The Electrostatic Field in Vacuum Tubes with Arbitrarily Spaced Elements

ACUUM tubes with close spacing between electrodes have become of increasing importance in recent years. The higher transconductances and lower electron transit times thus obtained combine with other features to raise both the frequency and band width at which the tube may operate satisfactorily as an amplifier. Specific designs have been discussed in papers by E. D. McArthur and E. F. Peterson1, and by Fremlin, Hall and Shatford 2 . The important contributions to structural technique made by E. V. Neher have been described in the Radiation Laboratory Series3. Further important advances in the art have been recently announced by J. A. Morton and R. M. Ryder of the Bell Laboratories at the recent I.R.E. Electronics Conference held at Cornell University in June, 1948. The material of the present paper represents work done by the authors over a decade ago, and naturally there has been considerable publication on related topics in the intervening years. It has been suggested by our colleagues, however, that some of the results are not available in the technical literature and are of sufficient utility to warrant a belated publication. These results have to do with the variation of the electric intensity, amplification factor, and current density which takes place along the cathode surface because of the nearby grid wires. We shall deal mainly with the approximate solution which neglects the effect of space charge. The correction required to take account of space charge is in general relatively small as shown by both qualitative argument and experimental data in an early paper by R.