Statistical Theory of Electron Transport in the Smooth-Bore Magnetron

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Abstract
Electron transport across the magnetic field in the cutoff smooth‐bore magnetron is described on the basis of random fluctuations in the fields. The theory is formulated in terms of the slipping‐stream instability, so that a definite mechanism behind the fluctuations in the fields is established. The transport equation appropriate to the analysis is shown to be the diffusion equation; the diffusion tensor follows from the characteristics of the slipping‐stream instability. Application of the theory is made to find the cutoff characteristics of the smooth‐bore magnetron. Expressions for the electric field, the space‐charge distribution, the anode current, and the circulating current are obtained; the results are compared with available experimental results. The agreement between theoretical and experimental results is good, particularly for the anode current. The new theory thus provides, for the first time, an acceptable theoretical explanation of the cutoff characteristics of the smooth‐bore magnetron.

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