3D3V hybrid-kinetic simulations with electron inertia effects of kinetic-range solar-wind turbulence

Characterizing the nature of the turbulent fluctuations below the ion gyroradius in solar-wind turbulence and its dependence on the plasma parameters is a great challenge. Here we present a study of the sub-proton-scale cascade based on high-resolution hybrid-Vlasov (Eulerian) simulations of freely-decaying turbulence in 3D3V phase space, including finite electron inertia effects. Two proton plasma beta regimes are explored: $\beta_p=1$ and $\beta_p=0.2$ ($\beta$ is the ratio between thermal and magnetic pressures). At $\beta_p=1$, the magnetic energy spectum exhibit $k_\perp^{-8/3}$ and $k_\|^{-7/2}$ power laws, while they are slightly steeper for $\beta_p=0.2$. Nevertheless, both regimes develop a spectral anisotropy consistent with $k_\|\sim k_\perp^{2/3}$ at $k_\perp\rho_p>1$, and small-scale intermittency (the $\beta_p=0.2$ case being slightly more intermittent than the $\beta_p=1$ counterpart). In this context, we find that kinetic-range turbulence is consistent with a cascade of kinetic Alfv\'en waves type of fluctuations at $\beta_p=1$, whereas the low-$\beta$ case presents a more complex scenario suggesting the simultaneous presence of several type of fluctuations.