An interhemispheric plasma transport model has been used to study the flow characteristics of H+, He+, and O+ along closed geomagnetic field lines for solstice conditions at noon local time. The calculations were carried out for the flux tube that passes through Millstone Hill. Both symmetric and asymmetric neutral winds in the conjugate ionospheres were considered. Initially, the flux tube content was partially depleted, and the subsequent refilling was studied until a steady state flow was established between the winter and summer hemispheres. The main conclusion to be drawn from this study is that H+-He+ counterstreaming can be expected along a large segment of a plasmaspheric flux tube at solstice. For both symmetric and asymmetric wind patterns, the He+ flow is from the winter to the summer ionosphere not only in the steady state, but during flux tube refilling owing to the winter helium bulge and the depletion of N2. For symmetricc poleward neutral winds in both hemispheres, H+ and O+ flow up from the conjugate ionospheres during flux tube refilling, which leads to large-scale H+-He+ counterstreaming in the summer hemisphere. In the steady state, both H+ and He+ flow from the winter to the summer ionosphere and no light-ion counterstreaming occurs. When the neutral wind in the summer hemisphere is set to zero, which acts to reduce the F region 'winter anomaly,' H+-He+ counterstreaming occurs in the summer hemisphere during refilling and along the entire flux tube in the steady state. The H+ and He+ counterstreaming velocities obtained are too small to excite plasma instabilities, but large enough to be measured.