A Pierce-type dispersion relation is derived for the interaction of an intense relativistic electron beam with a cylindrical slow-wave structure of arbitrary corrugation depth. It is shown that near a resonance, the Pierce parameter can be expressed in terms of the vacuum dispersion function and the beam current. The dispersion relation is valid in both the low-current (Compton) regime and the high-current (Raman) regime. The dispersion characteristics of the interaction, such as the linear instability growth rate and bandwidth, are analyzed for both regimes.
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Chiping Chen (1994) studied this question.
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