Abstract
A general traveling wave analysis is given for electron beam parametric amplifiers in which the electron dynamical equation in the pump is a Hill's differential equation. Formulas are given for the complex wave number of beam waves, and clear conditions for growing wave solutions are presented. The special case of a sinusoidal pump field variation is treated, and the optimum pumping condition is found to result when the pump frequency is twice the beam natural frequency. It is shown that growing wave solutions exist at pump frequencies which are rational fractions of the beam natural frequency, but that the growth constants for these pumping conditions (at fixed pump power) are orders of magnitude less than under the optimum condition.
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