Time-Dependent Electron Flow

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Abstract
The conditions of self-consistency for electron flow through arbitrary static or time-varying electric and magnetic fields are established assuming (a) nonrelativistic flow, (b) single streaming–i.e., the velocity has a single value and direction at every point, and (c) the electrons originate on a cathode not threaded by magnetic lines of force. In the case where the magnetic field is constant and uniform, a single-vector differential equation can be written which determines all possible solutions. From this equation certain time-variant solutions are developed. These are fully self-consistent–that is, large signal–solutions which exhibit some of the nonlinear behavior that would be expected of such solutions. Probably the most interesting of these solutions–since it offers an explanation of an observed phenomenon that does fit previous theory–is a radial oscillation of the cloud in a filamentary cathode smooth bore magnetron at ω/2. The possible application of the other solutions to anomalous behavior in various magnetron type devices is also discussed.

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