Relaxation instabilities in high-perveance electron beams

Spurious low-frequency oscillations similar to those reported by Cutler have been observed in the form of large amplitude modulation of both the RF output and the collector current of klystrons utilizing high-perveance electron beams. This modulation, which appears typically as sawtooth-like relaxation oscillations with frequencies ranging from 10 cps to 100 kc, was observed to occur spontaneously only if the operating pressure was lower than a critical threshold (\approx 1 \times 10^{-7}mm Hg). Experiments are described which were designed to investigate this phenomenon using dc beam testers. Evidence is presented which indicates that the oscillations are due to a relaxation back and forth between two possible solutions to Poisson's equation which both satisfy all boundary conditions. One of the possible solutions corresponds to the existence of a virtual cathode within the beam, resulting in a partial reflection of electrons. Experimental evidence indicates that positive ions play an important role in triggering the relaxation. Both theoretical and experimental evidence are presented which point to relaxation instabilities of the type described as a potential hazard in utilizing depressed collector operation for improved efficiency of high-perveance microwave tubes. The same potential hazard exists in the use of periodic electrostatic focusing.