Transition to turbulence in a crossed-field gap

The transition from laminar to turbulent behavior of the electron sheath in a cross-field gap is examined for the regime B>BH, where B is the external magnetic field and BH is the Hull cutoff value. An analytic expression is presented for the critical emitted current beyond which laminar solutions cease to exist. A one-dimensional particle code is used to corroborate the analytic theory. This code shows several interesting properties when the emitted current exceeds the critical value. Chief among them is the presence of a turbulent microsheath near the cathode surface. The electrostatic potential in the gap's vacuum region is found to oscillate at a frequency that is quite insensitive to the emitted current and to the electrons' emission velocity