Space-Charge Waves in an Accelerated Electron Stream for Amplification of Microwave Signals

Space-charge waves in an accelerated or decelerated electron stream are studied in this paper using a one-dimensional small-signal approximation. Exact solutions are given for an idealized stream of infinite extent, accelerated or decelerated uniformly through a space where dc space-charge effects are assumed to be neutralized by positive ions. It is argued that the results obtained can be applied to streams of small diameter by use of an appropriate reduction factor on plasma frequency even in the absence of positive ions. The solution obtained indicates that space-charge waves on a decelerated stream grow in amplitude, and can thus provide a method for amplifying microwave signals. The amplifying mechanism which is discussed is one involving an electron stream which has a single value of velocity in any transverse plane, but which is decelerated and accelerated alternately by a set of properly spaced parallel electrodes. Three amplifiers of this type have been constructed and tested and the theoretical gain expression has been verified.