The free-electron laser (FEL)-induced modifications to the vacuum waveguide modes are calculated for low-frequency FEL’s. Typically, the mode modifications are large and exhibit complicated axial behaviors. In addition to the wave component with a near vacuum wavenumber, components at two upshifted wavenumbers must be analyzed. Electron beam surface charges and currents are also important. At low gain, effects from all three roots of the FEL dispersion relation must be included. The dominant modification is due to the electron beam space-charge wave.
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Fajans et al. (1989) studied this question.
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