Space-Charge Instabilities in Electron Diodes. II

Abstract

A detailed analysis of space‐charge instabilities in diodes is presented. The oscillation when the input current exceeds the ``limiting input current'' (from an earlier analysis for a short circuited diode with a zero temperature stream) persists with the addition of a diode resistance, or with a two‐velocity input or a Maxwellian velocity distribution input, or with streams of finite diameter. The time‐averaged value of the minimum potential is nearly zero, as in the classical solution; however, the time‐averaged minimum position and transmitted current differ considerably from the classical values. The recovery of the stable state is by a jump rather than gradually as in the classical solution. A small‐signal prediction of time growth of all first‐order variables (potential, current, velocity) at the point of limiting is given. An energy argument using the zero‐order variables is presented showing the onset of instability. Experiments agreed with some parts of the analysis but did not show oscillations with amplitudes as large as expected.