Rugged magnetohydrodynamic invariants in weakly collisional plasma turbulence

We investigate properties of ideal second-order magneto-hydrodynamic (MHD) and Hall MHD invariants  (kinetic+magnetic energy and different helicities) in a two-dimensional hybrid simulation of decaying plasma turbulence. The combined (kinetic+magnetic) energy decays at large scales, cascades (from large to small scales) via the MHD non-linearity at intermediate scales. This cascade partly continues via the Hall coupling to sub-ion scales. The cascading energy is transferred (dissipated) to the internal energy at small scales via the resistive  dissipation and the pressure-strain effect. The mixed (X) helicity, an ideal invariant of Hall MHD, exhibits a strange behaviour whereas the cross helicity (the ideal invariant in MHD but not in Hall MHD), in analogy to the energy, decays at large scales, cascades from large to small scales via the MHD+Hall non-linearities, and is dissipated at small scales via the resistive dissipation and an equivalent of the pressure-strain effect. In contrast, the magnetic helicity is very weakly generated through the resistive term and does not exhibit any cascade; furthermore, the magnetic and cross helicities are not coupled in the hybrid approximation, so that the corresponding helicity barrier does not exist.