Space-charge waves and stability of electron diodes

Use of the dc transit time as a new spatial variable and the use of RS beam current multiplied by the dc beam velocity as a new space-charge wave variable simplify the form of the equations for space-charge waves on one-dimensional accelerated electron streams. Using the simplified equations, RF impedance functions are found for electron diodes. Nyquist analysis is used to investigate the stability of diodes for varying current densities, voltages, and external loadings. The results of a number of past authors' studies of impedance, oscillations, and instabilities are correlated and treated from a unified point of view. The methods developed here are an alternative to the Llewellyn-Peterson technique, utilizing solutions of ordinary differential equations rather than integral equations.