Transformation of fluctuations along accelerating crossed-field beams

Equations are derived to express the ac potential difference and the transformation of fluctuations of velocity and current between two arbitrary planes along an accelerating crossed-field electron stream. The system of equations, after being simplified by the assumption of zero total ac current, is applied to the special cases of the temperature-limited diode, the space-charge-limited diode, and a diode in which the beam enters with appreciable average velocity. Finally, the open-circuit equations are applied to an approximate model of a beam in a crossed-field electron gun. A new mechanism of growth, peculiar to the crossed-field beam, is discussed as a possible explanation of the observed large sole current in beam-type magnetron amplifiers and related devices.