One-dimensional modulational instability in a crossed-field gap.

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. {copyright} {ital 1996 The American Physical Society.}