An approximate description of field‐aligned currents in a planetary magnetic field

Field‐aligned currents play a central role in the study of the magnetized plasmas of the solar terrestrial environment. In particular, if perturbations of flow develop on one part of a flux tube, field‐aligned currents must flow in order to communicate the changes to the entire flux tube. Field‐aligned currents cause the field to twist or shear, a feature that can be described in terms of the displacement of field lines from an unperturbed orientation. In this paper we derive expressions for the field‐aligned current density in a magnetized plasma that illuminate die relationship between twist or shear and current flow parallel to the background magnetic field. We show that the time evolution of the field displacements is closely linked to equations for Alfvén wave displacements and that they are driven by pressure gradient terms of the sort that are encountered in computations of interchange motions. We find that in the magnetosphere or in any other collisionless plasma regime, the field‐aligned current density is related closely to the time integral of the parallel vorticity. We make use of the fact that the field‐aligned current density in the ionosphere is related to the vorticity itself, not its time integral. Continuity relates the currents in the two regions and implies a decay time for the magnetospheric current inversely proportional to the ionospheric resistivity. The decay depends only on a magnetospheric scale length but on no other magnetospheric parameters and resembles the decay of current in an inductance caused by resistivity somewhere in the circuit.