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The linear dispersion relation for axisymmetric TM modes in a cylindrical waveguide lined with a dielectric material and enclosing a thin annular electron beam is derived and solved. Approximate analytic solutions are obtained for both weak and moderate beam regimes. A model of nonlinear saturation is developed. This model, combined with the linear theory in the moderate beam regime, defines the most efficient and compact Cherenkov maser.
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Lemons et al. (1986) studied this question.
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