On local and non-local energy transfers in Hall magnetohydrodynamic turbulence

A systematic study of inertial energy cascade in three-dimensional incompressible Hall magnetohydrodynamic turbulence is conducted to investigate the locality of energy conserving triads and the subsequent transfers. Based on the nature of triadic conservations, the energy transfer due to the Hall term is further decomposed into two channels script upper B script upper B B B $\mathcal{BB}$ and script upper J script upper B J B $\mathcal{JB}$ corresponding to the terms d Subscript i Baseline left parenthesis bold italic j bold dot bold nabla right parenthesis bold italic b d i ( j ⋅ ∇ ) b $d_i ({\boldsymbol{j}}\boldsymbol{\cdot }\boldsymbol{\nabla }){\boldsymbol{b}}$ and minus d Subscript i Baseline left parenthesis bold italic b bold dot bold nabla right parenthesis bold italic j − d i ( b ⋅ ∇ ) j $-d_i ({\boldsymbol{b}}\boldsymbol{\cdot }\boldsymbol{\nabla }){\boldsymbol{j}}$ , respectively, where bold italic b b $\boldsymbol{b}$ and bold italic j j $\boldsymbol{j}$ represent the magnetic field and the current density (in Alfvén units) respectively, and d Subscript i d i $d_i$ is the ion-inertial le