A Contribution to the Theory of Thermionic Vacuum Tubes

Citation

Begovich, Nicholas Anthony (1948) A Contribution to the Theory of Thermionic Vacuum Tubes. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/jv0b-2n11. https://resolver.caltech.edu/CaltechTHESIS:03082024-172323594

Abstract

The elementary treatment of electron streams in vacuum tubes is based on the assumption that the velocity of the stream can be represented by a single valued function of the spatial coordinate. The Lagrangian method of treating the resulti11g electronic equations was introduced by Muller and extended by Llewellyn to general boundary conditions. In part III, this method is carried to the second order solution, which is important in the computation of distortion and detection properties of vacuum tubes at medium frequencies.

With the refinement of electronic techniques in the past decade, the useful radio frequency range for communication has been increased. In treating very high frequency tunes, the assumption of single valued velocity electron streams in close spaced vacuum tubes diverges sharply from physical fact. There arises a need for an electronic theory which includes the velocity spread of the electron stream. In part IV, the foundation of a multi-velocity theory is laid. Though in part IV treatment has been confined to one dimensional electron motion with only an electric field, the method can be readily extended to two or three dimensional flow with magnetic fields. The multi-velocity theory is based on a combination of Maxwell's equations and Liouville's Theorem of classical statistical mechanics. This fundamental approach in treating vacuum tubes, by focusing attention on the electron motion instead of boundary parameters, has been bypassed by prior investigators. The theory contains within its structure the explanation of all previously obtained results on one dimensional electron flow plus new answers to multi-velocity problems. In part V, some examples of stationary electron flow are treated; and in part VI, the time dependent solutions are formulated (though not carried out in complete detail).

In part VII, an interesting high frequency loading phenomena, observed by a number of investigators, is treated. From the results of the stationary flow in part V, this problem can be solved without the general theory developed in part VI. The solution obtained suggests a modification in the construction of very high frequency close spaced vacuum tubes.

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