Abstract.A physical model for the existence of bipolar structures in the electric field that are parallel to the magnetic field and observed in the auroral ionosphere, is established by deriving the "Sagdeev potential" from the two-fluid equations in a cylindrical coordinate system. The model shows that the bipolar electric field structure can develop not only from an ion acoustic wave, but also from an ion cyclotron wave, when the Mach number and the initial electric field satisfy certain conditions. Moreover, in the auroral region, it shows that the polarity of this electric field structure can be oriented either negative to positive or the reverse polarity, its amplitude can be varied from 35 to 330 mV/m, and its duration can be 7 ms to 23 ms. These results are in agreement with observation. Therefore, our two-fluid model can interpret the bipolar structures observed in the auroral ionosphere.