Recent Polar observations indicate the presence of broadband plasma waves in the frequency range of ~101 Hz to about 104 Hz on magnetic field lines mapping into the polar cap boundary layer, at altitudes of about 6 to 8 RE (where RE is the Earth radius). These waves are quite similar to the broadband plasma waves observed in the low latitude boundary layer, and they appear to be a mixture of electromagnetic and electrostatic modes. A linear theory for the generation of these waves is developed. The theory is fully electromagnetic and takes into account the free energy available due to the presence of field-aligned currents, and gradients in the currents, plasma densities, and magnetic fields. A generalized dispersion relation for the coupled lower hybrid, whistler, and current convective modes is obtained. It is found that the presence of density gradients, the current convective modes develop a finite real frequency, but at the same time their growth rates are reduced. On the other hand, sharp density gradients can lead to the excitation of a lower hybrid drift instability when the hot ions are present in the boundary layer. In general, the current convective and lower hybrid drift modes are coupled, and the dispersion relation has to be solved numerically. The inclusion of electromagnetic effects leads to the reduction of the growth rates. ¿ 1999 American Geophysical Union