Local Cascade and Dissipation: The Coarse Graining approach as a robust tool to investigate Magnetic Reconnection

We derive the coarse-graining (CG) equations of  incompressible Hall Magnetohydrodynamics (HMHD) turbulence to investigate the local (in space) energy cascade rate as a function of the filtering scale. 
First, the CG equations are space averaged to obtain the analytical expression of the mean cascade rate. Its application to 3 dimensional (3D) simulations of (weakly compressible) HMHD shows a cascade rate consistent with the value of the mean dissipation rate in the simulations and with the classical estimates based on the "third-order" law.

 The strength of the CG approach is further revealed when considering the local-in-space energy cascade rate which is shown theoretically and numerically to match dissipative processes at a given position x, when both quantities are locally averaged over a small neighboring region (quasi-locality). This result supports the claim that the (quasi-)local cascade rate can provide a reliable estimate of the (quasi-)local energy dissipation, regardless of the nature of the dissipation processes involved.

The new model is further applied to magnetic reconnection sites observed in Hybrid-Vlasov (HVM) simulations and in spacecraft data. The results show the robustness of the new model over standard tools used to highlight energy dissipation processes and particles energization at the X points.