Absolute-instability growth rates and eigenmode structures in the electron-beam—backward-wave system with large excesses over the generation threshold

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We study the eigenmode structures with large excesses over the generation threshold in the electron-beam — backward-wave system in terms of the linear theory. It is shown that with increase in the length of the interaction space, the field maximum of both the fundamental and the higher-order modes shifts toward the collector end of the system. Asymptotic expressions for the growth rates, frequencies and spatial structures of the eigenmodes are obtained in the specified limiting case. When a superradiance pulse is generated in the system, a spatial field structure coinciding with the structure of the fundamental modes with a characteristic maximum near the collector end of the system is formed at the initial stage of interaction.