Current and Power in Velocity-Modulation Tubes

This paper gives a physical and mathematical analysis of velocity modulation. The velocity modulation is expressed in terms of a variation with time of density at any distance from the modulating source. This time-density variation is developed as a Fourier series having Bessel coefficients and has the same form as Webster's expression for current. The high-frequency current and power induced in a resonant circuit by the variable-density electron stream are calculated. The effects of transit time through the resonant circuit of the modulating source and of the output circuit are included in the calculations. The possibility of using a steady stream of electrons passing through a single resonator as a transit-time oscillator is discussed.