Plasma turbulence at ion scales: a comparison between PIC and Eulerian hybrid-kinetic approaches

Kinetic-range turbulence in magnetized plasmas and, in particular, in the context of solar-wind turbulence has been extensively investigated over the past decades via numerical simulations. Among others, one of the widely adopted reduced plasma model is the so-called hybrid-kinetic model, where the ions are fully kinetic and the electrons are treated as a neutralizing (inertial or massless) fluid. Within the same model, different numerical methods and/or approaches to turbulence development have been employed. In the present work, we present a comparison between two-dimensional hybrid-kinetic simulations of plasma turbulence obtained with two complementary approaches spanning about two decades in wavenumber - from MHD inertial range to scales well below the ion gyroradius - with a state-of-the-art accuracy. One approach employs hybrid particle-in-cell (HPIC) simulations of freely-decaying Alfv\'enic turbulence, whereas the other consists of Eulerian hybrid Vlasov-Maxwell (HVM) simulations of turbulence continuously driven with partially-compressible large-scale fluctuations. Despite the completely different initialization and injection/drive at large scales, the same properties of turbulent fluctuations at $k_\perp\rho_i\gtrsim1$ are observed. The system indeed self-consistently "reprocesses" the turbulent fluctuations while they are cascading towards smaller and smaller scales, in a way which actually depends on the plasma beta parameter. Small-scale turbulence has been found to be mainly populated by kinetic Alfv\'en wave (KAW) fluctuations for $\beta\geq1$, whereas KAW fluctuations are only sub-dominant for low-$\beta$.