A Small-RF-Signal Theory for an Electrostatically Focused Traveling-Wave Tube

This paper describes a small-RF-signal theory for a new type of electrostatically focused traveling-wave tube. Consideration is given to the effect on the gain of large periodic variations of dc electron velocity, resulting from electrostatic focusing. LlewellynPeterson equations which apply to dc voltage distributions, similar to those used in the electrostatically focused traveling-wave tube, are used for analysis. The limitation of the Llewellyn-Peterson equations to one-dimensional problems is overcome by use of correction factors derived from Pierce's theory for traveling-wave tubes. Generalized expressions taking into account the periodic variations of dc electron velocity are derived for the gain parameter C and spacecharge parameter QC. For uniform dc electron velocity, such as that found in a magnetically focused tube, these expressions reduce to the forms derived by Pierce. In addition to their suitability for analysis of electrostatically focused traveling-wave tubes, the LlewellynPeterson equations provide a method of analyzing magnetically focused traveling-wave tubes alternative to those used previously. It is shown that the gain of the electrostatically focused tube can be calculated by use of the gain and space-charge parameters of the electrostatically focused tube and graphical data available for magnetically focused tubes. Depending upon the voltage distribution in the region of electron flow, the gain and bandwidth of a travelingwave RF circuit employing an electron beam having a periodically varying dc velocity can be greater or smaller than the gain and bandwidth of the same RF circuit employing a uniform dc velocity electron beam.