Steady-state and superradiant many-mode dynamics in a high-gain amplifier with a waveguide

Abstract

We investigate many-mode dynamics in the steady-state and superradiant regimes of an FEL with a rectangular waveguide for high-gain amplification of microwave radiation. At steady state a recent many-mode Hamiltonian formulation allows us to derive analytical results for two-mode (TE 01 + TE 21) operation, such as the instability threshold for exponential gain, and to explain the main many-mode effects, i.e., higher peak powers, reduced saturation lengths and broader accessible energy ranges, compared with the amplification of the fundamental (TE 01) mode alone. Numerical investigation shows that multimode excitation leads to enhanced peak powers and shortened dynamics also both in strong and in weak superradiance. In these regimes, differently from steady-state, the fundamental TE 01-mode exhibits higher peak powers and efficiencies when higher-order modes are present.