A three-dimensional, stationary, two-fluid plasma model for electrons and one ion species was developed to understand the local interaction of Io's atmosphere with the Io plasma torus and the formation of Io's ionosphere. Our model calculates, self-consistently, the plasma density, the velocity and the temperatures of the ions and electrons, and the electric field for a given neutral atmosphere and imposed Io plasma torus conditions but assumes for the magnetic field the constant homogeneous Jovian field. With only photoionization in a pure SO2 atmosphere it is impossible to correctly model the plasma measurements by the Galileo spacecraft. With collisional ionization and photoionization the observations can be successfully modeled when the neutral atmospheric column density is Ncol=6¿1020 m-2 and the atmospheric scale height is H=100 km. The energy reservoir of the Io plasma torus provides via electron heat conduction the necessary thermal energy for the maintenance of the collisional ionization process and thus the formation of Io's ionosphere. Anisotropic conductivity is shown numerically as well as analytically to be essential to understand the convection patterns and current systems across Io. The electric field is very greatly reduced, because the ionospheric conductances far exceed the Alfv¿n conductance &Sgr;A, and also strongly twisted owing to the Hall effect. We find that the electric field is twisted by an analytic angle tan &THgr;twist=&Sgr;2/(&Sgr;1+2&Sgr;A) from the anti-Jupiter direction toward the direction of corotation for constant values of the Pedersen and Hall conductances &Sgr;1 and &Sgr;2 within a circle encompassing Io's ionosphere. Because the electron velocity is approximately equal to the E¿B drift velocity, the electron flow trajectories are twisted by the same angle toward Jupiter, with E and B the electric and magnetic fields, respectively. Since &Sgr;1~&Sgr;2, the electron flow is strongly asymmetric during convection across Io, and the magnitude of this effect is directly due to the Hall conductivity. In contrast, the ions are diverted slightly away from Jupiter when passing Io. Large electric currents flow in Io's ionosphere owing to these substantially different flow patterns for electrons and ions, and our calculations predict that a total electric current of 5 million A was carried in each Alfv¿n wing during the Galileo flyby. We also find a total Joule heating rate dissipated in Io's ionosphere of P=4.2¿1011 W. ¿ 1999 American Geophysical Union