One-Dimensional Modulational Instability in a Crossed-Field Gap

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Abstract
Cycloidal electron flows in a gap with crossed electric and magnetic fields are found to be violently unstable when a small ac voltage is imposed across the gap. This instability is electrostatic and one dimensional. It occurs over a wide band of frequencies and is insensitive to the precise level of the injected current density. The physical origin of this instability is the formation of a virtual cathode right in front of the cathode. An analytic theory is presented which accurately predicts the onset of the instability in the low-frequency limit.

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