Abstract
It is shown that the low-frequency backward wave in high-gain free-electron lasers may be excited by the electron bunch moving inside the undulator at power levels much higher than the noise level. A qualitative analysis is then given of the effects produced by the backward wave on the emission of radiation starting from noise as usually described in one-dimensional treatments. It is found that the low-frequency wave may considerably reduce the saturation lengths as predicted by the previous one-wave theory and that the time structure of the high-frequency pulse may be strongly modified by the bunching of the electrons of the beam in the low-frequency field.
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