Effects of energy loss and momentum transfer on the limiting current in a crossed-field gap

Summary form only given, as follows. Time-independent flows can exist in a crossed-field gap only when the emitted current J is below the limiting current J/sub c/. For B>B/sub H/ (B/sub H/ is Hall cutoff magnetic field), this time-independent cycloidal flow is highly unstable oven for J is significantly less than J/sub c/. It becomes turbulent by introducing some small perturbations, such as a small RF voltage, resistive loss or misalignment of the magnetic field. We calculate the limiting current by explicitly modeling the effects of energy loss and momentum transfer in the equations of motion, for both B>B/sub H/ and B<B/sub H/ regimes. The energy loss prevents the electrons from returning to cathode (for B>B/sub H/) it also causes the electrons to miss the anode (for B<B/sub H/). Our calculations show that, J/sub c/ decreases with increasing energy loss, and it is much more sensitive when B>B/sub H/ than B<B/sub H/. For example, a small energy loss of about 3% of the DC voltage per electron, J/sub c//spl rarr/0 at B/B/sub H/=1.58 (while B/B/sub H/= 0.5 requires about 78% loss). Thus with any perturbation that causes a finite energy loss, the laminar flow will collapse to turbulent flow when J>J/sub c/, which approaches zero rapidly with increasing energy loss. If the RF loading in a crossed-field microwave source is regarded as an energy loss mechanism for the electrons in the gap, it may readily leads to J/sub c//spl ap/0. Then a finite (though small) emitted current is intrinsically quite unstable. This is yet another indication of the high susceptibility of noise in crossed field devices.