Electric Field Effects on the Ion Velocity Distribution Function

Research Fig.19a:

Parallel component of the ion velocity distribution function (dashed curves, left ordinate) resulting from a force due to an (upward accelerating) height independent electric field E_p=3*10^-6 V/m and the earths gravitational field, assuming open boundaries at h_*=0 km and h_*=300 km (h=200-500 km) and a first order approximation which neglects the height dependence of the distribution function compared to the total density variation (ionization rate, recombination coefficient and elastic collisions correspond to conditions in the ionospheric F-region). The distribution functions are plotted at intervals of 30 km with the length of the dashes increasing from the lower to upper boundary (the solid curve gives a Maxwellian for comparison).

See FIG.19b for the related height profiles of the total density.
For the actual situation of closed magnetic field lines, one can assume that the distribution functions are more or less symmetric with regard to zero velocity, i.e. they should become doublehumped (FIG.19c). FIG.19d shows that this results also in the correct height dependence of the total density for an upwards accelerating force field, in contrast to a Maxwell distribution).