Intermittency and electron heating in kinetic-Alfvén-wave turbulence*

We report analytical and numerical investigations of sub-ion-scale turbulence in low-beta plasmas using a rigorous reduced kinetic model, focusing on the spectral properties and electron heating. In the limit of isothermal electrons, the numerical results support a description of the turbulence as a critically-balanced Kolmogorov-like cascade of kinetic Alfvén wave fluctuations, as amended by Boldyrev & Perez (Astrophys. J. Lett. 758, L44 (2012)) to include intermittent effects. With the inclusion of electron kinetic physics, we show that efficient electron heating occurs and is primarily due to Landau damping of kinetic Alfv'en waves, as opposed to Ohmic dissipation. This collisionless damping is facilitated by the local weakening of advective nonlinearities and the ensuing unimpeded phase mixing near intermittent current sheets, where free energy concentrates. The linearly damped energy of electromagnetic fluctuations at each scale explains the steepening of the energy spectrum with respect to its isothermal counterpart, where such damping is excluded. The use of a Hermite-polynomial representation to express the velocity-space dependence of the electron distribution function enables us to obtain an analytical, lowest-order solution for the Hermite moments of the distribution, which is borne out by numerical simulations. Our prediction of the direct connection between intense current structures, Landau damping, and electron heating, as well as of remarkable properties of the electron distribution function, provide important insights for interpreting recent high-resolution in-situ solar wind measurements from satellites.