Kinetic Theory of Space-Charge I: Cut-off Character of the Static Magnetron†

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Abstract
Collisional damping in the equations of motion for electrons in the magnetron space-charge is shown to lead to rather complex behaviour. The strong scattering limit manifests a current-voltage dependence which not only can account for departures from Child's Law, but also for failure of extant theories of the magnetron to predict the long puzzling observation of a smeared cut-off. While a Boltzmann transport refinement may provide a more rigorous approach to the problem, it is believed that the mystery of the cut-off phenomenon is essentially dissipated by the phenomenological development.