A local theory of effect of beam pre-modulation on gain and efficiency in a surface wave pumped free electron laser

A pre-modulated relativistic electron beam (REB) counter propagating to the surface wave in the vacuum region Compton backscatters the surface wave into a high frequency radiation. The surface wave extends into the vacuum region and can be employed as a wiggler for the generation of sub-millimeter waves. The growth rate and gain were evaluated for a typical FEL (Free Electron Laser) parameters and It is found that the growth rate and gain of the surface wave pumped free electron laser increases with the modulation index. Moreover, the growth rate of the FEL (Free electron Laser) instability scales as one-third power of the beam density in the Compton regime.