A mathematical model of the Earth's plasmasphere and its application in a study of He+ at L = 3

A fully time-dependent mathematical model of the Earth's plasmasphere is presented. In the model coupled time-dependent equations of continuity, momentum and energy balance for the O+, H+, He+, N2+, O2+ and NO+ ions, and the electrons, are solved along centred-dipole magnetic field lines. The model is used in a study of the distribution of He+ in the topside ionosphere at L = 3 during solar maximum and solar minimum. The modelled ion concentrations for winter solstice and equinox during solar maximum show altitude regions in the nighttime topside ionosphere where He+ is the dominant ion. Such regions, which arise from the nighttime decrease in O+ concentration combined with the nighttime maintenance of He+, are most pronounced in the results for winter solstice when the high value of n(He) associated with the winter helium bulge lead to enhanced He+ concentrations. There is no indication in the results to suggest that He+ could become the dominant ion during summer at solar maximum or at any time during solar minimum