Impedance Properties of Electron Streams

N the early stages of vacuum tube history the theoretical work on d-c. space charge treated mainly potential distributions associated with fairly small initial velocities of the electrons. With the advent of multi-electrode tubes this situation changed for it then became necessary to consider also potential distributions occurring when electrons are injected with large initial velocities. Idealizations were introduced to the extent that consideration was given only to space charge conditions which can exist between two parallel planes at known potentials when electrons with normal velocities corresponding to these potentials are injected into the region through one or both planes.1 Some time ago it was discovered experimentally that space charge may under certain conditions produce a negative capacitance. The negative capacitances were found during a series of low-frequency measurements of the control-grid-to-ground capacitance of an experimental space-charge-grid tube. In the course of these measurements it was found that with all the electrodes carefully by-passed to ground for a-c. except the negatively polarized control grid, the input capacitance as well as the input conductance was negative in certain domains which depended upon the d-c. operating voltages. In order to arrive at an understanding of this fact, a-c. phenomena must be considered under the general d-c. space charge conditions 1 Plato, Kleen, Rothe, Zeitschrift f. Phys., 101, J u l y 1936. C. E. Fay, A. L. Samuel, W.