Misalignment effects of segmented undulator in self-amplified spontaneous emission

Effects caused by misalignment of undulator segments on the gain of a free electron laser (FEL) based on the process of self-amplified spontaneous emission are theoretically studied. The well-known FEL equations are solved analytically and numerically with boundary conditions describing the misalignment effect in order to obtain the amplification gain as a function of the distance from the undulator entrance. The two worst cases of alignment are considered. One is that the phase slip over the drift section between the adjacent segments is π, and the other is that the radiation is cut off at the drift section. Calculations show that if the undulator segment is several times as long as the gain length, the radiation power is close to that of no segmentation in both cases.