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In this paper, the linearized relativistic Vlasov equation is solved and a dispersion relation is calculated for the interaction between a relativistic electron beam and the electromagnetic fields of a rectangular waveguide supporting TE mn modes. The dispersion relation is simplified to the special case of a frame of reference moving with the electrons and the resulting coupling coefficient εmin{mn}max{l} is calculated for various TE mn modes. The dependence of εmin{mn}max{l} on the parity of the harmonic number l and various mn modes of the waveguide are discussed.
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Ferendeci et al. (1984) studied this question.
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