Space-charge effects in a free-electron laser with a two-frequency undulator

A set of single-electron equations, including the space charge effects, is developed to describe the evolution of the radiation field in a free electron laser with a two frequency undulator (or wiggler). These basic equations are analysed in the weak field, low gain regime to obtain the single pass gain. Owing to the repulsive force between the electrons, the gain is saturated with decreasing growth rate for high electron density. The numerical results show that the saturation gain is greatly dependent upon the parameters of the two frequency undulator, and that it is smaller than that of the ordinary undulator. (Original abstract-amended)