We investigate properties of plasma turbulence from magneto-hydrodynamic (MHD) to sub-ion scales by means of two-dimensional, high-resolution hybrid particle-in-cell simulations. We impose an initial ambient magnetic field, perpendicular to the simulation box, and we add a spectrum of largescale magnetic and kinetic fluctuations, with energy equipartition and vanishing correlation. Once the turbulence is fully developed, we observe a MHD inertial range, where the spectra of the perpendicular magnetic field and the perpendicular proton bulk velocity fluctuations exhibit power-law scaling with spectral indices of −5/3 and −3/2, respectively. This behavior is extended over a full decade in wavevectors and is very stable in time. A transition is observed around proton scales. At sub-ion scales, both spectra steepen, with the former still following a power law with a spectral index of ∼ −3. A −2.8 slope is observed in the density and parallel magnetic fluctuations, highlighting the presence of compressive effects at kinetic scales. The spectrum of the perpendicular electric fluctuations follows that of the proton bulk velocity at MHD scales, and flattens at small scales. All these features, which we carefully tested against variations of many parameters, are in good agreement with solar wind observations. The turbulent cascade leads to on overall proton energization with similar heating rates in the parallel and perpendicular directions. While the parallel proton heating is found to be independent on the resistivity, the number of particles per cell and the resolution employed, the perpendicular proton temperature strongly depends on these parameters.

A new path for the generation of a sub-ion scale cascade in collisionless space and astrophysical plasma turbulence, triggered by magnetic reconnection, is uncovered by means of high-resolution two-dimensional hybrid-kinetic simulations employing two complementary approaches, Lagrangian and Eulerian, and different driving mechanisms. The simulation results provide clear numerical evidences that the development of powerlaw energy spectra below the so-called ion break occurs as soon as the first magnetic reconnection events take place, regardless of the actual state of the turbulent cascade at MHD scales. In both simulations, the reconnection-mediated small-scale energy spectrum of parallel magnetic fluctuations exhibits a very stable spectral slope of ∼ −2.8, whether or not a large-scale turbulent cascade has already fully developed. Once a quasi-stationary turbulent state is achieved, the spectrum of the total magnetic fluctuations settles towards a spectral index of −5/3 in the MHD range and of ∼ −3 at sub-ion scales.

21 Corresponding author: J. E. Stawarz j.stawarz@imperial.ac.uk 2 Turbulent plasmas generate intense current structures, which have long been sug-22 gested as magnetic reconnection sites. Recent Magnetospheric Multiscale (MMS) ob-23 servations in Earth's magnetosheath revealed a novel form of reconnection where the 24 dynamics only couple to electrons, without ion involvement. It was suggested that 25 such dynamics were driven by magnetosheath turbulence. In this study, the fluctua-26 tions are examined to determine the properties of the turbulence and if a signature of 27 reconnection is present in the turbulence statistics. The study reveals statistical prop-28 erties consistent with plasma turbulence with a correlation length of ∼ 10 ion inertial 29 lengths. When reconnection is more prevalent, a steepening of the magnetic spectrum 30 occurs at the length scale of the reconnecting current sheets. The statistics of intense 31 currents suggest the prevalence of electron-scale current sheets favorable for electron-32 reconnection. The results support the hypothesis that electron-reconnection is driven 33 by turbulence and highlight diagnostics that may provide insight into reconnection in 34 other turbulent plasmas.35

A dynamical vectorial equation for homogeneous incompressible Hall-MHD turbulence together with the exact scaling law for third-order correlation tensors, analogous to that for the incompressible MHD, is rederived and applied to the results of two-dimensional hybrid simulations of plasma turbulence. At large (MHD) scales the simulations exhibits a clear inertial range where the MHD dynamic law is valid. In the sub-ion range the cascade continues via the Hall term but the dynamic law derived in the framework of incompressible Hall MHD equations is obtained only in a low plasma beta simulation. For a higher beta plasma the cascade rate decreases in the sub-ion range and the change becomes more pronounced as the plasma beta increases. This break in the cascade flux can be ascribed to non thermal (kinetic) features or to others terms in the dynamical equation that are not included in the Hall-MHD incompressible approximation.