I-V Characteristic of a High-Current Electron Gun with a Magnetically Insulated Thin Cathode

It is shown that the accelerating electric field has an integrable singularity-on the emitting edge of a thin-walled cathode. Therefore, emitted electrons accelerate with infinitely large acceleration from such a cathode either with limited electron emission or with the current of the magnetized electron beam limited by its own space charge. The impact of the singularity on the I-V characteristic of a coaxial electron gun is considered. In addition, we show that the same singularity is also realized in virtual cathodes appearing in thin-walled electron beams. This exerts a significant influence on conditions of the appearance and development of instabilities. We have qualitatively constructed I-V characteristics for a two-section channel. These characteristics allow us to determine reasons for and conditions of appearance of hysteresis transitions with associated instabilities and oscillatory regimes of electron beam motion.