Space-charge wavelengths in electron beams

The discrepancies between measured and calculated small-signal space-charge wavelengths are discussed. It is shown that conventional methods of calculation are inadequate, causing errors up to 40 percent in a typical case. It is demonstrated that these errors cannot be explained by beam scalloping action, and that they are most severe when a high-perveance beam is used at low voltages with a high magnetic field under conditions of low interception. Although these effects would not be noticed in klystrons with relatively short drift lengths, they may in many cases explain the critical variation of gain and efficiency with magnetic field. A more accurate method of calculating space-charge wavelengths is developed, and the effectiveness of this method is demonstrated by a comparison with measurements.