A model of a polar ion-exosphere in which the geomagnetic field lines are open is developed. The electrostatic field in this region has been calculated by taking into account two fundamental conditions: (1) quasi-neutrality has to be satisfied everywhere in the exosphere; (2) escape fluxes of electrons and ions have to be equal. The density distributions are calculated for different evaporative models in the case of two (O+ and e) and three (O+, H+ and e) constituents. In addition, the mean velocity, pressure and temperature distributions of the several constituents are derived.