Effects of velocity tapering and D-C gradients in traveling-wave tubes

In linear-beam tubes such as the traveling-wave amplifier successful conversion of the d-c kinetic energy of the electrons to r-f depends critically upon the successful maintenance of the center of gravity of the charge bunch in the proper phase relative to a collinear traveling r-f wave. To study phase focusing the large-signal equations have been modified to accommodate spatially varying parameters such as the circuit phase velocity or variable d-c energy through the application of a d-c gradient. These variations can be preprogrammed on a computer or the computer made to select optimum variations based on suitable criteria. Theoretical calculations indicate that tapering of the circuit phase velocity will result in a modest increase of the saturation efficiency and conditions for maximum small-signal gain and maximum saturation output are brought close together. The application of a d-c gradient leads-to higher gain in longer tubes with efficiencies comparable to the tubes before modification. The effects of these variations and modifications on gain and efficiency will be discussed in detail.