Explicit Brillouin Flow Solutions in Magnetrons, Magnetically Insulated Line Oscillators, and Radial Magnetically Insulated Transmission Lines

This article re-examines the Brillouin flow solutions in crossed-field diodes, with applications to magnetrons, magnetically insulated line oscillators (MILOs), and transmission lines (MITLs). The are constructed for various geometries, including planar MILOs, MITLs, cylindrical magnetrons electrons flowing azimuthal direction, MITLs MILOs axial radial direction. A common theme of this analysis is that two main external parameters used characterize flow: anode–cathode voltage ( $V_{a}$ ) total magnetic flux within diodes notation="LaTeX">$A_{a}$ ). These equivalent gap a specification degree insulation, which approximately equal ratio field Hull cutoff (HC) field. may be provided externally by magnet (as magnetron) or wall currents without an MILO MITL), some combination two, as intermediate case magnetron–MILO hybrid. Once these specified, electron speed at top hub uniquely determined. immediately yields Buneman–Hartree (BH) condition according model, whether it magnetron MILO. In so doing, we have obtained, first time using BH MILO, show same obtained from single-particle orbit model. We also found that, general, current contributes only very small fraction , regardless thereby correcting erroneous notion could responsible insulation. Another counter-intuitive finding given height decreases increases. conclusions, other results, were based on simple, explicit analytic expressions profiles, velocity, density, well self-magnetic self-electric profiles due electrons. From analytical expressions, deduce useful scaling laws applicable prevailing cases where exceeds 1.5 times HC field, they valid both relativistic non-relativistic regimes. Thus, contrast between ready assessment viability building moderate-current low-voltage hybrid might combine advantages MITL explicitly calculated. Additional issues addressed.