A number of independent and diverse ionospheric electric field, curren
t, particle, and plasma wave observations can be interpreted in terms
of intense parallel current density bursts that would require parallel
electric fields of the order of up to a few millivolts per meter to e
xist at ionospheric altitudes as low as 140 km at times. While such ob
servations are rare, they indicate that the upper limits on the values
of parallel current densities and electric fields could be extremely
high. In this paper, we theoretically explore the conditions under whi
ch the ionosphere could possibly sustain very large parallel fields an
d current densities. Since this is a first attempt at this question, w
e look for the simplest possible requirements; that is, we study the p
ossibility for the presence of a quasi-static electric field on timesc
ales greater than the electron collision time and the Alfven transit t
ime. Our initial focus is on two-dimensional linear situations, which
should apply if the parallel fields are less than about 0.1 mV/m. Nonl
inear effects are invoked in the event that stronger parallel fields w
ould be implied by the observations or when very strong horizontal gra
dients in conductivities are required. We link the problem to a magnet
ospheric source through the introduction of intense fluxes of medium t
o strong energy (hundreds of electron volts) electrons with and withou
t an abrupt latitudinal cutoff. When considering the presence of an ab
rupt latitudinal change in the precipitating energy spectrum, we also
require the presence of a ''background'' perpendicular electric field
which is assumed to be uniform on latitudinal scales 1 km or greater.
One important conclusion is that for the generation of parallel fields
intense enough to generate ion-acoustic waves along the geomagnetic f
ield as well as for the generation of shears of the order of meters pe
r second per meter, 100-m horizontal gradient scales are required. Ano
ther result is that for larger horizontal gradient scales, a substanti
al fraction of the returning currents carried by thermal electrons wil
l flow along the same magnetic field lines that precipitating electron
s are coming from; this leads to a substantial reduction in the net pa
rallel current densities when compared to the currents borne by each t
ype of carriers.