Analytical and numerical evidence of the cascade reversal due to electron inertia*

Astrophysical plasmas exist in a large range of length-scales throughout the universe. At sufficiently small scales, one must account for many two-fluid effects, such as the ion or electron skin-depths, as well as Larmor radii. These effects occur when ignoring electron mass, for instance, is no longer possible. We are interested in studying homogeneous turbulence in the context of such plasma models. In particular, we look at a 2D extended MHD model, where the effect of electron inertia may be non-negligible . This model has been applied to understanding collisionless reconnection in past. Two-dimensional simulations are less computationally intensive and thus allow us to perform a parameter study of many runs, in which we look at the cascade of conserved quadratic quantities as we vary the effective electron skin-depth. We find that the cascade directions depend strongly on whether the length scale is relevant in the system, and, furthermore, that the transition in cascade directions happens in a critical way, as was previously observed in other studies of the kind but in different systems.