  By means of a fully kinetic simulation of freely decaying plasma turbulence,
we study the spectral properties and the energy exchanges characterizing the
turbulent cascade in the kinetic range. We find that the magnetic field
spectrum follows the ${k^{-\alpha}\,exp(-\lambda\, k)}$ law at kinetic scales
with $\alpha\!\simeq\!2.73$ and $\lambda\!\simeq\!\rho_e$ (where ${\rho_e}$ is
the electron gyroradius). The same law with $\alpha\!\simeq\!0.94$ and an
exponential decay characterized by $\lambda\!\simeq\!0.87\rho_e$ is observed in
the electron velocity spectrum but not in the ion velocity spectrum that drops
like a steep power law $\sim k^{-3.25}$ before reaching electron scales. By
analyzing the filtered energy conversion channels, we find that the electrons
play a major role with respect to the ions in driving the magnetic field
dynamics at kinetic scales. Our analysis reveals the presence of an indirect
electron-driven mechanism that channels the e.m. energy from large to sub-ion
scale more efficiently than the direct nonlinear scale-to-scale transfer of
e.m. energy. This mechanism consists of three steps: in the first step the e.m.
energy is converted into electron fluid flow energy at large scales; in the
second step the electron fluid flow energy is nonlinearly transferred towards
sub-ion scales; in the final step the electron fluid flow energy is converted
back into e.m. energy at sub-ion scales. This electron-driven transfer drives
the magnetic field cascade up to fully developed turbulence, after which
dissipation becomes dominant and the electrons start to subtract energy from
the magnetic field and dissipate it via the pressure-strain interaction at
sub-ion scales.
