“…Here 1,2 are dipole coordinates, h 1,2,3 are dipole metric factors, and subscripts 1, 2, and 3 denote directions along the geomagnetic field, across the field line in the meridional plane, and in the azimuthal direction, respectively; see the definition in Sydorenko and Rankin [2013]. Subscripts e and denote electron and ion species, respectively (the list of ion species includes H + , N + , O + , N + 2 , NO + , and O + 2 ); and Ω denote frequencies of collisions with neutrals and gyromotion, respectively; T is the temperature, and [(u ⋅ ∇)u] 1 is the convective derivative term defined in Sydorenko and Rankin [2013]. In the ion velocity equation (5), the first term in the right-hand side corresponds to the ion polarization current in an Alfvén wave modified by collisions; the second term, where P ≡ e∕m (Ω 2 + 2 ) is the Pedersen mobility, corresponds to the Pedersen conductivity current.…”