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The amplifying properties of electron streams passing near nonpropagating or lossy walls have been calculated. The method of field analysis is used to obtain values of gain and phase velocity for walls of arbitrary complex admittance. It is shown how one may find easily and quickly these values for actual tube design through use of two contour maps of the complex functions encountered. The gain is found to be zero for open or short circuit, or capacitive wall impedance, low for resistive-capacitive, higher for resistive and resistive-inductive, and highest for inductive walls. The behavior of a physically realizable model of the resistive-capacitive wall is determined. In conclusion, some comment is offered concerning the usefulness of these structures in the realm of microwave tubes.
Birdsall et al. (1953) studied this question.