III. Theory of the Preoscillating Magnetron: 1

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Abstract
THE present investigation was started more than four years ago. It was based on the working hypothesis, for which some experimental evidence existed even at that time, that the so-called steady state of the cut-off full-anode cylindrical magnetron is a state of statistically stationary, turbulent oscillations rather than a true steady state. We soon realized that it was too early to start with a statistical attack, and had to be content with some preparatory work. This consisted of two stages. The first was an investigation of the question whether a steady state existed mathematically if not physically; a state which could be considered as a mean or zero state of the oscillations superposed on it. The second consisted in proving that this state was in fact unstable, because there exists an infinite variety of perturbation modes which can develop spontaneously. A linear theory could go no further than indicating the spectrum of the perturbations and their critical data; beyond this the mathematical difficulties became prohibitive. It now appears on the basis of the experimental results recently obtained by Twiss and Mathias (to be reported in this journal) that a small-amplitude theory is insufficient to account for the observed phenomena. Nevertheless our theoretical results may be of some interest for a general understanding, if not for a quantitative explanation of preoscillations in the cut-off magnetron.

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