Upward field-aligned currents and their associated parallel electric fields couple the ionosphere to the magnetosphere. It is desirable to know how such a potential drop is distributed along the flux tube, what controls its variation, and how it is balanced by the plasma. By considering the motion of the ionospheric and magnetospheric electrons and ions, under the influence of electrostatic and magnetic mirror forces, a quasi steady state, quasi-neutral electric field distribution along the magnetic flux tube can be obtained. A feature of the potential profiles is the occurrence of a potential jump that splits the profile into three distinct regions: below the jump, within the jump, and above the jump. Within a kinetic framework, we analyze how the plasma velocity distributions evolve along the flux tube, taking into account ionospheric, magnetospheric, mirroring, and precipitating electron populations. By calculating the moments of the governing Vlasov equation, we ascertain what balances the parallel electric field (E∥) and how it is maintained, establishing a dynamical equilibrium. Our calculations show that (1) earthward of the jump E∥ ≈ −(p⊥/enB)∇∥B associated with the ionospheric electrons, except for at the base of the F region where p∥ contributions become more significant; (2) within the jump magnetosphere electrons dominate and E∥ ≈ −(1/en)∇∥p∥; and (3) above the jump mirroring magnetospheric electrons make a principal contribution of E∥ ≈ −(1/en)∇∥p∥, with a secondary contribution of −(p⊥ − p∥)∇∥B/(ne) becoming comparable beyond ≈3 RE. Additionally, we found that although the precipitating electrons carry the field-aligned current, it is the mirroring population that determines where E∥ is concentrated and hence where precipitating electrons are accelerated.
Stark, C. R., Cran-McGreehin, A. P., & Wright, A. N. (2011). Contributions to the magnetospheric parallel electric field. Journal of Geophysical Research: Space Physics, 116(A7). https://doi.org/10.1029/2010JA016270