The field-aligned current of standing Alfv¿n waves is mainly carried by electrons travelling parallel to the magnetic field. During the upward current phase, magnetospheric electrons travel downward to the ionosphere. In large-amplitude Alfv¿n waves, where current densities reach a few ¿Am-2 above the ionosphere, the electrons achieve energies of the order of keV. This problem has been addressed recently in terms of two-fluid theory. The present paper builds on these studies by employing a distribution function formulation. When the electron motion is dominated by the parallel velocity component, we find the B/n curve is central to interpreting the solution: B/n has a peak (i.e., d(B/n)/dℓ = 0, where ℓ is path length along the field line) below which ionospheric electrons are trapped. Above the peak we find the parallel electric field is balanced by the convective plasma acceleration, as suggested by R¿nnmark <1999> and has a value of the order of mV/m for ~1 RE above the B/n peak. The maximum E∥ occurs where d2(B2/n2)/dℓ2 = 0 and is located a couple of density scale heights beyond the B/n peak.