The dispersion relation is derived for the interaction of a sheet beam propagating between parallel plates in a planar wiggler magnetic field. Instead of the usual free electron laser (FEL) mode, one is considered in which the radiation field is perpendicular to the quiver velocity and couples either to betatron or plasma oscillations. In the cold beam limit, coupling to betatron oscillations leads to an absolute instability. This mode competes with the conventional FEL and can disrupt the beam unless suppressed. The effects of energy spread are investigated, and a critical energy spread is found that suppresses the instability. For ultrarelativistic beams, this energy spread is an exponentially decreasing function of the beam energy. For moderately relativistic high current beams, it is proportional to the square root of the beam current. In this regime, there is a limit to the current that can propagate stably in the FEL circuit. Coupling to plasma oscillations also leads to an instability. However, the instability associated with this mode can be made convective with a suitable choice of parameters, and thus is not particularly dangerous to the conventional FEL. It is, however, interesting because the dispersion relation is characteristic of a second harmonic FEL, even though the wiggler is planar.