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A nonwiggler free electron laser, operating in uniform guide magnetic field, is analyzed. The amplifier problem is solved self-consistently on the basis of the kinetic theory. It is shown that the asymmetry in the azimuthal distribution of the electrons' momentum leads to a coupling between the transverse and the space-charge modes. This, in turn, enhances the gain in the amplifier. In the case of a cold beam, with the electrons gyrating coherently, the spatial growth in the collective nonwiggler free electron laser (FEL) is comparable to that found in conventional free electron lasers operating in similar regimes.