The dependence of the oscillation frequency of an FEM on beam voltage

A waveguide free electron maser oscillator operating in the X-band frequency range has been constructed. It has been observed that the frequencies of oscillation, although close to the longitudinal modes of the cavity, vary slightly with electron beam voltage. It is proposed that this effect is due to the voltage-dependent variation in the phase of the radiation caused by the interaction with the electron beam. An initial comparison has been made between the observed variation of frequency with voltage and simple calculations carried out using the small signal approximation