Abstract
The effect of an arbitrary beam thickness is investigated for a two-dimensional Raman-type free-electron laser composed of a hollow relativistic electron beam and a parallel plate waveguide containing it. On the basis of the fluid theory for electron beams, analytical expressions are given for the dispersion relation and the spatial growth rate of a scattered wave (even TE mode) and an electron plasma wave (even TM mode) coupled under the influence of a pump wave (even TE mode). Then, from the numerical analysis for an important case where both the pump and scattered waves are the lowest-order even TE mode, the following interesting results are obtained. First, the hollow beam can propagate two distinct modes of the electron plasma wave with even symmetry characterized by different field distributions. One mode (mode 1) corresponds to the normal mode of the solid beam while the other mode is inherent to the hollow beam. In addition, the growth rate for the mode 1 is considerably larger than that for the mode 2. In particular, the optimum beam thickness is found for which the growth rate for the mode 1 becomes maximum and yet that for the mode 2 is sufficiently small.
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