How does the ionospheric rotational Hall current absorb the increasing energy from the field-aligned current system?

It has been well recognized that field-aligned current (FAC) systems lose their energy in the ionosphere through the Joule dissipation that is caused by their closure via the ionospheric Pedersen current, and that the ionospheric Hall current cannot contribute the total energy dissipation. However, it is also true that the rotational Hall current is excited by the incident FAC, and it radiates a Poynting vector that grows a poloidal-type magnetic field. Even if the Hall effect cannot do work on an external system, what does its contribution to the accumulation of poloidal magnetic energy really mean? In this paper, it is clarified that the divergent Hall current, excited during the transient phase of magnetosphere-ionosphere coupling, closes via the FAC and produces a Hall current generator, which pumps up the energy of the FAC system to increase the ionospheric rotational Hall current (together with its associated poloidal magnetic field).