Dynamics of magnetic insulation failure and self-organization of an electron flow in a magnetron diode

The dynamics of back cathode bombardment (BCB) instability in a magnetron diode (a coaxial diode in a magnetic field, B ≡ B _0z ≡ B ₀) is numerically simulated. The quasi-stationary regime of electron leakage across the high magnetic field (B ₀/B _cr > 1.1, where B _cr is the insulation critical field) is realized. An electron beam in the electrode gap is split into a series of bunches in the azimuthal direction and generates the electric field component E _θ(r, θ, t), which accelerates some of the electrons. Having gained an extra energy, these electrons bombard the cathode, causing secondary electron emission. The rest of the electrons lose kinetic energy and move toward the anode. Instability is sustained if the primary emission from the cathode is low and the secondary emission coefficient k _se=I _se/I _{e, BCB} is greater than unity. The results of numerical simulation are shown to agree well with experimental data. A physical model of back-bombardment instability is suggested. Collective oscillations of charged flows take place in the gap with crossed electric and magnetic fields (E × B field) when the electrons and E × B field exchange momentum and energy. The self-generation and self-organization of flows are due to secondary electron emission from the cathode.