Abstract
Free Electron Laser dynamics is investigated in the presence of a rectangular waveguide for high-gain amplification of microwave radiation. Scale hamiltonian equations for the electrons and many radiation modes are derived in the steady-state Compton regime. In the relevant case of two-mode (TE 01 + TE 21) operation, the linear theory predicts the instability threshold of the system and explains basic effects of mode competition, such as higher peak powers, broader accessible energy ranges and reduced saturation lengths, compared with the amplification of the fundamental (TE 01) mode alone.
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