The gain of a Compton laser

The gain of a Compton laser is determined for arbitrary propagation directions of the electrons, the pumping wave, and the amplified wave. It is shown for electron beams with a sufficiently large energy spread that the gain increases with the deviation (when this is small) of the direction of propagation of the amplified wave from the direction of electron motion. The optimal value of the angle between these directions is found for which the gain is maximum. Numerical estimates are presented which determine the possibility of constructing a Compton laser under the optimal geometrical conditions of the experiment.