A New One-Dimensional Modulational Instability in a Crossed-Field Gap

Cycloidal electron flows in a gap with a crossed electric and magnetic field are found to be violently unstable when a small AC voltage is imposed across the gap footnote P. J. Christenson and Y. Y. Lau, Phys. Rev. Lett. 76, 3324 (1996). This instability is electrostatic, one dimensional and, therefore, it has nothing to do with the diocotron or magnetron instability. It occurs over a wide band of frequencies, possibly from 1/10 to a few times of the electron cyclotron frequency. Its excitation is insensitive to the precise values of the electron current density, and may occur even if the AC voltage is less than one per cent of the DC voltage. This instability is quite violent. In the low frequency regime, breakdown of the flow may occur in less than one rf cycle of the AC voltage. The physical origin of this instability is the formation of a virtual cathode right in front of the cathode.