This article re-examines the Brillouin flow solutions in crossed-field diodes, with applications to magnetrons, magnetically insulated line oscillators (MILOs), and magnetically insulated transmission lines (MITLs). The Brillouin flow solutions are constructed for various geometries, including planar magnetrons, MILOs, and MITLs, cylindrical magnetrons with electrons flowing in the azimuthal direction, cylindrical MITLs and MILOs with electrons flowing in the axial direction, and radial MITLs and MILOs with electrons flowing in the radial direction. A common theme of this analysis is that two main external parameters are used to characterize the Brillouin flow: the anode-cathode voltage (V a ) and the total magnetic flux within the crossed-field diodes ( A a ). These two parameters are equivalent to the gap voltage and a specification of the degree of magnetic insulation, which is approximately equal to the ratio of the magnetic field to the Hull cutoff (HC) magnetic field.The magnetic flux may be provided externally by a magnet (as in a magnetron) or by the wall currents without an external magnet (as in a MILO or MITL), or by some combination of the two, as in the intermediate case of a magnetron-MILO hybrid. Once these two parameters are specified, the electron flow speed at the top of the Brillouin hub is uniquely determined. This immediately yields the Buneman-Hartree (BH) condition according to the Brillouin flow model, whether it be a planar magnetron or a cylindrical MILO. In so doing, we have obtained, for the first time using the Brillouin flow model, the BH condition for a cylindrical MILO, and we show that the same condition is obtained from the single-particle orbit model. We also found that, in general, the electron current within the Brillouin hub Manuscript
The magnetically insulated line oscillator (MILO) is a high power microwave source that has received increased attention recently because it does not require an external magnetic field. Self-magnetic insulation typically requires operation at high currents, ∼50 kA in previous experiments (at ∼10 Ω). This paper reports the first MILO experiment operating at moderate current, less than 10 kA, at a lower voltage of 240 kV, driven by the Michigan Electron Long Beam Accelerator. The viability of this lower current operation was predicted by our recently developed theory on Brillouin flow, which also led to the rigorous derivation, for the first time, of the Buneman–Hartree condition for the cylindrical MILO using both the Brillouin flow and single particle model. The experiments show that more than 90% of shots operate at a magnetic field less than 1.3 times the Hull-cutoff magnetic field, and this magnetic field is significantly lower than the magnetic field required at the Buneman–Hartree condition. These experiments also oscillated at less current than the Hull cutoff condition on over 80% of shots, suggesting that MILOs might operate at a current lower than that expected at exactly Hull cutoff; this peculiar feature was also predicted by the theory. Particle-in-cell simulations from the improved concurrent electromagnetic particle-in-cell (ICEPIC) and CST codes are detailed, which corroborate MILO operation at lower currents than the Hull cutoff condition. The maximum efficiency achieved in these experiments is 1%, at a resonant frequency of 1 GHz. An initial comparison of the newly developed theory against prior MILO experiments is presented.
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