A Re-Examination of Brillouin Flow in a Crossed-Field Diode

The Brillouin flow is widely considered the preferred equilibrium state in a magnetically insulated diode, when the magnetic field, B, exceeds the Hull cutoff magnetic field, BH. The Buneman-Hartree condition for a cylindrical magnetically insulated line oscillator (MILO) was derived, for the first time, using the Brillouin flow model [1] . Recent experiments at the University of Michigan [2] , [3] showed that MILOs tend to operate close to Hull cutoff, i.e., B/BH close to unity. They even showed that MILOs might operate at a current level slightly less than that required at Hull cutoff. The latter is a peculiar property also noted in our recent Brillouin flow theory [1] . Crossed-field flow is known to be particularly difficult to characterize in the transition regime, where B/BH ~ 1 [4] . The presence of a slow wave structure in a MILO thus likely leads to additional uncertainties in the flow characterization. This paper presents our ongoing investigations into the Brillouin flow, using high-fidelity 1D and 2D simulation codes, as well as analytic modeling. Various issues will be addressed.