Conventional dynamo theories start from wind fields which are considered as external forces independent of the ionospheric plasma. These dynamos are called kinematic dynamos. Coupling between the neutral wind and the ionospheric plasma in a self-consistent manner results in a hydromagnetic dynamo. In this paper a theory of a hydromagnetic dynamo of the geomagnetic Sq current is developed assuming a thin shell model with constant elements of the electric conductivity tensor. Coupling between neutral gas and plasma is described by the Ampere force j¿B0 (j being electric current density and B0 geomagnetic field) which depends not only on the velocity difference between neutrals and plasma (ion drag) but also on the electric polarization field. The electric polarization field includes a source free component which is not negligibly small at dynamo layer heights, so that the electric field cannot be represented by an electric potential. This theory leads to a modified Laplace equation of tidal theory which can be solved numerically. Calculations are presented for the diurnal and the semidiurnal tidal wave modes. Their equivalent depths, their vertical wavelengths, and their attenuation factors are discussed as functions of a plasma parameter Δ which is proportional to a Cowling conductivity. The horizontal structures of pressure and electric current of the dominant symmetric tidal waves are determined for different values of Δ representing the lower atmosphere (Δ=0), the dynamo region (Δ~1), and F layer heights (Δ~10). It is shown that waves with positive equivalent depths at Δ=0 are heavily attenuated at Δ>1 and drastically change their horizontal structure there. On the other hand, waves with negative equivalent depths at Δ=0 are only weakly affected by the Ampere force. From our calculations we suggest that tidal wave theory at thermospheric heights should be reconsidered taking into account electric coupling between the models. In particular, we predict that the semidiurnal (2, 2) wave so far considered as the dominant semidiurnal mode above about 200 km height may have lost its significance and may in fact be replaced by the symmetric (2, -3) wave.