A numerical model calculates densities, fluxes and temperatures of H+ and O+ ions and the temperature of electrons on a convecting magnetic field line. The one‐dimensional fluid equations are solved along a field line path extending from 100 km altitude to many tens of Earth radii out in the magnetotail. Effects of photochemical reactions and charge exchange are included in the low altitude regions while dynamical effects due to field line convection, such as centrifugal acceleration and flux tube compression/dilation, are important at the higher altitudes. The model employs a variable spatial step to accommodate the disparate size scales. The evolution of O+ and H+ densities is calculated on field lines convecting over the polar cap. The simulation starts on a closed field line configuration on the dayside of the polar cap, the field line opens out into the magnetotail over the polar cap and eventually closes again on the nightside aurora zone. The results show that (1) centrifugal force is effective in accelerating ionospheric H+ plasma outward into the magnetotail, (2) the smothering effect of the H+ plasma on top of the O+ plasma prevents any ejection of O+ plasma, so long as the scale height of the O+ plasma is smaller than that of the H+ plasma (this indicates that heating processes specific to O+ are necessary for the appearance of O+ in the magnetotail) and (3) the upward component of the E×B drift on the dayside of the polar cap lifts the F region ionosphere to altitudes where charge exchange with neutrals and recombination is very slow so that ionization created on the dayside is transported across the polar cap with little loss. An enhanced F region peak in ionization density is created on the nightside of the polar cap because of compression of the O+ plasma by the subsequent downward component of the E×B drift.