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Single-flow electron motion in a magnetized coaxial diode

Summary form only given. The Brillouin flow equilibrium is one of the most widespread models of electrons drifting around cathodes in crossed radial electric and axial magnetic fields. In this present work we describe electron flow with non-crossed trajectories of electrons with azimuthal and axial velocities, with full space charge of electrons taken into account, unlike another popular model that is a two-flow model of space charge fields. We consider the single-stream model, which is generalized Brillouin flow that can be used for consideration of the operating characteristics of many devices where space charge is very important, as, for example, in relativistic magnetrons, magnetically insulated linear oscillators (MILOs), and coaxial transmission lines. In the consideration, the self-azimuthal and-longitudinal magnetic fields of electrons moving along spiral trajectories are included in addition to the applied magnetic field. We obtained analytic solutions for electron flow with non-crossed trajectories around the cylindrical cathode whose surface is not intercepted by magnetic field lines and which include the radial structure of space charge, self-electric and - magnetic fields, and velocity distribution accounting for the screening of self-magnetic fields of short pulse drifting electrons by the metallic boundary condition of the vacuum transport channel and including relativistic velocities. In the derivation we followed the basic considerations in. In particular, we found a condition for magnetic insulation including the case when there is no externally applied axial magnetic field (as is the case for the MILO). In addition, we identified the condition of synchronism of the electron flow with the electromagnetic wave, similar to the Buneman-Hartree condition in magnetrons and the condition of synchronism in MILOs.