Abstract: basis of the developed theoretical method, the ordinary optical scheme of free electron laser with a hole on the exit mirror was investigated with consideration of gain saturation in a wiggler. The intracavity mode power and output radiation power were considered in relation to the radius of mirror curvature, the value of wiggler gain, hole dimensions, the range of mirror tilt angle, etc. The transverse structure of the intracavity field was calculated, and configurations with a local minimum and with 'saddle' points near the center of exit mirror were obtained. The dislocations of wavefront were obtained. Such points in degenerated cases formed rings situated far from the mirror center.!10
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