Gain in spatially varying optical fields: Applications to high emittance beams and gas dielectric FEL´s

The conventional free-electron laser small-signal linear gain equation is revised to include the effects of nonuniform optical mode area, finite electron beam emittance, and electron beam energy spread. It is shown for a typical case that the conventional equation overestimates gain by more than 50 percent. The results further show that gain can result from FEL designs with interaction lengths longer than the conventional maximum given by the criterion of accumulated phase shift equal to π. This makes possible a gas-loaded FEL which utilizes a long wiggler and an asymmetric mode to enhance the electron-optical field interaction. Although substantial emittance is induced by scattering, the gas-loaded FEL should have modest gain at wavelengths down to the ultraviolet.