A note on low-frequency ion noise and its reduction in linear beam microwave tubes

A simple theory based on electron motion in the spatially periodic potential produced by beam scalloping due to focusing mismatch is presented to explain some key features of low frequency ion-induced phase noise. In particular, the theory presented here predicts: 1) relatively high sensitivity of phase noise levels to the strength of the magnetic focusing field and cathode voltage; 2) marginal sensitivity of phase noise to cathode heater filament voltage; and 3) relatively low sensitivity of phase noise to radio frequency (RF) drive level and collector voltage. It is shown that, in the event that beam scalloping due to mismatch cannot be avoided, a simple and effective way to suppress low-frequency phase noise is adjustment of the magnetic field so that the interaction length is an integral multiple of the scalloping wavelength. This conclusion is independent of the details of the dynamics of the ions, and therefore independent of the details of the ion noise spectrum.