Space-charge effects in klystrons

The effects due to the dc field of the space charge in a reflex klystron have been calculated on a digital computer. It is found that the electronic efficiency may be reduced by a factor as large as 10 under space charge conditions which may exist in a typical low-voltage tube. Small signal theories which include the effects of the dc space charge are presented for the reflex klystron and two-gap klystron amplifiers and oscillators. The small signal theory is used primarily to aid in the interpretation of the computer calculations. The theory predicts that the efficiency of the two-gap oscillator may be reduced by a factor no greater than 3.7, but that the power gain of the two-cavity amplifier may be increased by as much as 13.7. It is also found that the inclusion of space charge effects will in general require different applied dc voltages for operation at the center of the various electronic modes, as compared with the infinitesimal-space-charge conditions. Upon comparing the theoretical calculations with actual reflex klystron data, it has been found that the theory adequately explains the behavior of the power output, efficiency, and electronic bandwidth as the beam current is varied, for conditions of moderate or small space charge. For conditions of large space charge the theoretical model does not represent the conditions in an actual tube with sufficient accuracy; it is pointed out how the theory may be improved and how the present work may be useful as a starting point for further calculations.