Theory of Parametrically-Pumped Longitudinal-Field Electron Beams

The general equations describing electron beams which have been excited by both a moderately strong pump source (or local oscillator) and a weak signal source are formulated in terms of coupled modes, including coupling to slow-wave circuits, and solved numerically for four problems of interest: a) space-charge pumped longitudinal parametric amplifiers b) circuit-pumped longitudinal parametric amplifiers c) parametric cooling of slow space-charge waves, and d) traveling-wave tubes with pump space-charge waves excited on the electron stream. Emphasis is placed on the parametric amplifier solutions, and realization of noise temperatures as low as 55°K are indicated. A discussion of the form of the general equations leads to new concepts about the coupling of positive and negative energy carriers through the action of parametric pumping. Experimental results are presented which tend to verify qualitatively some of the theoretical predictions for the behavior of the parametric amplifiers.