Anisotropy of plasma turbulence at ion scales: Hall and pressure-strain effects

Aims: We investigated the properties of plasma turbulence at ion scales in the solar wind context. We concentrated on the behaviour of the Hall physics and the pressure strain interaction and their anisotropy owing to the ambient magnetic field. Methods: We studied the results of a three-dimensional hybrid simulation of decaying plasma turbulence using the Kármán-Howarth-Monin (KHM) equation, which quantifies different turbulent processes. Results: The isotropised KHM analysis shows that kinetic plus magnetic (kinetic+magnetic) energy decays at large scales; this energy cascades from large to small scales via the magneto-hydrodynamic non-linearity that is partly continued via the Hall coupling around the ion scales. The cascading kinetic+magnetic energy is partly dissipated at small scales via resistive dissipation. This standard dissipation is complemented by the pressure-strain interaction, which plays the role of an effective dissipation mechanism and starts to act at relatively large scales. The pressure-strain interaction has two components, compressive and incompressive. Compressive interaction is connected with the velocity dilatation, which mostly reversibly exchanges kinetic+magnetic and internal energies. Incompressive interaction mostly irreversibly converts the kinetic+magnetic energy to internal energy. The compressive effects lead to important oscillations of the turbulence properties, but the compressibility is strongly reduced when averaged over a time period spanning a few periods of the oscillations. The ambient magnetic field induces a strong spectral anisotropy. The turbulent fluctuations exhibit larger scales along the magnetic field compared to the perpendicular directions. The KHM results show the corresponding anisotropy of turbulent processes: their characteristic scales shift to larger scales in the quasi-parallel direction with respect to the ambient magnetic field compared to the quasi-perpendicular direction. This anisotropy is weak at large scales owing to the initial isotropic spectrum, and becomes progressively stronger at small scales.