A new resistive instability in a crossed-field gap

Summary form only given. When the voltage across a simple parallel plate crossed-field gap is maintained at a constant value all electrons emitted from the cathode simply return after one cyclotron period (if the magnetic field is above the Hull value), with the same energy with which they were emitted. When the gap is loaded with a resistor in series with an ideal DC supply, the resulting loss in energy during the cyclotron motion can cause some electrons to miss the cathode. If a steady rate of electron emission is maintained, as by a thermionic cathode, the consequence can be a rapid build up of charge density adjacent to the cathode, the final density being limited by the balance between magnetic confinement and mutual repulsion in the space charge layer. The equilibrium layer is turbulent, with average density near the Brillouin limit. We have carried out an analysis of this instability and have found a threshold condition. Results from the analysis and from computer simulations are shown.