  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.
