Graphical Methods for Analysis of Velocity-Modulation Bunching

A review of the theory of velocity-modulation tubes is used as an introduction to a number of graphical representations of electron bunching. These methods are applied to single-resonator tubes as well as multiple-resonator designs. The curves are used to illustrate a method of obtaining the efficiency and the effective phase angle of the bunched electron beam from a simple graphical integration. These methods are not new, and correspond to the equations which have been used in the past to represent electron bunching, but the graphical representation offers a convenient method of using these equations.