Small-signal analysis of the helitron oscillator

In this paper, a small-signal analysis of a microwave oscillator discussed by Watkins and Wada¹is presented. This tube, the helitron, has an electron beam describing the trajectory of a helix between two concentric cylinders. Interaction is with a TEM mode supported on the inner cylinder, and the beam is focused by having a potential difference between the cylinders. This has been termed anE-type tube. TheE-type tube had originally been conceived as a device for exchanging electron potential energy of an electrostatically focused beam for RF energy. In this manner, one would expect to obtain the high efficiencies associated with anM-type tube, without requiring a magnetic field. Watkins and Wada presented experimental results in their paper, and they indicated that the theory that had been developed did not predict the observed behavior. In particular, it was stated that if the propagation constants were those of anM-type tube, the measured starting current would be one-fiftieth of the theoretical starting current. The small-signal analysis of theE-type tube developed in the main body of this paper has yielded two interesting results: 1) The electrons bunch along the direction of rotation, and lose kinetic energy. In this sense theE-type tube behaves similar to theO-type oscillator. Electron motion transverse to the dc path, which is important in theM-type tube, is not important forE-type operation. 2) Space charge forces tend to increase the bunching along the direction of rotation. This results in a negative value for the space-charge parameter, and an attendant reduction in starting current. Growing waves can exist on an electron beam that is electrostatically focused between two conducting cylinders, even without the presence of a circuit field. In this sense theE-type oscillator is similar to theM-type tube.