to their Fourier energy spectra $E(k_\perp)\propto k_{\perp}^{-8/3}$, where $k_\perp$ is the wave-vector component normal to the strong background magnetic field. The results are shown to be in good agreement with numerical simulations, and they can explain recent observations of magnetic and density fluctuations in the solar wind at sub-proton scales.