  Recent observational and analytical studies suggested that a new regime of
kinetic turbulence may exist in plasma environments with low electron beta
(Chen and Boldyrev, 2017). Such a regime, termed inertial kinetic-Alfv\'en
turbulence, is relevant for the solar corona, Earth's magnetosheath, and other
astrophysical systems where the electron and ion plasma beta parameters satisfy
the condition $\beta_e\ll \beta_i\lesssim 1$. In this paper we present kinetic
numerical simulations that confirm existence of the iKAW regime. Specifically,
the simulations demonstrate a transition at scales below electron inertial
length $d_e$ when $\beta_e\ll \beta_i\lesssim 1$. Spectral slopes and other
statistical properties of turbulence at sub-$d_e$ scales are consistent with
the phenomenological theory of inertial kinetic-Alfv\'en turbulence proposed by
Chen and Boldyrev (2017) and with the recent observations in the Earth's
magnetosheath.
